Sree Bash

Chandra Debnath

Carole Fauquet

Agnes Tallet

Anthony Goncalves

S Ebastien Lavandier

Franck Jandard

Didier Tonneau

Julien Darreon

High spatial resolution inorganic scintillator detector for high-energy X-ray beam at small field irradiation

Keywords: inorganic scintillator detector, micro-scintillators, real-time radiation dose, small field irradiation, X-ray detector

Purpose: Small field dosimetry for radiotherapy is one of the major challenges due to the size of most dosimeters, for example, sufficient spatial resolution, accurate dose distribution and energy dependency of the detector. In this context, the purpose of this research is to develop a small size scintillating detector targeting small field dosimetry and compare its performance with other commercial detectors. Method: An inorganic scintillator detector (ISD) of about 200 µm outer diameter was developed and tested through different small field dosimetric characterizations under high-energy photons (6 and 15 MV) delivered by an Elekta Linear Accelerator (LINAC). Percentage depth dose (PDD) and beam profile measurements were compared using dosimeters from PTW namely, microdiamond and PinPoint three-dimensional (PP3D) detector. A background fiber method has been considered to quantitate and eliminate the minimal Cerenkov effect from the total optical signal magnitude. Measurements were performed inside a water phantom under IAEA Technical Reports Series recommendations (IAEA TRS 381 and TRS 483). Results: Small fields ranging from 3 9 3 cm 2 , down to 0.5 9 0.5 cm 2 were sequentially measured using the ISD and commercial dosimeters, and a good agreement was obtained among all measurements. The result also shows that, scintillating detector has good repeatability and reproducibility of the output signal with maximum deviation of 0.26% and 0.5% respectively. The Full Width Half Maximum (FWHM) was measured 0.55 cm for the smallest available square size field of 0.5 9 0.5 cm 2 , where the discrepancy of 0.05 cm is due to the scattering effects inside the water and convolution effect between field and detector geometries. Percentage depth dose factor dependence variation with water depth exhibits nearly the same behavior for all tested detectors. The ISD allows to perform dose measurements at a very high accuracy from low (50 cGy/min) to high dose rates (800 cGy/min) and was found to be independent of dose rate variation. The detection system also showed an excellent linearity with dose; hence, calibration was easily achieved. Conclusions: The developed detector can be used to accurately measure the delivered dose at small fields during the treatment of small volume tumors. The author's measurement shows that despite using a nonwater-equivalent detector, the detector can be a powerful candidate for beam characterization and quality assurance in, for example, radiosurgery, Intensity-Modulated Radiotherapy (IMRT), and brachytherapy. Our detector can provide real-time dose measurement and good spatial resolution with immediate readout, simplicity, flexibility, and robustness.

INTRODUCTION

Radiation dosimetry plays a very important role in radiotherapy to accurately measure the exact radiation dose delivered to the patients to ensure a high treatment quality assurance. [START_REF] Vordermark | Ten years of progress in radiation oncology[END_REF] To enhance treatment efficiency, several radiotherapy techniques have been developed for cancer treatment modalities such as intensity-modulated radiotherapy (IMRT), volumetric modulated arc therapy (VMAT), stereotactic body radiation therapy (SBRT), and stereotactic radiosurgery (SRS) etc. These techniques require small irradiation field sizes and high dose spatial gradients to ensure the delivery of accurate high doses with tighter margins around the targeted tumors, enabling possible sparing of organs at risk. [START_REF] Arnfield | Dosimetric validation for multileaf collimator-based intensity-modulated radiotherapy: a review[END_REF][START_REF] Duggan | Small photon field dosimetry for stereotactic radiosurgery[END_REF][START_REF] Galvin | Implementing IMRT in clinical practice: a joint document of the American Society for Therapeutic Radiology and Oncology and the American Association of Physicists in Medicine[END_REF] Unfortunately, accurate measurements are usually hampered due to the size of the conventional dosimeters [START_REF] Stasi | The behavior of several microionization chambers in small intensity modulated radiotherapy fields[END_REF][START_REF] Lauba | The volume effect of detectors in the dosimetry of small fields used in IMRT[END_REF][START_REF] Wrya | Different dosimeters/ detectors used in small-field dosimetry: pros and cons[END_REF] for proper dose distribution in the treatment planning system and patient quality control.

Due to the lack of charged particle equilibrium, chamber size, dose perturbation, corrections of volume averaging effects, and nonequivalence material regarding soft tissue, the measurement with these conventional detectors is complex and hence requires many correction factors especially in the small field dosimetry. [START_REF] Wrya | Different dosimeters/ detectors used in small-field dosimetry: pros and cons[END_REF][START_REF] Palmans | Dosimetry of Small Static Fields used in External Beam Radiotherapy: An IAEA[END_REF] Hence, several international organizations such as AAPM and IAEA suggested various dosimetry sensors when working under small fields. Some recent researches indicate that the suitable detectors for small field dosimetry are plastic scintillation-based exradin W1, W2, and radiochromic films, owing to their good correction factor. [START_REF] Huet | Characterization and optimization of EBT2 radiochromic films dosimetry system for precise measurements of output factors in small fields used in radiotherapy[END_REF][START_REF] Therriault-Proulx | Quality assurance for gamma knife perfexion using the exradin W1 plastic scintillation detector and Lucy phantom[END_REF][START_REF] Galavis | Characterization of the plastic scintillation detector Exradin W2 for small field dosimetry[END_REF][START_REF] Hoehr | Characterization of the exradin W1 plastic scintillation detector for small field applications in proton therapy[END_REF][START_REF] Gonzalez-Lopez | Small fields measurements with radiochromic films[END_REF][START_REF] Carrasco | Characterization of the Exradin W1 scintillator for use in radiotherapy[END_REF] However, the spatial resolution of these detectors is not yet up to the mark due to the minimum size of the sensor head requirement and radiochromic films suffer from time consuming techniques while being used. Furthermore, the major drawback of using plastic scintillator-based detectors is their high sensitivity to Cerenkov radiation (known as "stem" effect) observed when charge particles generated within the fiber at high energy are slowed down in the fiber core, producing a strong Cerenkov luminescence. [START_REF] Beddar | Water-equivalent plastic scintillation detectors for high-energy beam dosimetry: I. Physical characteristics and theoretical considerations[END_REF][START_REF] Beddart | Water-equivalent plastic scintillation detectors for high-energy beam dosimetry[END_REF][START_REF] Gagnon | Dosimetric performance and array assessment of plastic scintillation detectors for stereotactic radiosurgery quality assurance[END_REF][START_REF] Andersen | Fiber-coupled Luminescence Dosimetry in Therapeutic and Diagnostic Radiology[END_REF] Hence, we developed an inorganic scintillator detector (ISD) based on a scintillating inorganic cluster optically coupled with a silica optical fiber, very promising on realtime dosimetry. [START_REF] Andersen | Fiber-coupled Luminescence Dosimetry in Therapeutic and Diagnostic Radiology[END_REF][START_REF] Kertzscher | Inorganic scintillator detectors for real-time verification during brachytherapy[END_REF] Under irradiation, the cluster emits visible light that is driven through the optical fiber toward a photon counter. The detector has been tested for different dosimetric parameters under high-energy beams of 5-15 MV and experimental conditions close to the real patient treatment scenario. In this context, the aim of this research work is to demonstrate the performances of this ISD detector by quantitative comparison with microdiamond dosimeter (a suitable detector for small fields [START_REF] Palmans | Dosimetry of Small Static Fields used in External Beam Radiotherapy: An IAEA[END_REF][START_REF] Coste | Is the PTW 60019 microDiamond a suitable candidate for small field reference dosimetry?[END_REF] ). PinPoint three-dimensional (PP3D), another commercial dosimeter used for regular beam in the patient treatment planning, was also considered to show the behavior of ISD with respect to it. Lateral profiles of small and very small size fields (ranging from 3 9 3 cm 2 down to 0.5 9 0.5 cm 2 ) as well as percentage depth dose (PDD) were systematically performed with all the detectors.

