Daniel Mcdu
email: damcdu@microso.com

Christophe Hurter
email: christophe.hurter@enac.fr

Mar Gonzalez-Franco

Pulse and Vital Sign Measurement in Mixed Reality using a HoloLens

Keywords: •Human-centered computing → Mixed / augmented reality, Visualization, •Computing methodologies → Biometrics, Mixed reality, remote sensing, physiology, interoception, health

Cardiography, quantitative measurement of the functioning of the heart, traditionally requires customized obtrusive contact sensors. Using new methods photoplethysmography and ballistocardiography signals can be captured using ubiquitous sensors, such as webcams and accelerometers. However, these signals are not visible to the unaided eye. We present Cardiolens -a mixed reality system that enables real-time, hands-free measurement and visualization of blood ow and vital signs from multiple people. e system combines a front-facing webcam, imaging ballistocardiography, and remote imaging photoplethysmography methods for recovering pulse signals. A heads up display allows users to view their own heart rate whenever they are wearing the device and the heart rate and heart rate variability of another person simply by looking at them. Cardiolens provides the wearer with a new way to understand physiological signals and has applications in human-computer interaction and in the study of social psychology.

INTRODUCTION

Analyzing physiological and emotional states is important for understanding health and well-being, memory, decision-making, as well as enabling more meaningful social interactions. Convenient, unobtrusive measurement of these signals has many applications. Vital signs are important basic health parameters and simultaneously provide information about a person's a ective state. When DOI: 10.1145/3139131.3139134 Figure 1: Cardiolens is a mixed reality system that allows simultaneous physiological measurement of multiple people, including the wearer.

e physiological signals are visualized in the real-world allowing the wearer to see magni ed blood perfusion and vital signs in real-time.

rendered in real-time these signals may be powerful tools for interoceptive awareness (i.e. the consciousness of our physiological and inner bodily state, which relates to the experience of emotions [START_REF] Bechara | Listening to your heart: interoceptive awareness as a gateway to feeling[END_REF]) and synchronization. We present Cardiolens -a mixed reality system that enables real-time, hands free measurement of blood ow and vital signs of multiple people (including the wearer) concomitantly. Cardiolens presents new possibilities for immersive experiences, augmented social interactions and as a tool for practitioners in several contexts such as healthcare and personal training. Figure 1 shows an overview of the system.

Figure 2: Schematic of the Cardiolens system. Images from the front-facing camera are used to extract the physiological state of the wearer and the person they are looking at. Imaging photoplethysmography is used to recover the pulse wave of the person being looked at. Imaging ballistocardiography is used to recover the pulse wave of the wearer. ese signals are used to augment the appearance of the real-world allowing the wearer to see the normally "hidden" physiological information in real-time.

Cardiolens leverages the embedded camera of the mixed reality device and two forms of cardiography for recovering physiological measurements from the person wearing the device (from now on referred to as the wearer) and a person they are looking at (from now on referred to as the partner) simultaneously. e rst form of cardiography is based on photoplethysmography, a method of capturing the blood volume pulse (BVP) via small variations in light re ected from the skin [START_REF] Allen | Photoplethysmography and its application in clinical physiological measurement[END_REF]]. Remote imaging photoplethysmography (iPPG) is an advanced set of computer vision methods that enables PPG measurement using just a webcam and ambient light [START_REF] Poh | Non-contact, automated cardiac pulse measurements using video imaging and blind source separation[END_REF][START_REF] Poh | Advancements in noncontact, multiparameter physiological measurements using a webcam[END_REF]. A survey of these techniques can be found in [START_REF] Mcdu | A survey of remote optical photoplethysmographic imaging methods[END_REF]]. We utilize iPPG to retrieve the pulse signal of the partner.

e second form of cardiography is based on ballistocardiography, a technique for sensing heart functioning via minute motions of the body due to the mechanical movements resulting from blood ow [START_REF] Starr | Studies on the estimation of cardiac ouptut in man, and of abnormalities in cardiac function, from the heart's recoil and the blood's impacts; the ballistocardiogram[END_REF]]. We use imaging ballistocardiography (iBCG) as a complementary set of video processing methods for capturing the physiological signals of the wearer. As with iPPG, iBCG measurements can also be obtained from webcam videos. is is possible because the device is head-mounted to the wearer [START_REF] Hernandez | Bioglass: Physiological parameter estimation using a head-mounted wearable device[END_REF]. Ballistic and inertial techniques can also be used to retrieve the physiological state from accelerometer and gyroscope sensors [START_REF] Da He | An ear-worn continuous ballistocardiogram (BCG) sensor for cardiovascular monitoring[END_REF][START_REF] Hernandez | Biowatch: estimation of heart and breathing rates from wrist motions[END_REF]; however, in this work we use an entirely vision based system. As such, it is generalizable to any head worn camera apparatus.

In both iPPG and iBCG analyses the heart rate of an individual can be recovered from the pulse waveforms (see Figure 2). Other information, such as breathing rate or heart rate variability can also be extracted. Preliminary work has shown that these remotely measured physiological signals can be used for contact-free prediction of more complex states, such as whether an individual is under cognitive load [START_REF] Mcdu | COGCAM: Contact-free Measurement of Cognitive Stress During Computer Tasks with a Digital Camera[END_REF]. Heart (or Pulse) Rate Variability (HRV) is a useful non-invasive measure of phenomena such as the cardiac regulatory system response, anxiety, or cognitive stress. Being able to measure and visualize this signal from another individual at distance has numerous applications. We discuss the potential use cases and ethical considerations in the Discussion section. is is the rst work to our knowledge to a empt to measure HRV from a head mounted device. Furthermore, our results show that HRV time and frequency domain information can be detected.

For the rst time, Cardiolens combines iPPG and iBCG measurements from a head-mounted camera to calculate the heart rate, not only of the partner but also of the wearer. Furthermore, this is the rst mixed-reality system allowing the wearer to see these physiological signals, such as pulse rate and pulse rate variability, in real-time, in the real-world.

In this regard, new technology can not only provide new ways to measure physiological signals, but can also change how one visualizes or interacts with them. Augmented/mixed reality provides the ability to overlay information onto the real-world. e system brings information from unobtrusive physiological sensing into the user's perceived real-world experience.

is can help users associate physiological information with speci c physical articles and events. e unaided human eye does not have the acuity to notice changes in blood perfusion, let alone understand how this physiological phenomenon is changing over time. erefore, methods for post-processing videos to magnify the subtle changes due to the pulse have been proposed [START_REF] Wu | Eulerian video magni cation for revealing subtle changes in the world[END_REF]]. However, many of these magni cation approaches do not work in real-or near-real time. Additionally, video magni cation does not provide an intuitive real-world visualization of the signals and requires an individual to look at a screen rather than the person, or body part, of interest. New head-mounted wearable devices (e.g., Microso HoloLens1 or Meta 22 ) that feature transparent displays allow dynamic digital information to be overlaid on the real-world and present new opportunities for physiological visualization.

RELATED WORK

Over the past 10 years there have been considerable advances in the performance of unobtrusive physiological sensing methods [Poh [START_REF] Poh | Non-contact, automated cardiac pulse measurements using video imaging and blind source separation[END_REF][START_REF] Poh | Advancements in noncontact, multiparameter physiological measurements using a webcam[END_REF][START_REF] Shao | Noncontact monitoring breathing pa ern, exhalation ow rate and pulse transit time[END_REF][START_REF] Wang | Exploiting Spatial Redundancy of Image Sensor for Motion Robust rPPG[END_REF][START_REF] Zhang | Webcam-based, non-contact, real-time measurement for the physiological parameters of drivers[END_REF]]. ese methods have been shown to be robust in the presence of head motions [START_REF] Wang | Exploiting Spatial Redundancy of Image Sensor for Motion Robust rPPG[END_REF] and to be able to detect subtle aspects of the pulse waveform morphology [START_REF] Mcdu | Remote detection of photoplethysmographic systolic and diastolic peaks using a digital camera[END_REF]].

Fernando et al. [START_REF] Fernando | Feasibility of contactless pulse rate monitoring of neonates using google glass[END_REF]] validated remote physiological measurement in neonates using a Google Glass device.

e camera on the device was used to recover the PPG waveform and infants' average heart rates. However, no visualization of this signal was proposed and validation of heart rate variability measures were not provided. Google Glass also presented limitations including a very constrained eld-of-view (FOV) in the heads-up display and limited processing power. With Cardiolens, we overcome those problems and present a novel mobile system that allows users to view "hidden" physiological signals overlaid in real-time via a semi-transparent mask augmenting the skin color.

Visualization of the blood perfusion signal in videos is possible via Eulerian Video Magni cation (EVM) [START_REF] Wu | Eulerian video magni cation for revealing subtle changes in the world[END_REF]. Recently, less computationally expensive versions of these video magni cation approaches have been proposed [START_REF] Wadhwa | Riesz pyramids for fast phase-based video magni cation[END_REF]. ese methods a empt to magnify speci c signals within videos (i.e. color change or motion of the face/skin due to the pulse) without e ecting other parts of the video (i.e. color or motion in the background). However, inevitably some artifacts are generated. erefore, augmenting the real-world with physiological signals has some advantages as holograms can be displayed in speci c locations without interfering with other elements.

CARDIOLENS 3.1 Image Processing Pipeline

Cardiolens combines iPPG and iBCG methods for recovering physiological measurements from the wearer and the partner simultaneously. In both cases the features are extracted from the front-facing camera images of the Hololens head mounted device. e Hololens has a front-facing, high-de nition (1216x684 pixel) camera. We describe the physiological measurement methods below and include results of the validation in the following section. Figure 2 shows the approach graphically.

3.1.1 Imaging Photoplethysmography. A face detector [START_REF] Viola | Rapid object detection using a boosted cascade of simple features[END_REF] is used to identify the largest face within the images from the front-facing camera. A skin pixel segmentation is applied to the pixels in the facial region of interest. A spacial average of the color channel values for all the skin pixels is calculated. is leads to three time series signals x 1 , x 2 , x 3 . In the Validation section we report results for time windows of 20, 30 and 60 seconds. We tried preprocessing these signals with the method proposed by Wang et al. [START_REF] Wang | Color-Distortion Filtering for Remote Photoplethysmography[END_REF]], however, we did not nd it consistently improved the results on our dataset and thus we did not employ this method in the remainder of our analysis.

