Lu Zhang
email: vyouyzhang@tencent.com

Tencent Youtu

Miaojing Shi
email: miaojing.shi@inria.fr

Qiaobo Chen
email: chenqiaobo@sjtu.edu.cn

Crowd counting via scale-adaptive convolutional neural network

The task of crowd counting is to automatically estimate the pedestrian number in crowd images. To cope with the scale and perspective changes that commonly exist in crowd images, state-of-the-art approaches employ multi-column CNN architectures to regress density maps of crowd images. Multiple columns have different receptive fields corresponding to pedestrians (heads) of different scales. We instead propose a scale-adaptive CNN (SaCNN) architecture with a backbone of fixed small receptive fields. We extract feature maps from multiple layers and adapt them to have the same output size; we combine them to produce the final density map. The number of people is computed by integrating the density map. We also introduce a relative count loss along with the density map loss to improve the network generalization on crowd scenes with few pedestrians, where most representative approaches perform poorly on. We conduct extensive experiments on the ShanghaiTech, UCF CC 50 and WorldExpo'10 datasets as well as a new dataset SmartCity that we collect for crowd scenes with few people. The results demonstrate significant improvements of SaCNN over the state-of-the-art.

Introduction

The crowd counting task in computer vision is to automatically count the pedestrian number in images/videos. To help with crowd control and public safety in many scenarios such as public rallies and sports, accurate crowd counting is demanded.

Early methods estimate the pedestrian number via detection, where each individual pedestrian in a crowd is detected by trained detectors [START_REF] Zhao | Segmentation and tracking of multiple humans in crowded environments[END_REF][START_REF] Li | Estimating the number of people in crowded scenes by mid based foreground segmentation and head-shoulder detection[END_REF][START_REF] Ge | Marked point processes for crowd counting[END_REF][START_REF] Idrees | Detecting humans in dense crowds using locally-consistent scale prior and global occlusion reasoning[END_REF]. This can be very hard if pedestrians are heavily occluded or densely spread. Present methods instead regress the pedestrian number on the whole image and achieve significant improvements [START_REF] Chan | Privacy preserving crowd monitoring: Counting people without people models or tracking[END_REF][START_REF] Chan | Bayesian poisson regression for crowd counting[END_REF][START_REF] Liu | Bayesian model adaptation for crowd counts[END_REF]. Handcrafted features like HOG [START_REF] Idrees | Multi-source multi-scale counting in extremely dense crowd images[END_REF] were soon outperformed £ Equal contribution. y Lu Zhang and Qiaobo Chen have worked on this paper during their internships at Tencent Youtu Lab. by modern deep representations [START_REF] Onoro-Rubio | Towards perspective-free object counting with deep learning[END_REF][START_REF] Zhang | Cross-scene crowd counting via deep convolutional neural networks[END_REF].

Crowd counting via regression suffers from the drastic changes in perspective and scale, which commonly exist in crowd images (see Fig. 1). To tackle it, multi-column convolutional neural networks (CNN) were recently adopted and have shown robust performance [START_REF] Sam | Switching convolutional neural network for crowd counting[END_REF][START_REF] Boominathan | Crowdnet: a deep convolutional network for dense crowd counting[END_REF][START_REF] Zhang | Singleimage crowd counting via multi-column convolutional neural network[END_REF]. Different columns corresponding to different filter sizes (small, medium and large) are combined in the end to adapt to the large variations of perspective and scale. They regress a density map of the crowd (see Fig. 1). Pedestrian number is obtained by integrating the density map. [START_REF] Sam | Switching convolutional neural network for crowd counting[END_REF] further introduced a switch classifier to relay the crowd patches in images to the best CNN column. Each CNN column is trained with its own samples.