MATERIALS AND METHODS

2.A. Source

Experiments were performed under a LINAC (Elekta Synergy, VERSA) source with the photon beam energy of 6 and 15 MV at the Institute Paoli-Calmettes (IPC), Marseille, France. The MLC window of the LINAC can be opened down to a length of few millimeters . Elekta LINAC Synergy system can deliver a typical dose rate at 400 MU/min and VERSA can work in two modes of operation (with flattening filter and without flattening filter) in a very high dose rate of 2400 MU/min. The radiotherapy equipment is periodically calibrated so that 1_MU corresponds to 1_cGy under reference condition (IAEA TRS 381). The source can irradiate fields at 40 9 40 cm 2 , down to 0.5 9 0.5 cm 2 at the isocenter (100 cm from the source). The Elekta system can be rotated up to 360 0 during irradiation process.

2.B. Devices

The novel X-ray probe consists of a 10 -m-long silica (SiO 2 ) optical fiber with scintillator clusters grafted at one terminal. Under irradiation, the scintillating clusters fixed at the fiber extremity produce visible light proportional to the irradiation coming from the LINAC source. The visible photons are transmitted through the fiber core toward a photon counter (Aurea TM ). The core and cladding diameter of the fiber is respectively, 100 and 125 lm (Thorlabs TM ), and the fiber bandwidth is 400-2100 nm. The scintillating material, ZnS:Ag, is a powder of 2-3 µm grain size typically, mixed with PMMA resist diluted in Ethyl lactate (C 5 H 10 O 3 ) solvent. PMMA is a biocompatible resist commonly used in microelectronics industry. After removing the plastic protective coating from glass optical fiber, the extremity is dipped into this PMMA mixture and immediately removed for a drying step at 65°C. Consequently a nearly spherical PMMA droplet containing ZnS:Ag clusters is formed. Finally, the device is dipped in a liquid silver paste and dried at room temperature. This latter metallization step guided the device to be free from any ambient light noise. The head of this detector in comparison to other conventional dosimeters is shown in Fig. 1(b). The sensitive volume is assumed to be a cylinder of diameter 100 µm (fiber core diameter) and 1.5 µm in length. Indeed, light emitted by scintillating grains at distances higher than 1.5 µm from the fiber core is re-absorbed before reaching the core. Thus, we estimate that the sensitive volume of ISD is about 1.2 9 10 À5 mm 3 . This sensitive volume is much lower than that of PP3D (0.016 cm 3 with an outer diameter of 7 mm) and microdiamond (0.004 mm 3 with an outer diameter of 4.8 mm).

2.C. Experimental set-up

Figure 1 represents the detailed experimental setup used with the LINAC Elekta source and the water phantom. This system is based on a largesize water tank (IBA TM ) equipped with X, Y, and Z stages that allows dose distribution measurements in arbitrary planes, according to international standards such as AAPM TG 142. Results presented in this paper were obtained by keeping the beam perpendicular to the water surface and moving the sensor in planes parallel to this surface. The scintillating active part of the fiber-based detector is fixed to the scanning unit inside the water tank, whereas the other extremity of the fiber is plugged to a photon Medical Physics, 0 (0), xxxx counter. The whole setup is remotely controlled from an external room avoiding any exposure of the electronics to high-energy irradiation.

2.D. Measurement protocol

To demonstrate the sensor performance, all the measurements were carried out simultaneously with a microdiamond dosimeter commonly used for small field dosimetry and a PP3D detector. Unless otherwise stated, each measurement in this research has been measured inside water phantoms in reference conditions, that is, SSD (source to water surface distance) of 90 and 10 cm depth in water during beam profiling and 100 cm SSD during PDD measurements. The sensitive photon counter measures the optical signal of the scintillation light in photons per second. Time integration of optical signal gives the total number of photons linked to the irradiation dose. A Matlab TM simulator was developed to calculate the total amount of photons during each irradiation. In order to compare the performance of the scintillator detector with other dosimeters, beam profiles and PDD curves have been normalized.