Next, we apply the method proposed by Poh et al. [START_REF] Poh | Non-contact, automated cardiac pulse measurements using video imaging and blind source separation[END_REF]] to recover the nal BVP waveform. Underlying source signals are calculated using Independent Component Analysis (ICA) and then normalized so that they have equal total power in the frequency domain.

e BVP estimate is selected as the source signal with greatest peak power in the range 45 BPM (0.75 Hz) and 180 BPM (3 Hz).

e Hololens presents a unique challenge not experienced with other cameras. First, as the device is head mounted this results in camera motion that compounds subject motion. Second, the device has a set of powerful infra-red LEDs used for depth and gesture sensing. When these ash they can alter the illumination of the face, this leads to irregular peaks in the video color channel signals. Despite these challenges our results show good performance in heart rate measurement and promising results for heart rate variability measurement.

Imaging Ballistocardiography.

To detect the BCG signal of the Cardiolens wearer we apply the Lucas-Kanade optical ow method to the camera images. Using this approach we compute the optical ow between subsequent frames. Lucas-Kanade assumes a constant velocity of subsections of the images and involves a weighted least-square t of the image derivatives. e resulting frame-to-frame orientation (angular velocity) measurements computed from the x-and y-velocities are concatenated for a time window. Due to the sensitive nature of the iBCG measurements, capturing subtle changes in head orientation, and the fact that the wearer is likely to have the device on for several minutes at a time we use a 60 second time window to recover the heart rate of the wearer.

Physiological Parameter Estimation

In both the iPPG and iBCG analysis we extract the heart rate as the frequency of the highest peak within the fast Fourier transform (FFT) frequency spectra of the pulse waveform between 45 BPM (0.75 Hz) and 180 BPM (3 Hz). ese values re ect conservative bounds on natural heart rates. e window size for analysis can be calibrated for speci c applications. A sliding window means the value can be updated frequently a er the initial windows -as frequently as once every frame.

Mixed Reality Implementation

We designed a mixed-reality visualization for Cardiolens, such that the wearer can observe the measured physiological signals in the real-world. is visualization has two components as we measure both the physiological state of the wearer and a partner.

We augment the appearance of the partner with the blood ow signal by altering the brightness of the skin on their face. is process presents the technical challenge of displaying a semi-transparent mask on a moving object to create a mixed reality experience. We developed a holographic overlay which shows the BVP signal superimposed onto the face using a linear image processing pipeline (see Figure 3).

We rst turn every captured image from the NV12 (Y, U (Cb) and V (Cr) pixel packing method) pixel format to the standard red, green and blue (RGB) pixel format. is process is performed using a compute shader (implemented on the GPU) to ensure a su cient frame rate for real-time performance. Next, the RGB stream is analyzed to extract detected faces. We only consider the largest detected face and we segment skin pixels from the Hololens camera. is is the point at which we perform the iPPG analysis (see the previous section for details). We modify the red channel values of the skin pixels over time to magnify the estimated pulse signal. Finally, we compute the position of the captured frame in the 3D environment. We place this image in the mixed reality space at the average distance of the user from the device (approximately one-meter). We also de ne a speed vector for this plane, which corresponds to its change of location when the user or subject moves his or her head. e speed estimation is very important to ensure that the overlaid hologram remains stationary on top of the subject's face from the perspective of the Cardiolens wearer. e resulting experience allows the user to see the pulsating blood ow signal that would otherwise be imperceptible. In addition, the heart e system magnies minute variations in blood ow captured via the frontfacing camera. rate is also displayed close to the subject's head. Information is placed onto oating billboards in the holographic space, see Figure 3. Screenshots of the visualization captured through Cardiolens are shown in Figure 4. e heart rate of the wearer is displayed in the top right-hand corner of the display. is information is displayed relative to the wearer and is not tied to a location in the real-world. Finally, an additional semi-transparent mesh can be applied in the wearers eld of view to illustrate their heart rate. A sketch of the resulting visual interface can be seen in Figure 2.

VALIDATION OF PHYSIOLOGICAL MEASUREMENTS

We collected one-minute recordings from 11 people (3 females) with a range of skin tones (east Asian, south Asian, white) using the Cardiolens system alongside gold-standard contact BVP measurements. Some participants were wearing make-up and others had facial hair, neither of these factors were deletarious to the results. Gold standard measurements were obtained from the index nger of the non-dominant hand using a Nonin Onyx II 9560 digital nger-tip pulse oximeter. e BVP waveform was streamed via Bluetooth and logged on a laptop computer. e Cardiolens recordings and nger-tip PPG measurements were synchronized by using the same computer to log and store the data. For validation purposes we stored the recorded videos. e pulse oximeter data was sampled at 75 Hz and the videos were stored at 24 frames-per-second (Hz) and at HD resolution.

e participants completed two tasks each of one-minute. During the tasks the participant was asked to not move around or speak but other than that their motions were not restricted. e recordings were captured indoors in a space that combined arti cial and natural light. No dedicated light sources were used for illumination, only those normally present in the environment. umbnail example frames from one of the recordings can be seen in Figure 5.

Tasks

4.1.1 Imaging Photoplethysmography. We recorded the face of the participant using the Hololens camera, worn by an experimenter, for one minute. e participant and the experimenter were seated one meter apart during the trial.

e participants were asked to relax but their head motions and facial expressions were not restricted.

4.1.2 Imaging Ballistocardiography. During this task the participant wore the Hololens and was asked to sit for one minute. We placed a reference grid in the eld-of-view of the camera so that there were edges/points that could be tracked for recovering the motion trajectories. e reference grid was placed at one meter from the participant.

Results

To evaluate accuracy we compared the Cardiolens measurements for each task with the gold-standard contact measurements. We computed the accuracy a er dividing the data into non-overlapping windows. We used three evaluation metrics: the median absolute error, mean absolute error and the root mean squared error (RMSE) between the heart rate estimates and the gold-standard. For the iPPG measurements we evaluated three window sizes 20, 30 and 60 seconds. For the 11 participants there were 11 60s windows, 22 30s windows and 33 20s windows. Due to the sensitive nature of the iBCG measurements, we used only a 60s window for recovering the BCG signal, thus there were 11 60s windows. 4.2.1 Imaging Photoplethysmography. Heart Rate: Table 1 shows the absolute error and RMSE between the iPPG measurements and the contact nger-tip pulse oximeter. e mean absolute error was 2.34, 1.62 and 1.85 BPM for window sizes of 20, 30 and 60s respectively. is suggests that a 60s window does not o er a performance bene t versus a 30s window. e median error for a 30s window was 0.12 PBM. With a range of heart rates in our iPPG dataset from 48 BPM to 76 BPM these errors show that heart rate detection via iPPG from the head worn device is very accurate.

Figure 5 shows examples of the detected waveforms from the contact sensor and the camera, alongside the power spectrum for each signal. Very li le frequency domain information is lost by the camera. Figure 7 shows the correlation (r=0.9, p<0.01) between the measurements for the 30 second window size.

Heart Rate Variability: Using a peak detection algorithm we identi ed the peaks within the iPPG and gold-standard waveforms.

ese were used to calculate inter-beat intervals (IBIs), this is the inverse of the instantaneous heart rate. Using the Lomb-Scargle method we calculated the HRV power spectrum which is useful for estimating parasympathetic (rest-digest) and sympathetic ( ghtight) responses. Figure 8 shows the IBIs and HRV power spectra for two participants. Power in the 0.15-0.4Hz range of the HRV power spectrum is connected to respiratory sinus arrhythmia (RSA), a cardiorespiratory phenomenon characterized by uctuations in the timing heart beats that are in phase with inhalation and exhalation. Dominant RSA peaks were observed in a majority of the power spectra; however, we do not a empt to rigorously validate respiration rate results here. While these are preliminary results they show promising evidence that we can recover subtle changes in physiological state using the head-worn device and visualize them in close-to real-time.

is opens the possibility to augment the world with a representation of the level stress an individual is experiencing [START_REF] Mcdu | COGCAM: Contact-free Measurement of Cognitive Stress During Computer Tasks with a Digital Camera[END_REF]. Table 1: e absolute error and root mean squared error in heart rate estimates between the contact nger-tip measurements from the pulse oximeter and the Cardiolens system. We compare results using a 20s, 30s and 60s window sizes for iPPG measurement. We use a 60s window for iBCG measurement. 1 shows the absolute error and RMSE between the iBCG measurements and the contact nger-tip pulse oximeter. e absolute error is under 3 BPM, which at an average heart rate is only about 4% error. Figure 6 shows an example of detected BCG waveform and the corresponding power spectra. It is clear that the signal captures much of the frequency information of the pulse wave. Figure 7 shows the correlation (r=0.9, p<0.01) between the measurements for the 60 second window size.

HR

Overall, the results show that using the head-mounted camera of the mixed-reality device we can accurately capture the pulse signal and heart rate of the partner and the wearer, using iPPG and iBCG methods respectively.

Heart Rate Variability: As with the iPPG analysis we a empted to recover the inter-beat intervals from the BCG signals; however, it was much more challenging given the iBCG waveforms. Although the dominant heart rate frequency was identi able the individual peaks were not. Using accelerometer or gyroscope data might lead to waveforms with more easily identi able peaks.

alitative Results

We experimented with several variations of the mixed reality visualization. We tried displaying the heart rate as a number, the pulsatile skin augmentation and showing the pulse waveform itself for the most recent 20 second window of analysis. Several individuals noted that viewing the waveform was not useful and was rather "distracting". e skin augmentation was very intuitive; however, it was di cult to interpret whether the pulsing was fast or slow in absolute terms. erefore, having the heart rate number was a useful aid. Furthermore, some people felt they could judge whether the measurements were accurate give their own knowledge of their resting heart rate. For some applications simply seeing the pulse information may not be enough. However, the participants noted that if it was possible to visualize a measure of "stress" based on the variability of the heart beats that may be very informative.

Several participants commented on the ethical issues presented by a device that could allow someone to "see" such private information in near real-time. ey mentioned that this might e ect how they interacted with the other person. ey reasoned that unlike with facial expressions they could not control their physiological responses and thus it might be particularly invasive. Humans have created social norms around facial expressions and use facial controls as a tool in social contexts, the same does not exist for physiology.