We notice that the selection among the multiple columns in [START_REF] Sam | Switching convolutional neural network for crowd counting[END_REF] is not balanced. Using one single column is able to retain over 70% accuracy of the multi-column model on some datasets. Building upon this observation, in this paper, we propose a scale-adaptive CNN architecture (SaCNN, see Fig. 2) for crowd counting. It offers several new elements as our contributions: [START_REF] Boominathan | Crowdnet: a deep convolutional network for dense crowd counting[END_REF] We design a single column CNN with a single filter size as our backbone, which is easy to train from scratch. Small-sized filters preserve the spatial resolution and allow us to build a deep network. [START_REF] Brostow | Unsupervised bayesian detection of independent motion in crowds[END_REF] We combine the feature maps of multiple layers to adapt the network to the changes in pedestrian (head) scale and perspective. Different layers share the same low-level feature representations, which results in fewer parameters, fewer training data required, and faster training. (3) We introduce a multi-task loss by adding a relative head count loss to the density map loss. It significantly improves the network generalization on crowd scenes with few pedestrians, where most representative works perform poorly on. [START_REF] Chan | Bayesian poisson regression for crowd counting[END_REF] We collect the new SmartCity dataset with high-angle shot for crowd counting. The existing datasets are taken from outdoors and do not adequately cover those crowd scenes with few pedestrians. The new dataset contains both indoor and outdoor scenes and has an average pedestrian number of 7.4 per image. [START_REF] Chen | Feature mining for localised crowd counting[END_REF] We conduct extensive experiments on three datasets: ShanghaiTech [START_REF] Zhang | Singleimage crowd counting via multi-column convolutional neural network[END_REF], UCF CC 50 [START_REF] Idrees | Multi-source multi-scale counting in extremely dense crowd images[END_REF] and WorldExpo '10 [33]; the results show that our SaCNN significantly outperforms the state-of-the-art crowd counting methods. We also compare SaCNN with other representative works on SmartCity to show the generalization ability of ours. Our code and dataset are publicly available1 .

Related work

We categorize crowd counting methods as either 1) detection-based methods or 2) regression-based methods. We shall describe both categories below and compare representative works to our method.

Detection-based methods

Detection-based methods consider a crowd as a group of detected individual entities [START_REF] Wang | Automatic adaptation of a generic pedestrian detector to a specific traffic scene[END_REF]32,[START_REF] Stewart | End-to-end people detection in crowded scenes[END_REF][START_REF] Viola | Detecting pedestrians using patterns of motion and appearance[END_REF][START_REF] Brostow | Unsupervised bayesian detection of independent motion in crowds[END_REF][START_REF] Rabaud | Counting crowded moving objects[END_REF]. Early works focus on video surveillance scenario so that the motion and appearance cues can be utilized [START_REF] Viola | Detecting pedestrians using patterns of motion and appearance[END_REF][START_REF] Brostow | Unsupervised bayesian detection of independent motion in crowds[END_REF][START_REF] Rabaud | Counting crowded moving objects[END_REF]. For example, [START_REF] Viola | Detecting pedestrians using patterns of motion and appearance[END_REF] trained a dynamic detector capturing motion and appearance information over two consecutive frame pairs of a video sequence. These works are not applicable in still images for crowd counting. Pedestrians are often occluded in dense crowds, and this is particularly challenging when estimating the crowds in still images. Partdetectors were therefore employed to count pedestrian from parts in images [START_REF] Wang | Automatic adaptation of a generic pedestrian detector to a specific traffic scene[END_REF]32]. [START_REF] Stewart | End-to-end people detection in crowded scenes[END_REF] took advantage of a recurrent deep network to detect the occluded heads in crowd scenes. Notwithstanding their improvements, detectionbased methods overall suffer severely in dense crowds with high occlusions among people.