2.E. Cerenkov light subtraction

The spectral distribution of Cerenkov light is most intense in the blue and ultraviolet regions of the electromagnetic spectrum. This effect has a huge contribution on signal amplitude when using plastic scintillators and optical fibers. [START_REF] Beddar | Water-equivalent plastic scintillation detectors for high-energy beam dosimetry: I. Physical characteristics and theoretical considerations[END_REF][START_REF] Beaulieu | Review of plastic and liquid scintillation dosimetry for photon, electron, and proton therapy[END_REF][START_REF] Ram Irez | Performance of ZnSe(Te) as fiberoptic dosimetry detector[END_REF][START_REF] Linares | Optimization of a multipoint plastic scintillator dosimeter for high dose rate brachytherapy[END_REF] Thus, the Cerenkov effect in this case must be considered and removed from the total acquisition signal. In our case, the inorganic scintillator is grafted to a narrow silica fiber core, so that the Cerenkov effect is expected to be weak. Moreover, in order to minimize this effect, the size of the inorganic scintillating head has been reduced as much as possible. [START_REF] Beaulieu | Review of plastic and liquid scintillation dosimetry for photon, electron, and proton therapy[END_REF][START_REF] Ram Irez | Performance of ZnSe(Te) as fiberoptic dosimetry detector[END_REF] However, even if the contribution of the Cerenkov Effect is weak, it was systematically quantitated and removed from the measurements presented in this article. A background fiber method [START_REF] Beddar | Water-equivalent plastic scintillation detectors for high-energy beam dosimetry: I. Physical characteristics and theoretical considerations[END_REF][START_REF] Pouliot | Miniature scintillating detector for small field radiation therapy[END_REF][START_REF] Liu | Plastic scintillation dosimetry: comparison of three solutions for the Cerenkov challenge[END_REF] has been used to accurately measure the real scintillating light. Indeed, the detector and a bare fiber were simultaneously exposed to radiation at the same x-position [Fig. 1(a)]. It relies on the assumption that the Cerenkov signal generated in the background fiber is of equal magnitude as the signal fiber. Finally, the actual signal of the detector is obtained by subtracting the signal of the bared fiber from the signal provided by the detector directly read from the photon counter. This Cerenkov correction was considered for all the recorded data given in this study.

RESULTS

3.A. Relative dose measurement

Figure 2(a) shows the optical signal magnitude variation with time and respective field sizes (ranging from 3 9 3 cm 2 down to 0.5 9 0.5 cm 2 ) at 6 MV. These measurements were performed with the sensor placed at the field center in reference conditions. For each field, the acquisition signal was recorded during the delivery of 100 MU dose. Each curve exhibits the same behavior with a rise time of 5 s followed by a plateau. Finally, a fall time in the microsecond range is observed when the beam is switched off automatically. The photon counter used in this study has a rise and fall time in the ns range (constructor data), so the long raise time demonstrates the LINAC source characteristic. Figure 2(a) also shows the Cerenkov effect magnitude (blue lines) under the same irradiation conditions. As mentioned in Section 2.E, this effect has a very low contribution to the signal recorded by our detector and can be easily eliminated from the total signal. Finally, the total number of photons (counts) corresponding to the actual scintillation during irradiation is calculated by integrating the optical signal (free from Cerenkov) with respect to time. This optical signal intensity reported in Fig. 2

3.B. Dose repeatability and reproducibility

Measurement repeatability was checked under standard conditions of 15 MV for 100 MU [Fig. 3(a)] and 20 MU [Fig. 3(b)] doses, delivered at a dose rate of 400 MU/min. For this test, ten consecutive irradiations were performed on the sensor placed at the center of 1 9 1 cm 2 and 0.5 9 0.5 cm 2 fields.

These results show that the ISD demonstrates a very good repeatability with a maximum standard deviation of 0.26% and 1.2% from the average doses of 100 and 20 cGy, respectively. The detector was also tested for seven consecutive days and <0.5% day-to-day variation of the collected signal was observed. This result demonstrates a very good reproducibility and highlights that ISD does not require regular calibration.

3.C. Dose and dose rate linearity

Detector's linearity was tested from very low dose (5 cGy) to high dose (500 cGy) at the center of smallest field and observed accurate linear behavior with a linear regression factor of 0.9997, as can be seen in Fig. 4. Figure 5(a) shows the variation in the optical signal measured with ISD as a function of time for different dose rates ranging from 50 to 800 cGy/min. The total dose was kept constant at 100 cGy for each experimental measurement point. As evident, the higher the dose rate, the shorter is the irradiation period. As expected, the detector provides an optical signal that is almost independent of dose rate. Indeed, the maximum standard deviation of the signal from the average value is as low as 0.15%, which is a very significant outcome when compared to that obtained with other detectors [see, e.g., [START_REF] Carrasco | Characterization of the Exradin W1 scintillator for use in radiotherapy[END_REF][START_REF] Beddar | Water-equivalent plastic scintillation detectors for high-energy beam dosimetry: I. Physical characteristics and theoretical considerations[END_REF][START_REF] Alharbi | Dosimetric characterization of an inorganic optical fiber sensor for external beam radiation therapy[END_REF] ]. This result shows that ISD can be successfully used at a low as well as a high dose rate, as it is important for a broad range of radiotherapies.

3.D. Beam profiling and comparison

Beam profiles were measured for fields ranging from 3 9 3 cm 2 ' down to 0.5 9 0.5 cm 2 with ISD, PP3D, and microdiamond dosimeters in reference conditions inside water phantoms. We have reported in [Figs. 2)% variation with respect to the reference detectors, which is in a very good agreement. The profiles shown in Fig. 6 exhibit a nearly sharp falloff at the field edges, as expected for all detectors. Indeed, because of scattered radiation and convolution effect between field and detector geometries, [START_REF] Yoo | Integral T-shaped phantom-dosimeter system to measure transverse and longitudinal dose distributions simultaneously for stereotactic radiosurgery dosimetry[END_REF][START_REF] Lee | Measurement of two-dimensional photon beam distributions using a fiber-optic radiation sensor for small field radiation therapy[END_REF][START_REF] Petric | Development and characterization of a tissue equivalent plastic scintillator based dosimetry system[END_REF] a perfect falloff cannot be achieved. Both effects are usually gathered in the penumbra region. Convolution effect contribution is roughly proportional to the detector sensitive head size. In our case, thanks to the small size of ISD, the penumbra profile (between 20-80%) is sharper in comparison to the other dosimeters considered in this research.

Using ISD, the measured full width half maximum (FWHM) is 3, 2, 1, and 0.55 cm, which is in very good agreement with the selected beam size. Little discrepancies between ISD and the microdiamond detector at field edges are observed at a level around 4.45%-13.3%.

3.E. PDD measurements and comparison

The central axis dose distribution is one of the most important clinical parameters and it is typically characterized by PDD factor measurements. The PDD curves obtained with ISD are presented in Fig. 7 for different small fields varying 3 9 3 cm 2 down to 0.5 9 0.5 cm 2 and comparison were shown with microdiamond detector. Due to the increasing number of scattered photons and secondary electrons created by the incident high energy beam penetration, the PDD steeply increases till maximum depth dose in the buildup region. After the maximum value, the PDD smoothly decreases with the depth due to the absorption of generated photons and/or charged particles by water. With ISD, the maximum PDD value is found at 15 mm from the water surface, a standard and expected value for the 6-MV incident photon beam. [START_REF] Beddar | Water-equivalent plastic scintillation detectors for high-energy beam dosimetry: I. Physical characteristics and theoretical considerations[END_REF][START_REF] Yoo | Integral T-shaped phantom-dosimeter system to measure transverse and longitudinal dose distributions simultaneously for stereotactic radiosurgery dosimetry[END_REF][START_REF] Lee | Measurement of two-dimensional photon beam distributions using a fiber-optic radiation sensor for small field radiation therapy[END_REF][START_REF] Fontbonne | Scintillating fiber dosimeter for radiation therapy accelerator[END_REF] This maximum dose depth is independent of the field size considered here. A very good agreement is found between the measurements given by the three detectors for 3 9 3 cm 2 and 2 9 2 cm 2 fields. However, far from the maximum dose depth, differences between detectors become visible and are more pronounced at small fields.