DISCUSSION

e ability to measure and visualize the physiological signals of ourselves and those around us in real-time presents numerous new opportunities for augmented reality and virtual reality (VR) applications. Cardiolens can be applied to any stereoscopic head-mounted display with a camera. e system allows for hands-free interactions while augmenting the natural scenes with physiological and a ective information. In this section we discuss the implications of integrating Cardiolens into current devices.

Immersive Experiences

Immersive experiences (such as those possible with mixed-reality devices) are likely to lead to more intense a ective and emotional responses than traditional computer interactions [START_REF] Gonzalez-Franco | Model of Illusions and Virtual Reality[END_REF][START_REF] González-Franco | A threat to a virtual hand elicits motor cortex activation[END_REF][START_REF] Slater | From presence to consciousness through virtual reality[END_REF]. ese emotions can be measured through physiological signals [START_REF] Meehan | Physiological measures of presence in stressful virtual environments[END_REF][START_REF] Gonc ¸alo Padrao | Violating body movement semantics: Neural signatures of self-generated and external-generated errors[END_REF][START_REF] Spanlang | How to build an embodiment lab: achieving body representation illusions in virtual reality[END_REF]. Importantly, monitoring the physiological state of the wearer and those around them in a non-invasive way could help indicate undesirable e ects, such as simulator sickness [START_REF] Smolyanskiy | Stereoscopic First Person View System for Drone Navigation[END_REF]. For example, the system could recommend participants take a break from the device when they exceed certain physiological thresholds. Eventually, presenting this information could not only help participants avoid nauseating e ects but also train them with coping mechanisms.

Social Interactions

Cardiolens can be used to increase the interoceptive awareness of the user during social interactions. Having a device that can provide this information in real-time, such as Cardiolens, would help augment the physiological states of both the user and the partner/interlocutor. is augmentation would build interoceptive awareness which is known to increase the intensity of emotional responses [START_REF] Hugo D Critchley | Neural systems supporting interoceptive awareness[END_REF]].

e system could help people with impaired social skills, or suffering from autism, increase awareness of their physiological state and thus adapt their social behavior. Arguably the same would be true for socially-able users. Indeed, social performance has long been linked to unconscious mimicry, which is most directly linked to the mirror neuron system [START_REF] Rizzola | e mirror-neuron system[END_REF]. Humans automatically enable these resonance mechanisms to reduce out-group biases [START_REF] Jessica L Lakin | I am too just like you: Nonconscious mimicry as an automatic behavioral response to social exclusion[END_REF]. Interestingly, the mimicry goes far beyond behavioral and speech pa erns and humans unconsciously change their own physiological interoceptive functioning to match others in many aspects in life. e inter-beat intervals (1/instantaneous heart rate) measurements are quite accurate and this allows us to recover the HRV power spectrum which is useful for estimating sympathetic and parasympathetic activation and respiration rate. For the example on the right the respiratory sinus arrhythmia (RSA) is clearly present in the IBI signal.

Emotional contagion (e.g. stress or anger passing from a mother to a child) is one example of physiological synchrony between people. In other cases, the process can be purely physiological and independent of the original emotions. Synchronization might take place over long exposures to others (e.g. menstrual synchronization [START_REF] Mcclintock | Menstrual synchrony and suppression[END_REF]), but also during short exposures (e.g. respiration rate and/or heart rate synchronization of interlocutors during conversations [START_REF] Sowden | e speci city of the link between alexithymia, interoception, and imitation[END_REF] ere are bene cial e ects of this interoceptive matching, as when synchronous physiological signals are achieved, participants are more likely to pass a job interview. On the contrary decreased interoceptive awareness has been shown to follow social exclusion [START_REF] Durlik | Decreased interoceptive accuracy following social exclusion[END_REF]. Cardiolens could be used to both learn more about how awareness might impact these mimicry effects, and potentially feed that information into real-life interactions to help boost synchrony between pairs.

Skilled Observer

In many situations there might not be social interaction but still an observer might bene t from knowing physiological variables before, during, and a er a critical activity. ere are many scenarios in which observers currently rely on their own intuition; however, explicit knowledge of a ective and physiological signals could help develop more objective decision-making.

In sports, trainers could evaluate athletes at a simple gaze or during a routine. On a more trivial note, it could be used to augment the performance of players during gambling sessions. We foresee that as camera technology continues to develop it will be possible to visualize subtle changes in blood perfusion across the body. is could aid surgeons interested in knowing whether a transplanted organ/tissue has blood owing to it. ese and other tasks could bene t from a system such as Cardiolens. Further research on image processing could nd particular pa erns that reveal blood oxygenation, body temperature or intoxication with chemical components. us making more information explicit for skilled observers to help them with objective decision-making.

Ethics and Privacy

From an ethical perspective there are some aspects that need to be addressed given the potential surveillance applications of this system. ere is a natural and well studied con ict between privacy and the advancement of technology in society [START_REF] Westin | Privacy and freedom[END_REF]]. In this regard, Cardiolens presents a non-invasive and non-explicit system able to retrieve physiological parameters from anybody just by looking at them. So far the discussion of the implications has focused on enabling positive scenarios. However, there are negative applications of this technology that would infringe on data privacy rights [START_REF] Slobogin | Public privacy: camera surveillance of public places and the right to anonymity[END_REF]].

When applied in-situ, this technology might be able to perform non-explicit monitoring of people who have not consented and are not aware of being recorded. We see a necessity to develop an antidote, a way to prevent this monitoring. ere is a need for a system that hinders heart beat retrieval. Based on our initial investigations, random IR light pa erns projected on to the skin will prevent the retrieval of a correct heart beat. One could imagine using an IR LED that lights up the user's skin with varying intensities. In that case, our system might confuse the LED signal with the actual heart beat and retrieve inaccurate information. We propose IR, precisely because it will be invisible to the unaided eye, although other types of illuminations would also result in interference.

Without appropriate consent people might start perceiving an otherwise positive device as a mere tool for surveillance. erefore, besides the ability to block or interfere with monitoring, we also see a need to make explicit when this technology is recording data and if/when it is storing the data. Recently devices, such as Google glass or Snapchat's spectacles, have miniaturized cameras to a point that they are no longer obvious. Hololens provides an LED that indicates when the camera is recording. With time, people will learn that they are being monitored. And in many cases, they will not care. We are already being surveilled at massive scales with CCTV cameras and more recently with microphones. However, it is clear that social norms need to exist around the acceptable use of such technology.

e concern would only increase further if Cardiolens also incorporated facial identi cation technology.

A secondary ethical question that stands out is related to the clear asymmetry in information power produced when this system is worn by one person but not others. e societal divisions between those who can a ord technology and those who cannot might cause social problems. However, in general we are very optimistic that if the proposed consent mechanisms are implemented this technology will have more positive than negative applications.

Feasibility

In our validation study we used the Microso Hololens and implemented the system in C#. All the processing is performed on the device and images captured using the front-facing camera. us the device does not need to be tethered to a computer, nor does the hardware require any custom adaptation. e results revealed good performance in physiological measurement despite motion of the camera and the head.

Nevertheless, the device su ers from some limitations. Some of these are inerrant to non-contact measurement of physiological signals, and others result from current technological restrictions of the device. e camera is sensitive to abrupt changes of lighting conditions. Which means, the video processing takes 20 seconds to retrieve a pulse waveform.

e holographic overlay layer that displays the subjects pulsating skin is limited by the device. is layer has to be accurately positioned on top of a face. Since Hololens operates in the 3D space and uses stereoscopic vision, this overlay has to be at the same depth as the partner's face. However, if the depth map of the environment is limited or inaccessible the overlay is not well displayed. To address this issue, in our demonstration we estimate the depth from the vertical height of the captured face: a smaller height means that the partner is further away; thus we render the overlay at a larger depth. is technique is su cient to present the information in real-time but could be more accurate. In the future, the device itself may give direct assess to the captured depth map.

CONCLUSIONS

Cardiolens is the rst mixed reality system that enables real-time, hands-free measurement and visualization of physiological signals.

e system uses images from the front-facing camera to recover the vital signs of both the wearer and the person they are looking at simultaneously. We presented the technical implementation of the system and describe the mixed reality interface that showcases realtime visualization of normally "hidden" physiological parameters.

We validated the system by capturing measurements of 11 subjects using Hololens alongside gold-standard contact signals. e results show accurate HR rate measurement of both the wearer and a person they are looking at. We achieved a mean absolute error below 3 BPM for both iPPG and iBCG measurements. We also presented baseline results for heart rate variability measurement using the iPPG signal.

alitative feedback revealed participants were intrigued by the ability to "see" these hidden signals and that numerical representation of the heart rate and skin augmentation were more e ective than a display of the pulse waveform itself.

We discussed the implications of our system and presented novel visualizations of the physiological measurements in the real-world. Users found the ability to magnify the blood volume pulse signal by augmenting the appearance of the skin particularly powerful, some refereed to it as having a "super power".

Figure 3 :

 3 Figure 3: Video transformation pipeline for analyzing the physiological signals of another person. e video is captured and processed to extract the subject's heart beat from the facial region-of-interest. en the system magni es minute variations in blood ow via modi cations to the skin pixel intensities. Finally, holograms are anchored to display the magni ed blood volume pulse and heart rate information.

Figure 4 :

 4 Figure 4: Screenshots of the Cardiolens blood ow augmentation captured during an interaction.e system magnies minute variations in blood ow captured via the frontfacing camera.

Figure 5 :

 5 Figure 5: Examples of pulse waveforms from the nger-tip sensor and iPPG measurements. Top) e PPG waveforms. Bottom) e power spectra of the BVP signal and the detected HR. umbnail example frames from the Hololens video capture are shown above.

Figure 6 :

 6 Figure 6: Examples of pulse waveforms from the nger-tip sensor and iBCG measurements. Top) e BCG waveform from the Hololens and the PPG waveform from the ngertip sensor. Bottom) e power spectra of the signals and the detected HR.

Figure 7 :

 7 Figure 7: Scatter plots of the heart rate estimates from iPPG and iBCG measurements against the gold-standard contact measurements. e heart rates ranged from 40 to 80 BPM.