Regression-based methods

Regression-based methods regress either a scalar value (pedestrian number) [START_REF] Chan | Privacy preserving crowd monitoring: Counting people without people models or tracking[END_REF][START_REF] Chan | Bayesian poisson regression for crowd counting[END_REF][START_REF] Liu | Bayesian model adaptation for crowd counts[END_REF][START_REF] Idrees | Multi-source multi-scale counting in extremely dense crowd images[END_REF] or a density map [START_REF] Chen | Feature mining for localised crowd counting[END_REF]11,12] on various features extracted from crowd images. They basically have two steps: first, extracting effective features from crowd images; second, utilizing various regression functions to estimate the crowd count. Early works utilize handcrafted features, like edge features [START_REF] Chan | Privacy preserving crowd monitoring: Counting people without people models or tracking[END_REF][START_REF] Chen | Feature mining for localised crowd counting[END_REF][START_REF] Ryan | Crowd counting using multiple local features[END_REF][START_REF] Regazzoni | Distributed data fusion for real-time crowding estimation[END_REF] and texture features [START_REF] Chen | Feature mining for localised crowd counting[END_REF][START_REF] Idrees | Multi-source multi-scale counting in extremely dense crowd images[END_REF][START_REF] Marana | On the efficacy of texture analysis for crowd monitoring[END_REF]. Regression methods include linear [START_REF] Regazzoni | Distributed data fusion for real-time crowding estimation[END_REF][START_REF] Paragios | A mrf-based approach for realtime subway monitoring[END_REF], ridge [START_REF] Chen | Feature mining for localised crowd counting[END_REF] and Gaussian [START_REF] Chan | Privacy preserving crowd monitoring: Counting people without people models or tracking[END_REF] functions.

Due to the use of strong CNN features, recent works on crowd counting have shown remarkable progress by regressing a density map of an image [START_REF] Zhang | Cross-scene crowd counting via deep convolutional neural networks[END_REF][START_REF] Zhang | Singleimage crowd counting via multi-column convolutional neural network[END_REF][START_REF] Sam | Switching convolutional neural network for crowd counting[END_REF][START_REF] Boominathan | Crowdnet: a deep convolutional network for dense crowd counting[END_REF][START_REF] Onoro-Rubio | Towards perspective-free object counting with deep learning[END_REF]. A density map provides much more information than a scalar value, and CNNs have been demonstrated to be particularly good at solving problems "locally" rather than "globally". Crowd counting is casted as that of estimating a continuous density function whose integral over any image region gives the count of pedestrians within that region. [START_REF] Zhang | Cross-scene crowd counting via deep convolutional neural networks[END_REF] designed a multi-task network to regress both density maps and crowd counts. They employed fully-connected layers to regress the absolute crowd count.

Comparison to our SaCNN

[34, 26, 1] utilized multi-column networks [START_REF] Ciregan | Multi-column deep neural networks for image classification[END_REF] to deal with the variation of head scale in one image. Different columns correspond to different filter sizes. The large-sized filters make the whole network hard to train. The network is pretrained on each column first and finetuned together in the end [START_REF] Zhang | Singleimage crowd counting via multi-column convolutional neural network[END_REF]; whilst our SaCNN employs a single column with a single filter size which can be trained from scratch. [START_REF] Sam | Switching convolutional neural network for crowd counting[END_REF] introduced a switch classifier using VGG net [START_REF] Simonyan | Very deep convolutional networks for large-scale image recognition[END_REF] to relay the crowd patches from images to the best CNN column. The switching is very costly and often not correct. While our SaCNN adapts the feature maps from multiple scales and concatenates them to relay each pedestrian to the best scale in the network.

Similar to [START_REF] Zhang | Cross-scene crowd counting via deep convolutional neural networks[END_REF], we perform a multi-task optimization in SaCNN to regress both the density map and head count. Differently, ours is a multi-scale fully convolutional network and we propose a relative count loss. The scaleadaptive architecture is similar in spirit to [START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF][START_REF] Lin | Feature pyramid networks for object detection[END_REF] by combining feature maps of multiple layers; but we use the deconvolutional layer [START_REF] Noh | Learning deconvolution network for semantic segmentation[END_REF] to adapt the network output instead of upsampling and element-wise summation. Our network design with a backbone of single filter size and multi-scale outputs is new in the crowd counting field. Plus, we claim five-fold new elements in total in Sec. 1.