The PDD difference between ISD and microdiamond detector varies from 0.1 to 13.3%, whereas the average percentage difference stays in a reasonable range, from 2.1 to 5.6% for all the measurements. Note that, the PDD difference around the maximum of the buildup region stays below 1% for all the small fields.

DISCUSSION

The developed ISD sensor detects a maximum dose delivery at a depth of approximately 15 mm inside water, a value in perfect agreement known to radiotherapy dosimetry. This value for maximum dose is independent of the field size from 3 9 3 cm 2 down to 0.5 9 0.5 cm 2 . The PDD exhibits almost the same behavior for all detectors unless a little discrepancy is observed for ISD, especially in water depths larger than 15 mm. This effect can be strongly reduced by necessary corrections of the reference detector. [START_REF] Das | TU-F-BRE-05: experimental determination of K factor in small field dosimetry[END_REF][START_REF] Das | Comments on the TRS-483 protocol on small field dosimetry[END_REF][START_REF] Underwood | Application of the Exradin W1 scintillator to determine Ediode 60017 and microDiamond 60019 correction factors for relative dosimetry within small MV and FFF fields[END_REF] FIG. 4. Inorganic scintillator detector signal linearity with dose. Moreover, some discrepancies that appear in small fields and nearby water surfaces can be due to the proper centering of the reference dosimeter. However, discrepancies observed at a higher depth can be attributed to the different sensitivities of each detector to incident and secondary photons as well as other charged particles.

The ISD detector has a very small scintillating active part (1.2 9 10 À5 mm 3 ) and thus allows to measure more accurately dose distribution at the edge of the beam profile. Indeed, the minimum step size of 200 µm available in the scanning unit (IBA TM ) was selected to characterize all the beam profiles.

For the 0.5 9 0.5 cm 2 field, we measured an experimental FWHM of 0.55 cm. The small discrepancy between expected and measured field sizes can be explained by three different effects. First, the measured field is wider due to scattered photons on the edge of the thick lead collimator of the LINAC. Secondly, the field also expanded due to charged particle generation inside water in the detector surface vicinity. Finally, the convolution effect between the actual field geometry (square of 5 mm side) and the detector geometry must be considered. This latter effect leads to an apparent side increase in 100 µm, that corresponds to the ISD sensor diameter.

The minimum step available on PTW translation stage is 200 µm. In these conditions, the signal difference between two consecutive measurements in the penumbra region is about 4000 photons/s, which is much higher than the photon counter sensitivity (20 photons/s). Thus, the step size could be decreased down to 100 µm and even less using a lower diameter core fiber keeping a significant signal to noise ratio. Note that, we already presented a few µm lateral resolution ISD, designed for low-energy (2-30 keV) X-ray beam profiling. [START_REF] Xie | Ultracompact x-ray dosimeter based on scintillators coupled to a nano-optical antenna[END_REF] In this study, we found a detection flux threshold as low as 10 3 X-ray photons/s/lm 2 . Thus, the design of an ISD detector for a high-energy beam offering a spatial resolution much better than 100 µm is realistic.

In contrast to the plastic scintillating detector (PSD), Cerenkov contribution in the developed detector was found to be negligible regarding the magnitude of the optical signal measured in the experimental conditions. Moreover, the ambient optical noise coming from the experimental room was avoided by coating the sensor head with a very thin metallic layer embedding the scintillators. Thus, the scintillating detector in this regard exhibits a higher signal to noise ratio.

Device stability and reproducibility tested at various dose rates ranging from 50 to 800 cGy/min will allow to use it at low dose application for small size tumor and high dose delivery in brachytherapy and radiosurgery. ISD is based on optical transitions that are less sensitive to ambient temperature and pressure variations than electrical charge-based detectors. Therefore, it is anticipated that the ISD detector is free from any perturbations due to temperature and pressure variations. This result is still under investigation by relevant experimentation.

Finally, the ISD provides 4.75*10 5 visible photons collected with the photon counter for a total dose of 100 cGy, independently of the dose rate (Fig. 5). The calibration is thus about 4700 visible photons generated per cGy of dose delivered. As the detector's signal magnitude is proportional to the dose, this system can easily be used on patients for radiotherapy dose measurement for small field irradiation with better accuracy.

CONCLUSIONS

Due to the tiny scintillating sensitive volume used at the optical fiber extremity (about 1.2 9 10 À5 mm 3 ), the developed detector in this article exhibits a very high lateral resolution in dosimetry measurements. Indeed, it allows to accurately define the lateral profiles of very small fields down to 0.5 9 0.5 cm 2 with a precision of around 200 µm. Owing to the detector's minimum size (nearly an ideal point detector), ISD is almost free from detector edge effects and no aberrant measurements were observed, while it was the case for the concurrent microdiamond and PP3D detectors. The high spatial resolution of the ISD was examined during the sharp falloff in the penumbra region of the smallest beam profiling in comparison with the commercial detector.

The real-time inorganic detector in this study is fast, robust, and nonsensitive to external noise and stem effect. As expected, the integrated total relative dose measurement in this study was found to be independent of the dose rate variability. Moreover, a perfect linearity with dose was observed for the smallest field considered in this study and lead to detector calibration of 4.7 10 5 photons collected/Gy. Further analysis on detector characterization and resolution improvement is ongoing, whereas the results presented in this research demonstrate the prospects of ZnS:Ag-based scintillator detector. The performance of ISD shown in this study demonstrates that the detector can be a suitable candidate for small field dosimetry, a proper quality control tool for possible early stage tumor treatment. However, further investigation of the detector must follow the comparison with water equivalent scintillating dosimeter, for example, PSD, radiochromic films etc., during absolute dose measurements. a)

  Figure2(a) shows the optical signal magnitude variation with time and respective field sizes (ranging from 3 9 3 cm 2 down to 0.5 9 0.5 cm 2 ) at 6 MV. These measurements were performed with the sensor placed at the field center in reference conditions. For each field, the acquisition signal was recorded during the delivery of 100 MU dose. Each curve exhibits the same behavior with a rise time of 5 s followed by a plateau. Finally, a fall time in the microsecond range is observed when the beam is switched off automatically. The photon counter used in this study has a rise and fall time in the ns range (constructor data), so the long raise time demonstrates the LINAC source characteristic. Figure2(a) also shows the Cerenkov effect magnitude (blue lines) under the same irradiation conditions. As mentioned in Section 2.E, this effect has a very low contribution to the signal recorded by our detector and can be easily eliminated from the total signal. Finally, the total number of photons (counts) corresponding to the actual scintillation during irradiation is calculated by integrating the optical signal (free from Cerenkov) with respect to time. This optical signal intensity reported in Fig.2(b) increases with the field size, as the diffusion inside the multileaf collimator is increasing. Due to the very low noise level (300 photons/s) and low signal fluctuations (<0.2%) during irradiation signal measured (about

  Figure 5(b) represents the variation in the total number of photons measured during each irradiation as a function of dose rate.