  Figure 8: e pulse wave (top), inter-beat intervals (middle) and HRV power spectra (bottom) for two participants. Comparisons between the contact sensor (thick line) and iPPG (thin line) signals are shown in each case.e inter-beat intervals (1/instantaneous heart rate) measurements are quite accurate and this allows us to recover the HRV power spectrum which is useful for estimating sympathetic and parasympathetic activation and respiration rate. For the example on the right the respiratory sinus arrhythmia (RSA) is clearly present in the IBI signal.

h ps://www.microso .com/microso -hololens

h ps://www.metavision.com

ACKNOWLEDGEMENTS

e authors acknowledge the support of the French National Agency for Research (Agence Nationale de la Recherche ANR) under the grant ANR-14-CE24-0006-01 project "TERANOVA" and the SESAR Research and Innovation Action Horizon 2020 under project "MOTO" ( e embodied reMOte TOwer).


R Le Boursicaud

L Pénard

A Hauet

F Thollet

J Le Coz

Gauging extreme oods on YouTube: Application of LSPIV to home movies for the post-event determination of stream discharges Running head: Application of LSPIV to ood home movies

Keywords: hydrometry, ood, LSPIV, discharge, home movie, video sharing

Movies taken by witnesses of extreme ood events are increasingly available on video sharing websites. They potentially provide highly valuable information on ow velocities and hydraulic processes that can help improve the post-ood determination of discharges in streams and ooded areas. We investigated the troubles and potential of applying the now mature LSPIV technique to such ood movies that are recorded under non-ideal conditions. Processing was performed using user-friendly, free software only, such as Fudaa-LSPIV. Typical issues related to the image processing and to the hydrological analysis are illustrated using a selected example of a pulsed ash-ood ow lmed in a mountainous torrent. Simple corrections for lens distortion (sheye) and limited incoherent camera movement (shake) were successfully applied and the related errors were reduced to a few percents. Testing the dierent image resolution levels oered by YouTube showed that the dierence in time-averaged longitudinal velocity was less than 5% compared to full resolution. A limited number of GRPs, typically 10, is required but they must be adequately distributed around the area of interest. The indirect determination of the water level is the main source of uncertainty in the results, usually much more than errors due to the longitudinal slope and waviness of the ow free-surface. The image-based method yielded direct discharge estimates of the base ow between pulses, of the pulse waves, and of the time-averaged ow over a movie sequence including a series of 5 pulses. A comparison with traditional indirect determination methods showed that the criticaldepth method may produce signicantly biased results for such a fast, unsteady ow, while the 1

Introduction 1.Large uncertainties in indirect post-ood discharge estimates

The accurate knowledge of river discharge during extreme ood events is key for most studies of the ood-related hydrological processes. Very often, ood discharge measurements are lacking because of a range of technical limitations in streamgauging eld operations. It often happens that deploying the instruments was too dangerous or too uncertain because of free-surface conditions, drag, oating debris, high suspended-load or moving bed. It also happens that the hydrometry sta cannot get to the gauging site when the ood wave was too sudden and too short or when roads and access are ooded. Last, discharge measurements may be lacking simply because discharge estimates are requested at a site where a hydrometric station did not exist or was destroyed by high ows. In such common situations, a post-ood analysis is required in order to support the indirect determination of peak discharge (WMO, 2010, chapter 9). The method is based on the eld collection of all relevant information on the ow magnitude and dynamics, especially high-water marks, channel geometry and roughness, control section geometry, etc. The aim is to feed conventional hydraulic formulations related to a channel control (slope-area method) using the Manning-Strickler equation, to dierent types of critical section controls (ow over dams and weirs, through culverts, at width contractions), or to other hydraulic properties such as free-surface superelevation in bends.

The uncertainty of indirect discharge estimates is usually much larger than the uncertainty of discharge measurements from streamgauging or stage-discharge relations calibrated at hydrometric stations. [START_REF] Jarrett | Errors in slope-area computations of peak discharges in mountain streams[END_REF] showed that the slope-area method can typically lead to 100% overestimation of ood discharges in mountain rivers where the critical-depth method is preferable. Lumbroso and Gaume (2012) highlighted the dicult estimation of reliable Manning's n ow resistance coecients, especially for supercritical ows. Amongst major sources of error are the uncertainty of high-water marks and derived longitudinal slope, the questionable applicability of hydraulic formulas established for ideal conditions, the unobserved scour and deposition processes during the ood [START_REF] Kirby | Linear error analysis of slope-area discharge determinations[END_REF][START_REF] Gaume | Hydrological analysis of the river Aude, France, ash ood on 12 and 13 November 1999[END_REF]. A major issue in the indirect discharge determination is the absence of ow velocity measurements. [START_REF] Borga | Surveying ash oods: gauging the ungauged extremes[END_REF] also insist on the limited spatio-temporal resolution of indirect peak discharge es-timates: the post-ood analysis aims at reconstructing the ood event dynamics at a synoptic scale.

Beyond the collection of hydraulic data, the post-ood eld survey usually oers the opportunity of interviewing eyewitnesses, which may provide valuable, though variably uncertain information on the ood dynamics and morphodynamical processes [START_REF] Gaume | Post ood eld investigations after major ash oods: proposal of a methodology and illustrations[END_REF]. They also often provide additional material such as pictures and movies: Lumbroso and Gaume (2012) recommend to use them to check the consistency of velocity estimates greater than 3 m/s, either from the displacement of visible ow tracers or from the height of ow superelevation against an obstacle.

Numerical simulation can also be used to investigate the hydrological response of the catchment and the stage-discharge relation along the river network: for instance, [START_REF] Bonnifait | ://oodscale.irstea.fr/ 29 Reconstruction of the 8-9 September 2002 catastrophic ood event in the Gard region, France[END_REF] successfully combined distributed hydrological and hydraulic modelling to reconstruct the 2002 ash-ood event in the Gard river catchment based on the post-ood analysis conducted by [START_REF] Delrieu | The catastrophic ash-ood event of 8-9 september 2002 in the Gard region, France: a rst case study for the Cévennes-Vivarais Mediterranean Hydro-meteorological Observatory[END_REF]. However, even the best numerical simulation cannot compensate for the scarcity and large uncertainty of post-ood ow velocity and discharge estimates.

Potential of LSPIV for post-ood analysis

Since oods are important events for the people living in the vicinity of the impacted rivers, witnesses often take pictures or record videos of those events. The fast-growing development of digital imaging technologies allows non-professional people to record high quality videos. Sharing videos in the Internet is nowadays very common, especially for videos of extreme natural events. As a consequence, each recent ood occurring in inhabited areas has its hundreds or thousands of videos in the Internet. As an example, searching "Flood Boulder 2013" and "Flood Brisbane 2011" on YouTube yields 65 000 and 43 000 results, respectively.

A simple look at those videos can bring a lot of information about the ow processes: how high was the water, how extended were the ooded areas, what kind of obstacles were opposed to the ow, what kind of objects were put in motion, or what was roughly the velocity and direction of the water. In this paper, we investigate the capability of calculating quantitative hydraulic data, such as water height, ow velocity and eventually discharge from home movies taken by ood witnesses.

Image-based methods can indeed be used for the calculation of hydraulic parameters. The rst 4 image-based velocimetry technique was developed for laboratory applications in the 1960's and called PIV for Particle Image Velocimetry [START_REF] Adrian | Particle-imaging techniques for experimental uid mechanics[END_REF]. In the following decades, dierent image analysis techniques were developed, such as the Particle Tracking Velocimetry PTV [START_REF] Perkins | Particle tracking in turbulent ows[END_REF][START_REF] Lloyd | Unsteady surface-velocity eld measurement using particle tracking velocimetry[END_REF], the Large-Scale Particle Image Velocimetry (LSPIV, [START_REF] Fujita | Large-scale particle image velocimetry for ow analysis in hydraulic engineering applications[END_REF], or the Space-Time Image Velocimetry STIV [START_REF] Fujita | Development of a non-intrusive and ecient ow monitoring technique: The space time image velocimetry (STIV)[END_REF]. Among those methods, LSPIV was chosen as a tool for the present study because it is currently the most mature and widely available image-based velocimetry technique.

The eciency of LSPIV for measuring free-surface velocities and discharge in rivers for ood conditions has been recurrently demonstrated since the proof-of-concept application by [START_REF] Creutin | River gauging using PIV techniques: a proof of concept experiment on the Iowa river[END_REF]. Flood discharges were successfully computed using images produced by commercial video cameras mounted on mobile systems [START_REF] Kim | Stream discharge using mobile large-scale particle image velocimetry: A proof of concept[END_REF] -recording of a sequence of images, knowing the time interval, δt, between two images in a pair; -orthorectication of the images, in order to correct perspective distortion eects and to georeference pixels. This geometrical correction of the pictures is usually achieved through a 3D plan-to-plan perspective projection calibrated with Ground Reference Points (GRP) [START_REF] Jodeau | Application and evaluation of LS-PIV technique for the monitoring of river surface velocities in high ow conditions[END_REF]; -statistical analysis applied to each pair of orthorectied images to determine the displacement of natural or articial tracers of the free surface ow such as boils, surface ripples, vegetation debris, etc. At each node of the computational grid, cross-correlation is applied to 256-level gray-scale square interrogation areas with a sub-pixel optimisation. More details about the data processing and the limitations of the technique can be found in Le [START_REF] Le Coz | Image-based velocity and discharge measurements in eld and laboratory river engineering studies using the free Fudaa-LSPIV software[END_REF].

The LSPIV analysis provides instantaneous 2-D velocity elds of the free surface velocities. Knowing the bathymetry of a cross-sectional transect and modelling the vertical velocity distribution lead to an estimation of the river discharge.

In a review of previous works on LSPIV accuracy, [START_REF] Muste | Large-scale particle image velocimetry for measurements in riverine environments[END_REF] reported an average total error in velocity of 10% and maximum error of 35%. Such numbers were supported by the consideration of 27 elemental error sources and the results of comparison to other velocimetry techniques taken as references, with observed dierences ranging from 3.5% in ideal laboratory conditions to 10% or even 16% in eld conditions. Though [START_REF] Muste | Large-scale particle image velocimetry for measurements in riverine environments[END_REF] stated that the uncertainty in estimated discharge should be lower than the uncertainty in velocities, the former is actually dicult to predict from the latter. Typically, from comparison tests at their gauging station, Le Coz et al.

(2010) estimated the uncertainty in velocity to be lower than 10% while the uncertainty in discharge was lower than 20% in good image conditions, but up to 30-80% in poor image conditions. Taking a well-established rating curve as a reference, [START_REF] Dramais | Advantages of a mobile LSPIV method for measuring ood discharges and improving stage-discharge curves[END_REF] estimated their uncertainty in discharge to be as low as 10% for ow and image conditions similar to those of many ood home movies.