Scale-adaptive CNN

In this section, we first generate the ground truth density maps for training data and then present the architecture of SaCNN.

Ground truth density maps

Supposing we have a pedestrian head at a pixel z j , we represent it by a delta function (z z j ). The ground truth

Network architecture

Many state-of-the-art works [START_REF] Zhang | Singleimage crowd counting via multi-column convolutional neural network[END_REF][START_REF] Sam | Switching convolutional neural network for crowd counting[END_REF][START_REF] Boominathan | Crowdnet: a deep convolutional network for dense crowd counting[END_REF] adopt the multicolumn architecture with different filter sizes to address the scale and perspective change in crowd images. We instead propose a scale-adaptive CNN (SaCNN) where we use a single backbone network with a single filter size (see Fig. 2). Density map estimation is performed at a concatenated layer which merges the feature maps from multiple scales of the network; it can therefore easily adapt to the pedestrian scale and perspective variations.

We use all filters in the network. The computation required for filters is far less than for large filters [START_REF] Zhang | Singleimage crowd counting via multi-column convolutional neural network[END_REF][START_REF] Sam | Switching convolutional neural network for crowd counting[END_REF][START_REF] Boominathan | Crowdnet: a deep convolutional network for dense crowd counting[END_REF]. Small filters preserve the spatial resolution of the input so that we can build a deep network. "Deeper" has a similar effect as "Wider" (multi-column architecture) does in a network: for instance, a large filter can be simulated by a small filter from deeper layer. The backbone design (until conv4 3 in Fig. 2) follows the VGG architecture [START_REF] Simonyan | Very deep convolutional networks for large-scale image recognition[END_REF] in the context of using 3*3 filters and three convolutional layers after each pooling layer.

SaCNN is built from low-level to high-level by gradually adding layers of different scales. For concatenation, we need to carefully adapt their output to be the same size. We first present a single-scale model that is illustrated in Fig. 3 sults in Fig. 5 show that our single-scale model converges fast and its performance is close to the state-of-the art.

Like the multi-column CNN, we want our model to fire on pedestrians (heads) of different sizes. We decide to go deeper. We have three max-pooling layers and several convolutional layers until conv4 3. We add pool4 and three convolutional layers (conv5 1 to conv5 3) after conv4 3 in the network (see Fig. 3 (b)). We propose a two-scale model by extracting feature maps from conv4 3 and conv5 3; we set the stride of pool4 to be 1 so that the two feature maps have the same size; we concatenate them to produce the final density map (refer to Fig. 3 (b)) . Results in Fig. 5 demonstrate a clear improvement of our two-scale model over the single-scale model.

Building upon the two-scale network, we construct our scale-adaptive model in Fig. 2. We add pool5 and conv6 1 afterwards in the network. In order to combine conv5 3 and conv6 1, we set the stride of pool4 as 2 and pool5 as 1. We upsample the concatenated output to I=V resolution of the input using DeConv layer to further concatenate it with conv4 3. The final density map therefore has a spatial resolution of I=V times the input Hence, we downsample the ground truth density map by factor 8.

Notice that we have also tried to regress the density map at a lower resolution: e.g. I=IT times the input resolution. The performance is slightly declined compared to concatenating at I=V resolution. We suggest it is due to the receptive field being too big in the deeper layer.

Network loss

Our network training first adopts the Euclidean loss to measure the distance between the estimated density map and the ground truth [START_REF] Zhang | Singleimage crowd counting via multi-column convolutional neural network[END_REF][START_REF] Sam | Switching convolutional neural network for crowd counting[END_REF][START_REF] Boominathan | Crowdnet: a deep convolutional network for dense crowd counting[END_REF]:

L D @¢A a I N N X i=1 kF D @X i Y ¢A D i k 2 ;
(2

)
where ¢ is a set of learnable parameters in the proposed network. N is the number of training images. X i is the in- put image and D i is the corresponding ground truth density map. F D @X i Y ¢A denotes the estimated density map for X i .