  FIG. 2. (a) Inorganic scintillator detector output signal with time for different fields of 100 MU doses delivered at 400 MU/min. (b) Integrated output signal as a function of field size.

FIG. 5 .

 5 FIG. 5. (a) Variation in signal as a function of time for 100 cGy delivered with dose rates ranging from 50 to 800 cGy/min. (b) Integrated number of visible photons generated by the inorganic scintillator detector corresponding to Fig. 5(a).

Debnath et al.: Inorganic scintillator detector

ACKNOWLEDGMENTS

This project has received funding from the European Union's Horizon 2020 Research and Innovation Program under the Marie Skłodowska-Curie grant agreement no. 713750. Also, it has been carried out with the financial support of the Regional Council of Provence-Alpes-Côte d'Azur and with the financial support of the A*MIDEX (n°ANR-11-IDEX-0001-02), funded by the Investissements d'Avenir project funded by the Aix Marseille University, managed by the French National Research Agency (ANR)

CONFLICT OF INTEREST

The authors have no conflict of interest to disclose.

Medical Physics, 0 (0), xxxx Author to whom correspondence should be addressed. Electronic mails: sree.debnath@univ-amu.fr, sreebashcuet@gmail.com.


domain: spi phys math info

text:
Marcela Carvalho

Bertrand Le Saux

Pauline Trouvé-Peloux

Frédéric Champagnat

Andrés Almansa

Multi-Task Learning of Height and Semantics from Aerial Images

Keywords: Multi-task learning, Aerial imagery, Semantic Segmentation, Single view depth estimation, Neural networks, Deep learning

come

I. INTRODUCTION

Aerial imagery has never been so common, even at Very High Resolution (VHR), now that everyone can access images from around the world in any computer. Its automatic analysis is also in progress and has been boosted in the last decade by the tremendous progresses of neural network models. It includes spectral analysis, change detection, and two applications which are of particular interest in this study: semantic mapping of the land surface and local height estimation.

Adding semantics to images by creating high-quality landcover maps is crucial for environment analysis or urban modelling. A standard way to formulate this problem is classification of each pixel, now reframed as semantic segmentation [START_REF] Paisitkriangkrai | Effective semantic pixel labelling with convolutional networks and Conditional Random Fields[END_REF], [START_REF] Audebert | Beyond RGB: Very High Resolution Urban Remote Sensing With Multimodal Deep Networks[END_REF]. Besides, providing the local height in the form of Digital Surface Models (DSMs) is useful for urban planning, telecommunications, aviation, and intelligent transport systems. It has been traditionally done by multiview stereo [START_REF] Facciolo | Automatic 3D reconstruction from multi-date satellite images[END_REF] until that recently, deep learning approaches also offer competitive performances [START_REF] Saux | IEEE GRSS Data Fusion Contest: Large-Scale Semantic 3D Reconstruction[END_REF]. Eventually, [START_REF] Srivastava | Joint height estimation and semantic labeling of monocular aerial images with CNNs[END_REF] made one step further by combining both tasks through multi-task learning. In part II, we explore more related work to give insight into these approaches.

We also tackle this problem by using a multi-task deep network that simultaneously estimates both height and semantic maps from a single aerial image and we show that both tasks benefit from each other. To reach this goal, our approach builds on powerful models for depth prediction from a single image [START_REF] Carvalho | On regression losses for deep depth estimation[END_REF]. Moreover, we investigate the model uncertainty [START_REF] Kendall | Bayesian SegNet: Model uncertainty in deep convolutional encoder-decoder architectures for scene understanding[END_REF] to bring a new regard to aerial imagery processing and better understand success and failure cases. We also perform a study with most recent multi-task techniques for scene-understanding to analyse their contributions when confronted to the DFC2018 dataset. Notably, we obtain stateof-the-art results using Very-High-Resolution (VHR) imagery only on reference datasets: IEEE GRSS DFC2018 [START_REF] Xu | Advanced multi-sensor optical remote sensing for urban land use and land cover classification: Outcome of the 2018 IEEE GRSS Data Fusion Contest[END_REF] and ISPRS Semantic Labeling [START_REF] Cramer | The DGPF-test on digital airborne camera evaluationoverview and test design[END_REF]. On challenging DFC2018 data, comparing true deep learning methods only, our approach achieves 8% more accuracy than the winning solution Fusion-Net without post-processing [START_REF] Xu | Multi-source remote sensing data classification via fully convolutional networks and post-classification processing[END_REF].

After the related work in part II, we will describe our multitask approach in part III and present results in part IV.

II. RELATED WORK

a) Semantic segmentation: this task consists in giving a class label to each pixel in the image [START_REF] Brostow | Semantic object classes in video: A high-definition ground truth database[END_REF] and has been commonly carried out in the recent years by Fully-Convolutional Networks (FCNs) since [START_REF] Long | Fully Convolutional Networks for Semantic Segmentation[END_REF]. In remote sensing, it corresponds to the old problem of land-surface classification [START_REF] Benediktsson | Neural network approaches versus statistical methods in classification of multisource remote sensing data[END_REF] and has been popularized again by recent benchmarks on urban landuse mapping [START_REF] Cramer | The DGPF-test on digital airborne camera evaluationoverview and test design[END_REF], [START_REF] Xu | Advanced multi-sensor optical remote sensing for urban land use and land cover classification: Outcome of the 2018 IEEE GRSS Data Fusion Contest[END_REF]. Current state-of-the-art approaches based on FCNs include [START_REF] Paisitkriangkrai | Effective semantic pixel labelling with convolutional networks and Conditional Random Fields[END_REF], [START_REF] Audebert | Beyond RGB: Very High Resolution Urban Remote Sensing With Multimodal Deep Networks[END_REF] or [START_REF] Marmanis | Classification with an edge: Improving semantic image segmentation with boundary detection[END_REF] which combines segmentation with boundary detection. When multi-source data is available, as in the 2018 DFC, dedicated network architectures such as Fusion-CNN [START_REF] Xu | Advanced multi-sensor optical remote sensing for urban land use and land cover classification: Outcome of the 2018 IEEE GRSS Data Fusion Contest[END_REF] can be designed to use this information.