A complete uncertainty analysis method for ood discharge measurements using the conventional LSPIV technique is still missing, mainly because: orthorectication and LSPIV image processing involve complex error propagation; errors in velocity are varying spatially according to ow and image conditions; errors in discharge estimate are signicantly aected by errors in water level estimate, cross-sectional geometry and assumptions on the unmeasured ow structure, which all are dicult to quantify under ood conditions in a natural stream. [START_REF] Hauet | Sensitivity study of large-scale particle image velocimetry measurement of river discharge using numerical simulation[END_REF] opened a promising way to conduct ecient sensitivity analysis using a numerical simulator that combined the river ow, the camera and the LSPIV processing. Nevertheless, LSPIV discharge uncertainty estimates from empirical studies are acceptably low to improve post-ood analysis results and the extension of stage-discharge rating curves to ungauged high ows.

Major issues related to the analysis of ood movies

In most cases ood movies are produced by non-professional witnesses in non controlled conditions with no velocimetric objective. Using such videos for LSPIV applications raises several issues that 6 have to be addressed.

The rst point is to select from the available movies those that are eligible for LSPIV processing.

Both river banks have to be visible in the image so that a complete cross-section is monitored.

Another selection factor is that the ow should not be too wavy and non uniform, and the water surface has to be planar according to usual LSPIV hypotheses.

The second issue regards image processing. Traditional LSPIV sequences are captured with a known camera, so that usually focal length and distortion are either known or can be calibrated. The camera is placed at a known and steady position and all the necessary topography measurements are made in the eld. Thus, the projection equations that relate ground and image reference systems can be determined and do not vary with time. In the case of home movies, the camera is unknown and hand-held, and parameters have to be estimated from the images. Automatic methods have been developed, such as self-calibration [START_REF] Maybank | A theory of self-calibration of a moving camera[END_REF]) and motion estimation [START_REF] Pollefeys | Visual modeling with a hand-held camera[END_REF], to overcome this problem.

The third point deals with the link between images and the scene. LSPIV velocity and discharge results are highly dependent on the water level, as noted by [START_REF] Dramais | Advantages of a mobile LSPIV method for measuring ood discharges and improving stage-discharge curves[END_REF]. In the case of home movies, this parameter has to be estimated directly from the images. Moreover, in order to perform the absolute image registration, GRPs have to be present within the images, ideally placed on both sides of the ow.

Finally, issues related to the properties of the ow and of the hydrological event are also raised by the application of LSPIV technique to ood movies recorded by witnesses. To calculate discharge from surface velocity estimates, the bathymetry of the reach has to be known and a realistic depthaverage to surface velocity ratio, or `velocity coecient' has to be selected. A specic attention should be paid to mobile bed conditions and to the subsequent morphodynamical evolutions during the event, which may dramatically increase the uncertainty in the ow structure and in the wetted area, hence in the discharge estimate. Another diculty is to determine the precise location, date and time of the movie relative to the whole hydrological event.

Objectives of this study

The scope of this methodological paper is to cover the main issues related to the application of the conventional LSPIV technique to ood home movies. Technical problems and solutions are illustrated using the same application example, a typical movie taken by the observer of a storm ood in a channelized torrent of the French Alps. The sensitivity of discharge estimates to the identied sources of errors is investigated. The specic issues related to the image processing of ood home movies are presented rst. We eventually discuss the limitations and added value of the proposed method for the indirect determination of ood discharges, especially when pulsating ows occur.

2 Material and methods

Study case: A ash-ood in an alpine torrent

The study site is located in the French Alps in the Saint-Julien torrent at Saint-Julien-Mont-Denis, France. The catchment area of the river at the point where the video was recorded is about 20 km 2 .

The geographic coordinates at this point are 6 • 24'08.8 E / 45 • 15'26.1 N. The Saint-Julien torrent is a typical concrete-lined, steep mountain stream prone to ash ood. No hydrometric station is available in that stream.

The bed of the Saint-Julien torrent is entirely articialized from 200 meters upstream of the study site, to the conuence with the Arc river 1.6 km downstream. The straight channel has a trapezoidal cross-section which is ∼5 m wide at the bottom. Banks are 45-degree slopped and made of concrete sealed riprap rocks, while the bottom is paved with rectangular concrete agstones. One meter high steps were built every 20 m along the channel to reduce the local longitudinal slope. The area of interest of the recorded pictures includes a uniform section with a gradient of 0.063 m/m downstream of a step acting as a weir.

Beside periods of snow melting during Spring and occasional storm events with heavy precipitation, the stream has a very low, if not zero discharge, as is the case at the beginning of the studied video. Flash oods during Summer storms may form and propagate extremely rapidly. On the 22 nd 8 (a) Measuring the cross-section of the main weir (b) Measuring a GRP on the agstone edges of August 2011, heavy precipitations resulted in a ash ood that lasted about 40 min. Such a hydrological event is not unusual in the torrential tributaries of the Arc river. The response of the Arc river was recorded at the Pontamafrey station located 10 km downstream of the junction with the Saint-Julien torrent. The peak discharge was very limited: 80 m 3 /s, while the 2-year return period discharge is 260 m 3 /s (cf. [START_REF] Dramais | Advantages of a mobile LSPIV method for measuring ood discharges and improving stage-discharge curves[END_REF]. However, the suspended load concentration (8.5 g/L at peak) and ux (7 t/s at peak, 31 000 t over the event) were signicant.

As will be discussed later, the event is characterized by violent pseudo-periodic pulses that appear as translatory breaking waves with obviously much higher velocity and discharge than the quasi-steady base ow between those pulses. The water is almost black, which suggest that the suspended load is very high, likely higher than 50 g/L. Still, the ow seems to behave as a Newtonian uid, except for the rst dry front that pushes a lot of debris and rocks as a slug.

The complementary measurements necessary to the LSPIV analysis, such as topography, ground reference point coordinates, and the water level at dierent moments of the video were later performed by our sta (cf. Fig. 1). The topography survey was achieved using a total station (Leica TC305). Due to unavoidable alignment errors, the positioning uncertainty was estimated to be roughly ±1 cm (within the 95% condence level).

A reference transect for computing discharge was measured in the uniform reach downstream of the weir, which was also measured. The bottom width is equal to 5.1 m in the reference transect. It 9 can be seen in Fig. 1 that bedload transport produced limited deposits in the recorded reach and likely led to negligible changes in the cross-section area during the event.

Study case: Images and camera

The event was captured by Alexandre Modesto, a local ash-ood enthusiast who posted a montage of the video online 1 and further authorized us to use his lm for research purpose. The recording starts before the arrival of the ash ood, showing the geometrical pavement of the dry bed, as visible in Fig. 2(a). The stream is lmed from a bridge facing upstream, at a 1920×1080 pixels resolution and a 25 frames per second sampling rate, using a Canon EOS 5D mark II with a 16 mm sheye Zenitar lens. The sheye lens produces a large amount of distortion. Besides, due to the absence of a tripod during the recording, the video presents a typical camera shake. This ood home movie was chosen to illustrate this paper because of three main advantages. Firstly, the author is identied, which opened the possibility to have access to the full resolution original video and to get informations on the hydrological event. Secondly, the hydrological event itself is of great interest, especially for the study of the pseudo-periodic pulses. Finally, the recording starts before the arrival of the water ow and the presence of a regular grid on the dry bed is a key point for image processing tests such as distortion removal, or impact of slope correction.

The selected movie is not particularly favourable to the application of LSPIV, at least because of camera movements, wide-angle lens distortion, scarce xed reference points in a semi-urban environment and streamwise shooting along an inclined ow in a steep channel. It is therefore useful to investigate the errors related to these frequent limitations of ood home movies. The main favourable property of this study case is that the channel geometry is almost perfectly known since the bed is concrete-lined and bedload deposits are clearly negligible (cf. Fig. 1). In many other cases in natural, alluvial streams, possible bed evolutions during the ood are a major source of uncertainty in the discharge estimates.

The studied ood home movie lasts for more than 17 minutes. A reference sequence of 50 images was selected, starting at time 5:00. All the image processing and LSPIV analyses were performed on this reference sequence (cf. sections 3.2, 3.3, 3.4, 3.5 and 4.2), except the larger movement in section 1 http://www.youtube.com/watch?v=V1H7V90o8JY 10 Author-produced version of the article published in Hydrological Processes (2016), Volume 30, Issue 1, p 90-105

The original publication is available at http://onlinelibrary.wiley.com DOI: 10.1002/hyp.10532

3.3 for which a specic sequence was required (time 7:27), and the pulse ow analysis detailed in section 4.4. Additionally, an image of the beginning of the video when the torrent bed is still dry is used for the geometric evaluation of the orthorectication step (cf. section 3.1).

LSPIV parameters were kept constant for all the tests presented in this paper. The time interval δt between consecutive frames sampled from the original movie is equal to 0.04 s. The resolution of the orthoimages was set to 0.03 m/pixel. The size of the interrogation area (IA), i.e. the square image pattern on which correlation is computed, is 30 pixels. The extent of the search area (SA), i.e. the rectangle within which the center of the IA is positioned to compute all the investigated correlation coecients, is 25 pixels, 0 pixels and 15 pixels in the downstream, upstream and spanwise directions, respectively. No data screening was applied to the obtained velocity vectors.

A free software approach for a reproducible method

For this study, the LSPIV analysis was conducted using Fudaa-LSPIV, a free software available online 2 that uses the Fudaa libraries released under the GPL licence ( As such, the method described in this paper is fully reproducible by any reasonably skilled reader who would be willing to study similar ood home movies. The presented study case is also reproducible since all the necessary parameters are provided in this paper, the raw video material is available on YouTube and the Fudaa-LSPIV zip le containing the reference image sequence, computational parameters and topography data is provided as online additional materials.

Image processing issues

In this section, two dierent kinds of image processing issues are addressed. Some issues are strictly specic to ood home movies: Creation of undistorted images; Image alignment; Impact of image resolution. On the other hand, issues dealing with the selection of GRPs and longitudinal slope correction are not specic to home movies only and may be needed for all LSPIV image sequences.

The investigation of such error sources is important for home movies since the eld is unknown a priori, and eldwork is particularly costly.