b) Elevation / depth estimation: the problem at hand here is to estimate the distance between the sensor and the observed scene, which means depth in computer vision or elevation (up to an affine transformation) in remote sensing. For nearly 40 years, stereo or multi-view stereo have been the means of choice, and still give excellent results [START_REF] Facciolo | Automatic 3D reconstruction from multi-date satellite images[END_REF]. However, recently 3D estimation from a single image became popular thanks to the conjunction of availability of image-and-depth datasets with finally powerful-enough neural network models [START_REF] Eigen | Predicting depth, surface normals and semantic labels with a common multi-scale convolutional architecture[END_REF], [START_REF] Laina | Deeper depth prediction with fully convolutional residual networks[END_REF]. In remote sensing, several networks for predicting elevation were also proposed, first [START_REF] Srivastava | Joint height estimation and semantic labeling of monocular aerial images with CNNs[END_REF] then [START_REF] Mou | IM2HEIGHT: Height estimation from single monocular imagery via fully residual convolutional-deconvolutional network[END_REF], [START_REF] Ghamisi | IMG2DSM: Height simulation from single imagery using conditional generative adversarial net[END_REF], [START_REF] Amirkolaee | Height estimation from single aerial images using a deep convolutional encoder-decoder network[END_REF]. In particular, [START_REF] Amirkolaee | Height estimation from single aerial images using a deep convolutional encoder-decoder network[END_REF] uses a ResNet-based FCN to produce the DSM while [START_REF] Ghamisi | IMG2DSM: Height simulation from single imagery using conditional generative adversarial net[END_REF] adds an adversarial loss to improve the likelihood of the synthesized DSM. Some works show how the estimated DSM is an useful additional information for building detection [START_REF] Mou | IM2HEIGHT: Height estimation from single monocular imagery via fully residual convolutional-deconvolutional network[END_REF] or semantic segmentation [START_REF] Ghamisi | IMG2DSM: Height simulation from single imagery using conditional generative adversarial net[END_REF]. It is worth noting that the 2019 Data Fusion Contest [START_REF] Saux | IEEE GRSS Data Fusion Contest: Large-Scale Semantic 3D Reconstruction[END_REF] comprises one challenge about Single-view Semantic 3D Challenge which should yield to new methods to tackle this problem in remote sensing. With respect to previous methods, our approach jointly learns height and semantics, using only VHR imagery.

c) Multi-task Learning: It aims at discovering the latent relatedness among tasks to improve generalization. In practice, it leverages the domain-specific information contained in the training signals of related tasks to build a better model which benefits all tasks [START_REF] Caruana | Multitask learning[END_REF]. Recent works include the simultaneous prediction of depth, normals and semantic labels [START_REF] Eigen | Predicting depth, surface normals and semantic labels with a common multi-scale convolutional architecture[END_REF] or normalized DSM and semantic labels [START_REF] Srivastava | Joint height estimation and semantic labeling of monocular aerial images with CNNs[END_REF]. In the latter, the network consists mostly in shared hidden convolutional layers followed by task-specific heads: one fully-connected layer and the appropriate loss. With respect to theirs, our multi-task architecture favors a middle split for the division in two taskspecific branches, a more suitable strategy for tasks as diverse as semantic mapping and DSM regression as this gives the model more specialized layers for each objective. As Caruana pointed out, backpropagation is one of the mechanisms to discover task relatedness [START_REF] Caruana | Multitask learning[END_REF]. Several recent works have dealt with the balance of the influence of each task during backpropagation. They weight task specific losses according to their intrinsic uncertainty [START_REF] Kendall | Multi-task learning using uncertainty to weigh losses for scene geometry and semantics[END_REF], directly the gradient magnitude for GradNorm [START_REF] Chen | GradNorm: Gradient normalization for adaptive loss balancing in deep multitask networks[END_REF], or to Pareto improvements between the conflicting tasks for MTL-MGDA [START_REF] Sener | Multi-task learning as multi-objective optimization[END_REF].

III. METHOD

Network Architecture. We adapted D3-Net, an encoderdecoder deep network originally created for depth estimation, to a multi-task architecture by adding a semantic classification decoder. This architecture favors hard parameter sharing: as illustrated in Fig. 1, the contractive and the early decoder layers are common for both semantics and height estimation. Last layers of the decoders are specific for each objective and generate respectively as many channels as classes for semantics and one channel for height. We also implemented various mechanisms for balancing tasks during optimization following literature in [START_REF] Chen | GradNorm: Gradient normalization for adaptive loss balancing in deep multitask networks[END_REF], [START_REF] Sener | Multi-task learning as multi-objective optimization[END_REF] Multi-Objective Loss. As discussed in section II, learning multiple tasks requires to correctly balance each objective's contribution at every training iteration. Indeed, each output is evaluated with a corresponding loss function: we adopt the absolute error (L 1 ) for height regression and the cross entropy loss (L CE ) for semantics evaluation. Thus, when errors are backpropagated, the resulting gradient in the common layers will correspond to the sum of all task gradients. A simple way to control the contribution of each task consists in multiplying each loss term in the final loss 1 by a scalar k t . However, finding the optimal values for each k t is still challenging.

L f inal = T ∑ t=1 k t L t (1)
Consequently, many methods have been proposed to effectively estimate k t in order to converge common parameters values to the best model for all tasks. Here, we propose to evaluate these methods in the context of aerial imagery. In the following, we explain the main idea of each approach.

a) Equal weights: is the most common approach and consists on weighting all losses uniformly. This approach does not handle cases when the training errors have different scales. In consequence some tasks can be dominant and predictions may be degraded for the other ones. However, this technique can still be effective in the case we can not appropriately measure the best contribution of each task to the global model. b) GradNorm [START_REF] Chen | GradNorm: Gradient normalization for adaptive loss balancing in deep multitask networks[END_REF]: dynamically learns the scaling factors with respect to the gradients of the last common layer and the rate balance, defined as the relative inverse training rate for each task. By directly modifying gradient magnitudes with learnable parameters, this method does not rely on empirical values for k t . c) MTL-MGDA [START_REF] Sener | Multi-task learning as multi-objective optimization[END_REF]: Sener et al. proposed to adapt the Multiple Gradient Descent Algorithm (MGDA) to the multiobjective optimization. This approach uses the Frank-Wolfe algorithm [START_REF] Jaggi | Revisiting Frank-Wolfe: Projection-free sparse convex optimization[END_REF] to find a common descent direction to the gradients of the shared layers at each iteration. Besides that, the paper also proposes to reduce memory use by applying the MGDA to the upper-bound MTL-MGDA-UB of the objective by means of the gradient of task losses with respect to the intermediate representation on the last common layer.

IV. EXPERIMENTS

In this section, we first describe the two datasets and the metrics used in this study. Experiments are as follows. First, we compare the general approach of multi-task using equal weights to single-task objectives and also to current state-ofart results on the proposed datasets to validate our approach and architecture. Then, we extent our study by analyzing the uncertainty map of the proposed model, according to [START_REF] Kendall | What uncertainties do we need in bayesian deep learning for computer vision?[END_REF]. Finally, we compare various flavors of recent state-of-art multitask in this context.

A. Datasets and Metrics

The ISPRS Vaihingen [START_REF] Cramer | The DGPF-test on digital airborne camera evaluationoverview and test design[END_REF] dataset comprises IRRG (Infra-Red, Red and Green) images at 9cm / pixel, DSM, and 2D and 3D semantic labeled maps for urban classification and 3D reconstruction. It contains 33 patches of different sizes, of which 16 images are used for training and the remaining 17 are used for testing. Semantic maps were annotated with 6 classes including impervious surfaces, building, low vegetation, tree, car and clutter/background. We ignore this last class during training and testing. As in [START_REF] Srivastava | Joint height estimation and semantic labeling of monocular aerial images with CNNs[END_REF], for height estimation we adopt the normalized DSMs (nDSM) from [START_REF] Gerke | Use of the Stair Vision Library within the ISPRS 2D semantic labeling benchmark (Vaihingen)[END_REF].

The 2018 Data Fusion Contest (DFC2018 [START_REF] Xu | Advanced multi-sensor optical remote sensing for urban land use and land cover classification: Outcome of the 2018 IEEE GRSS Data Fusion Contest[END_REF]) dataset is a collection of multi-source optical imagery over Houston, Texas. In particular, it contains Very High Resolution (VHR) color images resampled at 5cm / pixel, hyperspectral images, and LiDAR-derived products such as DSMs, and Digital Elevation Models (DEMs) at a resolution of 50cm / pixel. A 20-class, handmade ground-truth exists: 4 tiles (corresponding to the VHR images in the red frame in Fig. 3) are available for training, while 10 tiles remain undisclosed for evaluation on the the DASE website1 . The original DFC2018 dataset does not include height maps originally, thus we generate them by substracting the DEM to the DSM, as illustrated in Fig. 2.

Pre-processing. For both datasets, we perform training using 320x320 crops from the original images. As mentioned, RGB images from DFC2018 are 10 times bigger than the height and semantic models. So, we perform training with two different strategies: first, to deal with VHR images, we upsample the height and semantic maps to the same resolution of the input image before performing crops; second, to speed up training and testing, we downsample the RGB images by a factor of 10. We refer to these pre-processing strategies as VHR Multi-task and LR (low-resolution) Multi-task.

Data augmentation. To improve generalization, we perform the following online data augmentation: random crops from original tiles, rotation, horizontal and vertical flips.

From crops to tiles. Inference is implemented using a Gaussian prior over patches to avoid a checkerboard effect on the output. We predict patches sequentially with a stride smaller than the window size and weight overlapping areas with a 2D Gaussian map. Results are improved when using bigger windows and small strides as we can leverage more information from neighbor patches. For our experiments, we use a test window of 1024 and a stride of 256. When generating VHR outputs, these are posteriorly downsampled to compare to ground truth maps.

Training is performed with PyTorch [START_REF] Paszke | Automatic differentiation in pytorch[END_REF] framework, we used Adam [START_REF] Kingma | Adam: A method for stochastic optimization[END_REF] as our optimizer with learning rate of 2e-4 and we train our model with a Nvidia GTX 1080 GPU.

Metrics. To evaluate our models, we use common metrics from [START_REF] Eigen | Predicting depth, surface normals and semantic labels with a common multi-scale convolutional architecture[END_REF] and [START_REF] Srivastava | Joint height estimation and semantic labeling of monocular aerial images with CNNs[END_REF]. For height estimation, we use the mean absolute error (mae):

1 N ∑ N i=0 |di -di|; the mean squared error (mse), 1 N ∑ N i=0 di -di 2 ;
and the root mean squared error (rmse),

√ 1 N ∑ N i=0 (di -di) 2 .
For classification, we use overall accuracy (OA), average accuracy (AA) and Kappa, as in [START_REF] Xu | Advanced multi-sensor optical remote sensing for urban land use and land cover classification: Outcome of the 2018 IEEE GRSS Data Fusion Contest[END_REF].

B. Improving Height and Semantic Estimation with Multi-task

In this experiment, we use the original D3-Net with the corresponding task decoder for single task training, and the proposed model with equal weights for multi-task.

If we focus on the bottom lines of Table I, we observe that performances are improved for both objectives by the multitask model if compared to the single-task. It has the advantage of learning complementary features, using less parameters compared to single models for each task. In the upper lines, we observe state-of-art results for DFC2018. Please note these methods use multi-source data from DSM, DEM, Hyperspectral image and VHR RGB as input to estimate semantic maps only. For fairness of comparison, results with a * refer to methods without ad-hoc detector nor post-processing.It appears our model overcomes past learning-based approaches by 10 percentual points on OA.

The above results are inferred in nearly 13 minutes for each 10 4 × 10 4 pixels tile, when using the inference proposed in section III. For large batch processing, this time can even be reduced by using the LR model, which reduces time to nearly 10 seconds per tile at the cost of losing efficiency.

We can also observe results in Fig. 3 and crops for specific regions in Fig. 4. In general, the network produces nearly accurate results for ground, residential buildings and vegetation, while some structures are more challenging, like high buildings or stadiums. These classes have various shapes, colors and heights. Thus, it is hard to estimate precise height values from bird-view. Semantics are detailed, with even plastic seats, playground or concrete elements in the stadium.