Creation of undistorted images

Home movies are captured by uncalibrated sensors whose internal parameters are unknown. Since the LSPIV technique was originally developed for calibrated perspective cameras, its direct applicability to this type of images was questionable. A rst processing step is therefore introduced to remove distortion from the images. In the case under study , the camera that acquired the images has a sheye lens, which induces a large amount of barrel distortion (cf. Fig. 2(a)). Since the LSPIV technique was originally developed for perspective cameras, its direct applicability to this type of images was uncertain. On the one hand, the image projection equations used for orthorectication are not valid anymore, calling for distortion correction. On the other hand, the area of interest in the image is located near the image center, where the distortion eect is minimal. In order to estimate the impact of distortion on LSPIV results, we performed the whole LSPIV process with both the original images and the geometrically corrected images. Moreover, the GRPs should surround the area of interest and not be aligned.

Distortion correction was conducted with

Fig. 3 shows the impact of the number and location of GRPs on the surface velocity eld. In Fig. 3 3 /s for 9 and 7 GRPs, respectively. The process therefore appears to be robust to GRP alignment. However, when the GRP P8 is also removed, even if there are still 6 GRPs remaining, the orthorectication algorithm is not able anymore to process the images correctly.

Image alignment

Home movies are commonly made with a hand-held camera, which means camera movements. In the movie of our study case, two dierent types of typical camera movements are present. The rst movement is a coherent movement in one identied direction followed by the return to the stable position (seq. time 7:27) and the other one is a shake movement with limited amplitude and random directions (reference sequence). Results of the same analysis in the camera shake case are also shown in Fig. 4(cde). The movement amplitude in the area of the reference cross-section is now 4 pixels only. The blur eect in the raw average image is still present but limited. Cumulative averaged values of the longitudinal velocity with and without image alignment are given in Fig. 4(e). Very low discrepancy (< 2%) is observed between the two curves. As soon as the results of ∼20 image pairs are averaged, the dierence is negligible (< 0.4%). Since the camera shake movement is random in direction and has a limited amplitude, the discrepancy in the average velocity rapidly falls to zero.

Correction of longitudinal slope

The LSPIV technique conventionally assumes that the ow free-surface is planar and the image orthorectication is made on this plane. It is also usually considered that the planar free-surface is horizontal since river slopes are generally negligible. Moreover, due to image perspective velocity vectors are more precisely estimated when images are taken from the side of the ow. The present case study faces adverse conditions because the torrent slope is steep (0.063 m/m) and the camera was placed on a bridge and aligned with the main ow direction. The example movie is typical of many situations where the ood home movie is shot longitudinally along a quite steep ow.

In the orthoimage of the dry bed, agstones have uniform sizes when a sloped plane is considered. In turn, when a horizontal plane is considered, agstones sizes vary from 0.9 m long in the foreground to 1.05 m long near the weir. In images with active water ow, orthorectication on a horizontal plane instead of on the sloped free-surface plane results in an overestimation of longitudinal velocities. This is illustrated in Fig. 5 that presents the longitudinal velocity component, V X , as a function of distance X along the torrent axis, as is represented in red in Fig. 2(d). It may be observed that the discrepancy between the curves increases with distance from camera upstream of the reference cross-section. The maximum relative deviation is equal to +22.9% and is reached at X = -5.75 m.

In the vicinity of the reference cross-section the velocity error remains low (+5.3%) because the elevation of the horizontal free-surface plane was estimated at this precise location.

The slope eect depends on the viewpoint of the camera (whether it is side-looking or not) and on the geometry conguration relating the position of the camera, the position of the reference crosssection and the slope of the free-surface. However, in many usual cases the slope eect is negligible because free-surface slopes are lower and videos are often recorded from the river side.

Impact of the image resolution

Flood movies available in the Internet are acquired with a large diversity of sensor resolution and are often compressed to spare bandwith and storage capacity. The impact of the image resolution on velocity estimation is investigated in this section. Image resolution may indeed have an impact on two LSPIV steps: the manual selection of GRPs positions in the image and the automatic correlation-based matching.

As a typical video sharing website, YouTube enables the view of videos with dierent resolution levels. Fig. 6 shows the LSPIV results on the reference sequence with the dierent resolution options oered by YouTube. Results at resolution 720p are very similar to those obtained for the 1080p full resolution. At lowest resolutions 360p (image size 640 × 360 pixels) and 240p (426 × 240 pixels), the dierence in longitudinal velocity, V X , averaged over 50 consecutive images is less than 5% compared to full resolution. LSPIV appears to be very robust to a decrease in image resolution. Contacting the authors of the collected movies is the best option to solve such problems and to get additional information. This must be done as soon as possible after the ood event so that they remember as precisely as possible the time and location of their recording. Also, authors must be contacted in order to get their personal agreement for the use and distribution of their movie materials. Finding the author of a video posted in the Internet, on YouTube for example, can be very sharp as the author is only mentioned by his user name, which is often very non-informative except for professional or semi-professional ood chasers or meteorological enthusiasts who give direct contacts. 20

Water level assessment

Since it is directly related to the orthorectication, velocity estimation and discharge computation, the determination of the water level simultaneously to the recording of the images is a key point of LSPIV. Videos recorded by witnesses usually do not encompass sta gauge and are not associated with direct measurements of the water stage. The water level must be therefore estimated from the recorded images and complementary topography measurements only.

The method used in this study is based on the relative positioning of the ow free-surface with stationary elements that are visible nearby the reference cross-section. One can identify in the images some characteristic objects reached by the water surface. The elevation of such objects can be measured after the ood during the topography campaign that is necessary to the GRP and cross-sectional transect positioning. During oods, the water surface is often deformed by waves created by hydraulic jumps, obstacles, roughness elements or pulsating ows. The high frequency of images acquired with conventional cameras (25 to 60 frames per second) oers a detailed sampling of waves and a good average of the free-surface elevation.

As pointed out by [START_REF] Dramais | Advantages of a mobile LSPIV method for measuring ood discharges and improving stage-discharge curves[END_REF], water level errors impact the orthorectication, hence the estimation of surface velocities, as well as the computation of the wetted cross-sectional area in opposite ways, which may mutually compensate but usually lead to errors in discharge results. The sensitivity of the LSPIV process to the uncertainty on the assumed water level was tested using the reference image sequence. The water level during this sequence was estimated to be 60 cm, with an uncertainty of 15 cm based on the resolution of images and on the ow conditions. For a lower video quality, it is assumed that this uncertainty could reach 30 cm. Tab. 1 shows the results in discharge, mean velocity and wetted area obtained with dierent water level values 15 cm and 30 cm above and below the reference stage.

The results conrm the opposite impacts of a water level error on the velocity and area estimates.

That velocity is slightly underestimated (-2%) when the stage is underestimated by 15 cm is due to modications induced in the PIV analysis, in addition to the orthorectication error. However the area error dominates in the discharge error since discharge is systematically overestimated when the water level is overestimated. Errors in mean velocity are smaller than 3% for a 15 cm stage Water level error bias, while the error magnitude in the wetted cross-sectional area is 27%, which approximately corresponds to the error in the nal discharge value (+24% and -28% respectively). Water level is conrmed to be the dominant source of uncertainty in our study case for which the uncertainty of this parameter reaches 25%. Due to the unsteadiness of the ow, no similar test was performed for higher water levels.

Q Q deviation Mean velocity V V deviation Wetted area A A deviation (cm) (m 3 /s) (%) (m/s) (%) (m 2 ) (%

Comparison with traditional methods for a quasi-steady ow

As introduced in the presentation of the studied ood event, the movie shows a pulsed ow with pseudo-periodic breaking waves overriding the base ow. To assess their agreement with the LSPIV method, traditional methods for the indirect determination of discharge were applied to the quasisteady base ow that established between 5 successive pulses. The whole sequence lasted less than 2 min, so that the discharge was assumed to keep constant over the 5 steady state periods.

The most commonly used method is the slope-area method, which basically consists of applying the Manning-Strickler equation to the channel geometry and to the high-water marks: Another way to estimate discharge is to apply the critical-depth method to the rst trapezoidal weir that is visible in our images. Approximating its shape by an equivalent rectangle, the weir equation is:

Q = 1 n AS 1/2 R 2/3 h (
Q = CB s 2gH 3/2 (2)
where C is a discharge coecient (C ≈ 0.4), B s is the ow width above the weir, g is the gravitational acceleration (g = 9.81 m/s 2 ), and H is the hydraulic head in the approach of the weir cross-section.

Ideally, the hydraulic head should be computed as H = D s +V 2 /(2g), with D s the ow depth above the weir and V the approach velocity. However, since V estimate is usually lacking, H is sometimes abusively approximated by D s in Eq. 2, which leads to:

Q = CB s 2gD 3/2 s (3)
Discharge estimates for the 5 quasi-steady ow sequences are presented in Tab. 2 (columns tagged BASE FLOW). The four methods were applied: LSPIV, slope-area (Eq. 1), and critical-depth method with (Eq. 2) and without (Eq. 3) consideration of the velocity head. All relevant variables were obtained from the geometry data and the movie analysis (cf. Tab. 3). The velocity coecient was set at the 0.85 [0.80-0.90] default value, valid for a uniform ow over an intermediately rough bed. Note that since the water stage above the weir was very dicult to assess from images, it was roughly estimated to be 0.15 m (±0.10 m) for all pulses. Since the hydraulic control is quite sensitive to the stage, such a large uncertainty in stage leads to a wide uncertainty interval, from 0.1 to 1 m 3 /s.

For this base ow, the LSPIV and slope-area (Eq. 1) methods yielded consistent discharge estimates (+7.7%), considering the uncertainty in the LSPIV velocity coecient and in the Manning's n coecient, respectively. The results actually suggest that the base ow was actually not constant and signicantly decreased over the pulse series, from 3.7 m 3 /s to 1.3 m 3 /s (LSPIV values). As could be expected, the velocity head dominates the total hydraulic head and when ignoring it, the critical-depth method (Eq. 3) severely underestimates the discharge. When correctly applied using LSPIV-derived velocities, the critical-depth method (Eq. 2) signicantly overestimates the LSPIV discharge (by 65%). This may be because we used the velocities measured downstream of the weir, which are potentially higher than the actual approach velocity upstream of the weir, where LSPIV application is not practicable. The main issue for applying the critical-depth method remains that velocity measurements are usually not available to compute the hydraulic head accurately.

Pulsed ow and time-averaged discharge estimate

The issue of determining the discharge of pulsed ows was rst introduced by Holmes (1936).

Heggen (1986) pointed out the fact that `Post-event surveys of oods in surged channels is likely to yield overestimates of discharge if high-water marks and displaced bed material are assumed to be representative of peak uniform-ow conditions'. The same author summarized state-of-the-art formulas for describing the height, shape, wavelength and velocity of the periodic surges created in pulsating ows.

A simple method for computing the time-average discharge, Q, of a pulsating ow in a channel of width B is to separately consider the time-average discharge, Q w , of the overriding translatory wave ow, and that, Q 1 , of the base ow. Assuming that the latter base ow is quasi-steady and uniform and that the wave shape can be approximated as a triangle wedge, [START_REF] Thompson | Determination of discharge during pulsating ow[END_REF] (see also WMO, 2010, chapter 8.7) proposed the following equation (cf. Fig. 7(a) for a denition of the variables):

Q = Q 1 + Q w = V 1 D 1 B + h w L w B 2 T p (4)
Using this method, [START_REF] Thompson | Determination of discharge during pulsating ow[END_REF] obtained acceptably accurate results from controlled tests in a concrete-lined, rectangular, ood control channel. However, it should be noted that the solution technique provided by [START_REF] Thompson | Determination of discharge during pulsating ow[END_REF] is simplied since based on a geometrical approximation taken for the wave shape, and originally evaluated against measurements of uncertain quality. According to Brock's experiments (1967,1968,1970) reported by [START_REF] Richard | A new model of roll waves: comparison with Brock's experiments[END_REF], the actual prole of roll waves is composed of three segments: a vertical front followed by a progressive rise to the wave peak, then a slightly concave falling limb (cf. Fig. 7a). [START_REF] Richard | A new model of roll waves: comparison with Brock's experiments[END_REF] recently introduced a model based on a sounder description of the physical processes and While [START_REF] Heggen | Periodic surges and sediment mobilization[END_REF] explained that there is no absolute maximum for breaking waves such as those observed here, the D 2 /D 1 ratio is actually much higher than the upper bound he suggests, i.e. 2. The LSPIV analysis also provided direct estimation of velocities, V 1 and V w , which were not available to [START_REF] Thompson | Determination of discharge during pulsating ow[END_REF] typically. The wave velocities obtained using LSPIV were found to be in reasonable agreement with robust visual checks by tracking visible oating objects (cf. Tab. 3).

The observed velocity ratio, V w /V 1 = 2.41, is again much higher than what suggests the theoretical relation reported by [START_REF] Heggen | Periodic surges and sediment mobilization[END_REF], that yields V w /V 1 = 1.67 for a wide channel, and even lower for a narrow trapezoidal channel such as ours. It subsequently appears that the recorded pulses were more severe than was reported in previous studies.

Tab. 2 summarizes the discharge estimates provided by all tested methods for the base ow (Q 1 ), pulse ow (Q 2 ) and time-average ow (Q) over the series of 5 pulses. The same decreasing trend is observed for Q 2 and Q as for Q 1 , except for the fourth pulse which was the strongest in the series. From LSPIV data, the ensemble-averaged discharges of the base ow, pulse ow and timeaveraged ow were found to be 2.6 m 3 /s, 62.8 m 3 /s and 22.1 m 3 /s, respectively. The discrepancy between such values illustrate the highly transient nature of such a ow that cannot be captured by traditional high-water mark surveys. As was the case for base ow, the slope-area method (Eq. 1)

produced consistent, though slightly overestimated (+17.5%) estimates of the pulse ow discharge compared to the LSPIV reference, while the critical-depth method now underestimates the discharge by -75% when the velocity head is not accounted for (Eq. 3), and by -59% when it is (Eq. 2). This may be explained by the non-ideal ow conditions upstream of the weir, especially the unsteadiness of the wave ow and the very high approach velocity.

As mentioned by [START_REF] Holmes | Traveling waves in steep channels[END_REF] and [START_REF] Heggen | Periodic surges and sediment mobilization[END_REF], when direct observations of a pulsating ow are missing, the pulsed nature of the ow may often be ignored. Then, a typical mistake would be to estimate discharge by applying the slope-area method to the high-water marks with the underlying steady, uniform ow assumption. As expected, the slope-area method (Eq. 1) applied with D 2 as the ow depth would fail in providing a realistic time-averaged discharge, Q, which would be severely 5 Conclusions and perspectives

The selected example of a pulsed ash-ood ow recorded in Saint-Julien torrent illustrates the typical issues and interests of ood home movies taken by witnesses for improving post-ood discharge estimation. In spite of non-ideal conditions related to such movies, the Large Scale Particle Image Velocimetry (LSPIV) technique was successfully applied using user-friendly, free software only, such as Fudaa-LSPIV. Corrections for lens distortion (sheye) and camera movements are not dicult to apply and can reduce the related errors to a few percents. They may not always be necessary, especially when the area of interest is located at the image center and when camera movement is limited and incoherent over the sequence (camera shake). The lowest resolution levels oered by YouTube did not produce dierences in time-averaged longitudinal velocity greater than 5% compared to the results from full resolution image sequences, which suggests that image resolution is usually not a problem if not extremely poor. Orthorectication is more easily possible in urban areas where xed Ground Reference Points (GRP) are visible at both sides of the ow. A limited number of GRPs, typically 10, is required but they must be adequately distributed around the area of interest.

Locating precisely the video viewpoint is often easy whereas precise timing may be not, especially when the author of the video cannot be contacted. The indirect determination of the water level is the main source of uncertainty in the results, usually much more than errors due to the longitudinal slope of the ow free-surface and likely more than errors due to its waviness. The image-based method yielded direct discharge estimates of the base ow between pulses, of the pulse waves, and of the time-averaged ow over a movie sequence. A comparison with traditional indirect determination methods showed that the critical depth method may produce signicantly biased results for such a fast, unsteady ow with very uncertain approach velocity, while the slope-area method seems to be more robust but would overestimate the time-average ow rate if applied to the high-water marks of a pulsed ow.

We think that this application case covers all the major practical issues related to usable ood home movies but one, namely bed changes during the ood. The solutions applied and discussed if they are discontinuous and non simultaneous, are very valuable for reconstructing the dynamics of the ood processes at the relevant spatio-temporal scale. The proposed method therefore appears as a promising way to make ood studies more collaborative and more comprehensive thanks to the participation of volunteers amongst the men in the street, or more accurately amongst the men by the river. Typically, to encourage the production of valuable ood home movies simple recommendations and eld procedures were proposed as part of the FloodScale research project on Mediterranean ash-oods. The document was shared with local stakeholders and inhabitants and is available online and Q are the discharges of the base ow between pulses, of the pulse ow and of the time-average ow, respectively. Eq. 1 refers to the slope-area method, while Eq. 2 and Eq. 3 refer to critical-depth methods with and without considering the velocity head, respectively. Eq. 4 and Eq. 5 are two dierent methods for time-averaging the LSPIV-derived base and pulse ows (cf. text). Bold numbers are the best LSPIV-based discharge estimates. * : In LSPIV discharge computation, velocity coecients were assumed to be 0.85 for base ow and 1 within the pulse ow. * * : For base ow, the water stage above the weir is very dicult to assess from images; It was therefore roughly estimated to be 0.15 m (±0.10 m) for all pulses.

34

Author-produced version of the article published in Hydrological Processes (2016), Volume 30, Issue 1, p 90-105 The original publication is available at http://onlinelibrary.wiley.com DOI: 10.1002/hyp.10532

(a)
Overriding wave [START_REF] Richard | A new model of roll waves: comparison with Brock's experiments[END_REF]. D 1 , V 1 , Q 1 , are the depth, velocity, discharge, respectively, of the base ow.

V w Q w V w Q w V 1 Q 1 V 1 Q 1 L w D 1 D 2 h w
L w , h w , V w , Q w , are the length, height, mean velocity, mean discharge, respectively, of the surge. T p is the time period between pulses, and t b the transit time of pulse waves. The total ow depth at surge fronts, D 2 , is equal to D 1 + h w . The total discharge at surge fronts, Q 2 , is considered over the full ow depth. 7 and text for denition of variables. Velocities V 1 and V * w were measured using LSPIV with 0.85 and 1 as velocity coecients, respectively. V * * w is a visual check by tracking visible oating objects.

  ; Le Coz et al., 2010; Dramais et al., 2011), LSPIV-dedicated video stations (Hauet et al., 2008a; Le Coz et al., 2010), existing video monitoring (CCTV) system (Tsubaki et al., 2011) or even helicopter-borne cameras (Fujita and Hino, 2003; Fujita and Kunita, 2011). Muste et al. (2011) proposed a detailed review of the LSPIV technique. Basically, LSPIV entails three major steps :

Figure 1 :

 1 Figure 1: Views of the post-ood topography operations in the Saint-Julien torrent channel.

  Fig. 2(b).The issue is to determine the number of GRPs required to register the images along with their optimal arrangement in the image. According to the LSPIV theory (see[START_REF] Muste | Large-scale particle image velocimetry for measurements in riverine environments[END_REF], a minimum of 6 GRPs are required since there are 11 unknowns and each GRP brings 2 equations.

  Fig.3shows the impact of the number and location of GRPs on the surface velocity eld. In Fig.3(a)

Figure 2 :

 2 Figure 2: Comparison of original sheye images and the same images corrected for distortion using rectilinear projection. The GRPs used for registration are displayed. Orthorectication is made in the plane of the torrent bottom.

Fig. 4 (Figure 3 :

 43 Fig.4(a) shows the time-averaged image during the rst example of camera movement. For this movement, the estimated displacement in the image is ∼130 pixels in the area of the reference cross-section. The whole time-averaged image is blurred. Image alignment was then performed with Hugin using the "Align image stack" tool. It consisted in 3 steps: (1) Applying a control point detection over the image. The detector is gradient-based and produces a descriptor for each point;(2) Matching the control points in consecutive images according to their descriptor; (3) Aligning the images using these matches considered as stationary references. A time-average of the resulting images is shown in Fig.4(b). The water ow is the only region that remains blurred, which suggests that the image alignment was correctly done. Fig.4(e) shows the velocity component V X in the longitudinal direction estimated at the reference cross-section as a function of the number of image pairs on which results are averaged. With image alignment, averaged velocity rapidly (∼8 image pairs) converges to a stable value. Without image alignment, the convergence requires ∼16 image pairs and the resulting velocity appears to be biased: -8.6%, -7.2% and -4.2% for 16, 30 and 50

  (a) Time averaged image sequence (b) Time averaged aligned image sequence (c) Time averaged image sequence (d) Time averaged aligned image sequence Camera movement with image alignment Camera movement without image alignment Camera shake with image alignment Camera shake without image alignment VX Cumulative average values of streamwise velocity component, VX , calculated at the reference cross-section with and without image alignment for the two types of movement

Figure 4 :

 4 Figure 4: Impact of image alignment for two types of movement: coherent camera movement (a, b), incoherent (shake) camera movement (c, d), resulting LSPIV cumulative average velocity estimation (e).