Results with Vaihingen dataset are in Table II. We observe that our performances overcome Srivastava et al. [START_REF] Srivastava | Joint height estimation and semantic labeling of monocular aerial images with CNNs[END_REF]. This is likely due to a better network with skip-connections and an earlier split between task-specific decoders. It is worth noting that our multi-task approach only improves semantic classification if compared to single-task models. In [START_REF] Srivastava | Joint height estimation and semantic labeling of monocular aerial images with CNNs[END_REF], none of the tasks was improved by multi-task. Possible reason is that Vaihingen does not have much variance between train and test sets, so even single task models can overfit and also be performing during inference. Actually, multi-task improves generalization by leveraging complementary information between tasks.

C. Uncertainty

In addition to error measures, [START_REF] Kendall | Bayesian SegNet: Model uncertainty in deep convolutional encoder-decoder architectures for scene understanding[END_REF] proposed to evaluate the uncertainty of the network, which accounts for the ignorance of the model parameters with respect to the input images.

To perform this analysis, we follow the original paper and keep dropout layers active during inference. For each tile, we generate 30 samples from which we calculate the standard deviation of the predictions. We perform this test for height estimation only. The results in Fig. 5 allows us to understand which zones of the input are the most challenging to the network. Contours present high variance and are challenging. So are high buildings in general: indeed a plane rooftop appears the same whatever its altitude. We also note that trees are quite uncertain even if predictions were good: this is a difficult class due to texture variance or deciduousness.

D. Comparison between Multi-task Methods

In this section, we compare the classic approach with equal weights to state-of-art methods for multi-task learning. These techniques were previously tested on datasets for digit classification, multi-label classification, urban outdoor and indoor scene understanding (Cityscape [START_REF] Cordts | The Cityscapes dataset for semantic urban scene understanding[END_REF] and NYUv2 [START_REF] Silberman | Indoor segmentation and support inference from RGBD images[END_REF]). We now test them for the first time on VHR aerial images.

As the chosen methods originally rely on architectures without skip connections, we perform experiments with and without these features for best comparison. We observe results for the mentioned methods in Tables III and IV. From our experiments, we observed that aerial imagery requires less context for the objective tasks than sceneparsing datasets in [START_REF] Chen | GradNorm: Gradient normalization for adaptive loss balancing in deep multitask networks[END_REF], [START_REF] Sener | Multi-task learning as multi-objective optimization[END_REF]. We believe that subtle multitask techniques are more prone to better results on these kind of datasets,. Also, in the case of DFC2018, semantic annotations are very sparse and gradient values are impacted, which compromising other multi-task methods.

V. CONCLUSIONS

In this work, we have shown that multi-task learning methods work really well on aerial imagery and may lead to better results when compared to single-task techniques. We proved that complementary features from each objective can be learned by a deep model to improve performance independently. Our experiments on DFC2018 show that a model with less input data and no special post-processing can lead to results comparable to the much complex stateof-art results. Thus, this framework can be easily adopted for urban modelling without the any complementary information. However, experiments with very recent multi-task variants showed that surprisingly the simple equal-weight approach leads to best performances. Maybe subtle multi-task methods require larger and densely labeled datasets. Hence, we will further our work to understand the mechanisms of multi-task.

Fig. 1 .

 1 Fig.1. Architecture of our multi-task model for aerial imagery, based on D3-Net[START_REF] Carvalho | On regression losses for deep depth estimation[END_REF]. Left most layers share parameters between all tasks and right most layers are task-specific. Last layer of each decoder differs only on the output number of channels, followed by task evaluation metric (cross-entropy, or L 1 , for semantic and height estimation, respectively).

Fig. 2 .

 2 Fig. 2. Height map generation using the Digital Surface Model (DSM) and the Digital Elevation Model (DEM): height as DSM-DEM.

Fig. 3 .

 3 Fig. 3. Results on the DFC2018 dataset trained with equal weights (best results). Top row shows RGB image and height ground-truth, bottom row semantic prediction and height estimate. The training area is delimited by a red rectangle on the RGB image.

Fig. 4 .

 4 Fig. 4. Crop areas over the DFC2018 dataset. From left to right, input RGB image, semantic ground-truth and prediction (black is no information), height ground-truth and prediction. Top row show the Houston University stadium and bottom row shows a residential area.

Fig. 5 .

 5 Fig. 5. Uncertainty map of height (standard deviation of model predictions).

TABLE I COMPARISON

 I OF DFC2018 HEIGHT AND SEMANTICS PREDICTIONS WITH STATE-OF-ART APPROACHES, SINGLE AND MULTI-TASK MODELS.

		Height Errors mae↓ mse↓ rms↓	Semantic Errors OA(%)↑ AA↑ Kappa↑	Time 1 (s)
	Cerra* [29]	-	-	-	58.60 55.60 0.56	-
	Fusion-FCN* [10]	-	-	-	63.28	-	0.61	-
	Fusion-FCN [10]	-	-	-	80.78	-	0.80	-
	*learning only, without post-processing
	VHR Single task 1.480 9.544 3.000	73.40 67.82 0.72	-
	VHR Multi-task 1.263 7.279 2.599	74.44 68.30 0.73 7.74.10 2
	LR Multi-task	1.513 9.341 2.970	64.70 58.85 0.63	7.82

1

Mean test time per image (std. deviation)

TABLE II COMPARISON

 II OF MULTI-TASK STATE-OF-ART AND OUR ARCHITECTUREADOPTING AN EQUAL WEIGHT APPROACH.

	Height Errors	Semantic Errors
	mae↓ mse↓	rms↓	OA*(%)↑AA**↑Kappa↑
	Srivastava [5] 0.063	-	0.098	78.8% 73.4% 71.9%
	Single task 0.039 0.005 0.067	87.4% 84.4% 75.0%
	Multi-task 0.045 0.006 0.074	87.7% 85.4% 75.9%

TABLE IV COMPARISON

 IV OF DIFFERENT MULTI-TASK STATE-OF-ART APPROACHES WITH VHR INPUT IMAGES FROM DFC2018 DATASET.

			Height Errors↓	Semantic Errors↑
		MTL Method	mae mse rms	OA(%)AA(%)Kappa
	no skip	MTL-MGDA-UB [23] 1.475 9.911 3.047 GradNorm [22] 1.394 8.886 2.857 Equal Weights 1.520 8.589 2.826	52.98 47.59 0.50 58.00 54.23 0.56 58.26 54.74 0.56
		MTL-MGDA [23]	1.303 7.415 2.627	59.13 55.53 0.57
	skip	GradNorm [22] Equal Weights	1.340 7.898 2.743 1.263 7.279 2.599	63.07 58.92 0.61 74.44 68.30 0.73

GRSS Data and Algorithm Standard Evaluation website: http://dase. grss-ieee.org/