Figure 5 :

 5 Figure 5: Impact of longitudinal slope correction on the LSPIV longitudinal velocity component, V X , as a function of streamwise distance, X (cf. Fig. 2(d) for a representation of the X axis and the reference cross-section).

Figure 6 :

 6 Figure6: Impact of image resolution on the cumulative average LSPIV longitudinal velocity component, V X , at the reference cross-section (cf. Fig.2(d) for a representation of the X axis and the reference cross-section).

overestimated (73.8 m 3

 3 /s, instead of 22.1 m 3 /s). As also expected, both Eq. 4 and Eq. 5 provide very similar ensemble-averaged estimates of Q (22.2 m 3 /s and 22.1 m 3 /s, respectively). Similar results are obtained when equations are directly applied to the mean parameter values (21.8 m 3 /s and 22.4 m 3 /s, respectively, not shown in Tab. 2).

Figure 7 :

 7 Figure 7: Schematic longitudinal elevation prole (a, modied after Thompson, 1968) and discharge time series (b) of a pulsated ow showing all useful variables for time-averaged discharge estimation. A more realistic prole of the roll waves is plotted in light gray (a, according to Brock's experiments reported by

Table 1 :

 1 Simulated eect of dierent water level errors on the discharge, mean velocity and wetted crosssectional area. The gray box row indicates the reference computation.

	)

  Author-produced version of the article published in Hydrological Processes (2016), Volume 30, Issue 1, p 90-105The original publication is available at http://onlinelibrary.wiley.com DOI: 10.1002/hyp.10532[START_REF] Chow | Open-Channel Hydraulics[END_REF]. In our case, we took the value proposed for Concrete bottom oat nish with sides of riprap, i.e. n = 0.030 [0.020-0.035].

1) with Manning's n the ow resistance coecient, A the wetted cross-sectional area, S the longitudinal slope, R h the hydraulic radius. Manning's n values are often derived from the table provided by 22

  5 . Priority on safety rules is emphasized in the document: recording ood movies can be dangerous. Never risk your life for ood data.

	PULSE FLOW (Q 2 ) TIME-AVERAGE (Q)	LSPIV* Eq. 1 Eq. 3 Eq. 2 Eq. 4 Eq. 5	(m 3 /s) (m 3 /s) (m 3 /s) (m 3 /s) (m 3 /s) (m 3 /s)	71.9 91.2 28.7 42.7 28.4 25.8	65.7 67.2 6.4 19.7 22.4 24.6	53.8 54.4 10.0 19.7 18.6 19.2	79.1 101.7 24.7 36.0 28.6 27.2	43.6 54.4 9.8 12.9 13.2 14.0	62.8 73.8 15.9 26.2 22.2 22.1	12.7 19.4 9.0 11.2 5.9 4.9	20% 26% 56% 43% 26% 22%
	BASE FLOW (Q 1 )	LSPIV* Eq. 1 Eq. 3** Eq. 2**	(m 3 /s) (m 3 /s) (m 3 /s) (m 3 /s)	3.7 4.2 0.5 4.2	3.4 2.9 0.5 7.4	2.5 2.2 0.5 4.5	2.5 2.9 0.5 3.6	1.3 1.8 0.5 1.6	2.6 2.8 0.5 4.3	0.8 0.8 0.0 1.9	32% 29% 0% 44%
		time	(min:sec)	07:10	07:31	07:51	08:12	08:38
		Pulse	order	P1	P2	P3	P4	P5	mean	std	std/mean

Table 2 :

 2 Discharges estimated over 5 successive pulses recorded in the Saint-Julien torrent ood movie. Q

	, Q 2
	1

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  Author-produced version of the article published in Hydrological Processes (2016), Volume 30, Issue 1, p 90-105The original publication is available at http://onlinelibrary.wiley.com DOI: 10.1002/hyp.10532

	Pulse	time	D 1	D 2	D 2 /D 1	Tp	t b	B	Ds	V 1	V * w	V * * w
	order (min:sec) (m) (m) (-) (s) (s) (m) (m) (m/s) (m/s) (m/s)
	P1	07:10 0.25 1.55 6.2	21 14 8.0 1.6 3.1	7.1	7.8
	P2	07:31 0.20 1.30 6.5	20 14 6.2 0.7 3.9	8.0	6.6
	P3	07:51 0.17 1.15 6.8	21 14 6.6 0.9 3.2	7.5	7.8
	P4	08:12 0.20 1.65 8.3	26 17 7.6 1.5 2.9	7.2	7.2
	P5	08:38 0.15 1.15 7.7	28 17 6.5 0.9 1.9	6.1	9.1
	mean		0.19 1.36 7.1	23 15 7.0 1.1 3.0	7.2	7.7
	std		0.03 0.21 0.8	3	1 0.7 0.4 0.7	0.6	0.8
	std/mean		17% 15% 11% 14% 10% 10% 32% 22% 9% 11%

Table 3 :

 3 Flow characteristics observed over 5 successive pulses recorded in the Saint-Julien torrent ood movie. See Fig.

https://forge.irstea.fr/projects/fudaa-lspiv/les

https://www.libav.org

http://hugin.sourceforge.net

Acknowledgements

This work was supported by the French national hydrological services (SCHAPI). The FloodScale project is funded by the French National Research Agency (ANR) under Contract No ANR 2011 BS56 027, which contributes to the HyMeX program. We are grateful to Alexandre Modesto who, as a ood chaser, provided us with the movie material of this study, to Mickaël Lagouy (Irstea) who conducted the complementary eld measurements, and to Magali Jodeau (EDF) who leads the co-development of the Fudaa-LSPIV free software by EDF and Irstea. We appreciated the valuable comments from Prof. Marco Borga (University of Padova, Italy) and two other anonymous reviewers.

Author-produced version of the article published in Hydrological Processes (2016), Volume 30, Issue 1, p 90-105

The original publication is available at http://onlinelibrary.wiley.com DOI: 10.1002/hyp.10532

accurately reproduced the actual shape of roll waves reported from Brock's experiments. However, rening the shape of waves using such complex models would not signicantly improve discharge estimates from ood home movies, due to the uncertainty in estimated water levels as reported in Section 4.2. Typically, a more signicant improvement in the estimation of mean discharge can be expected from the accurate evaluation of pseudo-periods between pulses. Therefore, a simple method derived from Thompson's works seems to be ecient for ood discharge estimation purpose, even if in most favourable conditions it might be valuably rened according to most recent advances on the roll wave dynamics.

Considering that the LSPIV application directly provides us with discharge estimates during base ow, Q 1 , and during the pulse front, Q 2 , a similar time-averaging equation can be established as follows (cf. Fig. 7(b)):

Setting the velocity coecient in the pulse wave is problematic because the velocity distribution inside such a transient ow is highly uncertain. As a simple approximation, we chose to keep the velocity coecient equal to 0.85 in the overrun ow and to 1 in the overriding ow layer, assuming that the velocity is roughly homogeneous within the breaking wave. That means that V w is taken equal to the surface velocity yielded by the LSPIV and that the maximum surge discharge

The analysis of the St-Julien ood movie allows for applying both time-averaging equations for a series of successive pulses. The same sequence of 5 successive surges was investigated in order to estimate the geometrical properties and the velocities of the overriding waves and base ow (cf.

Tab. 3). The time period between the arrivals of consecutive wave fronts, T p , was easily derived from the video sequence and was found to be quite stable and close to 23 s on average. The two last pulses show slighty longer periods and lower velocities. Similarly, the time interval, t b , between the front and the tail of the surges was recorded and found to be 15 s on average. The length of the surge wedges was then computed as L w = V w t b .

The ow depths, D 1 and D 2 , were estimated using the method already presented in Section 4.2, with the same level of uncertainty. The surge ratio, D 2 /D 1 was found to be as high as 7 on average. in the paper are fully reproducible and are not site-specic. However, we highlight which situations may be detrimental to their successful application, such as the absence or lack of GRPs in fully natural environments. The ranking of error sources and limitations is deemed to be valid for most situations, based on our experience on several other cases.

This work also calls for further developments of the technique to extend it to more dicult ood home movies available in video sharing platforms and other sources. Implementing other image velocimetry techniques such as STIV or optical ow is an interesting perspective to enhance the robustness and versatility of the method. Stereo-photogrammetry could be a promising solution to the important issue of GRP availability: Though common people only use one camera, trained observers could use a calibrated system with two cameras. In the same vein, the issue of bed changes could be tackled with non-intrusive bathymetry measurements, or some inference of bathymetry changes from the comparison with numerical hydraulic simulations. Such ambitious developments should be eventually tested and validated in experiments under controlled conditions.

The analysis of ood movies oers a direct insight in ow processes and potentially answers to important issues for post-ood analyses. First, it provides direct measurements of the surface ow velocities, which are usually unknown. It is interesting to note that several ood movies, such as the one used to support this study, provided velocity estimates that signicantly exceed the velocity magnitudes commonly accepted as realistic in such extreme events. Typically, maximum velocities greater than 10 m/s and 7 m/s were observed in torrents and rivers, respectively, where 7 m/s and 4 m/s at most, respectively, would have been expected.

Second, the movies oer the direct observation of the ow conditions, which helps in assessing the applicability and uncertainty of the applied hydraulic formulas and models. The knowledge of the approach velocity upstream of a critical section and of the head losses homogeneity along the control channel are key for the application of the critical-depth method and of the slope-area method, respectively. The movies may also provide pictures of obstacles, log jams, pulsating ows, hydraulic jumps, and other complex hydraulic processes, especially in urban areas, that have a strong inuence on the high-water marks.

Last, the abundance of movies recorded by dierent people provides information at dierent locations of the river catchment and at dierent moments of the ood event. Such synoptic results, even