The Euclidean distance is computed at pixels and summed over them. Apart from the density map regression, we introduce another loss function regarding the head count (see Fig, 2). We notice that most representative approaches perform poorly on crowd scenes with few pedestrians. This problem can not be resolved via [START_REF] Brostow | Unsupervised bayesian detection of independent motion in crowds[END_REF], because the absolute pedestrian number is usually not very large in sparse crowds compared to that in dense crowds. To tackle this, we propose a relative head count loss:

L Y @¢A a I N N X i=1 k F Y @X i Y ¢A Y i Y i C I k 2 ; (3)
where F Y @X i Y ¢A and Y i are the estimated head count and the ground truth head count, respectively. The denominator Y i is added by I to prevent division by zero. (3) con- centrates the learning on those samples with relatively large prediction errors. Results on those very sparse crowd scenes (Sec. 4: Table 6) demonstrate significant improvements by employing the relative head count loss in the network.

We directly train our SaCNN from scratch by randomly initializing the network parameters. Because the head count regression is an easy task, we first regress the model on the density map (2); once it converges, we add (3) in the objective loss to jointly train a multi-task network for a few more epochs. We set the density map loss weight as 1 and the relative count loss weight as 0.1.

We note that it will be 1.5¢ faster for the model to converge if we train a two-scale model first and then finetune SaCNN on it; the performance difference between the two training manners is trivial.

Experiments

We shall first briefly introduce three standard datasets and a new created dataset for crowd counting. Afterwards, we evaluate our method on these datasets.

Datasets

ShanghaiTech dataset [START_REF] Zhang | Singleimage crowd counting via multi-column convolutional neural network[END_REF] consists of 1198 annotated images with a total of 330,165 people with head center annotations. This dataset is split into two parts: PartA and PartB. Refer to Table 1 for the statistics of the dataset: the crowd images are sparser in PartB compared with PartA. Following [START_REF] Zhang | Singleimage crowd counting via multi-column convolutional neural network[END_REF], we use 300 images for training and 182 images for testing in PartA; 400 images for training and 316 images for testing in PartB.

WorldExpo'10 dataset [START_REF] Zhang | Cross-scene crowd counting via deep convolutional neural networks[END_REF] includes 3980 frames, which are from the Shanghai 2010 WorldExpo. 3380 frames are used as training while the rest are taken as test. The test set includes five different scenes and 120 frames in each one. Regions of interest (ROI) are provided in each scene so that crowd counting is only conducted in the ROI in each frame. Some statistics of this dataset can be found in Table 1.

UCF CC 50 dataset [START_REF] Idrees | Multi-source multi-scale counting in extremely dense crowd images[END_REF] has 50 images with 63974 head annotations in total. The head counts range between 94 and 4543 per image. The small dataset size and large variance in crowd count make it a very challenging dataset. Following [START_REF] Idrees | Multi-source multi-scale counting in extremely dense crowd images[END_REF], we perform 5-fold cross validations to report the average test performance. Some statistics of the dataset is in Table 1.

SmartCity dataset is collected by ourselves. There are in total 50 images collected from ten city scenes including office entrance, sidewalk, atrium, shopping mall etc.. Some examples are shown in Fig. 4. They are all high-angle shot for video surveillance. Existing crowd counting datasets consist of images of hundreds or even thousands of pedestrians, and nearly all the images are taken outdoors. We therefore specifically create the dataset that has few pedestrians in images and consists of both outdoor and indoor scenes. Some statistics of this dataset is shown in Table 1: the average number of pedestrians per image is only 7.4 with minimum being 1 and maximum being 14. We use this dataset to test the generalization ability of the proposed framework on very sparse crowd scenes. 1. Dataset statistics in this paper. #Images is the number of images; Min, Max and Avg denote the minimum, maximum, and average pedestrian numbers per image, respectively.

Implementation details and evaluation protocol

Ground truth annotations for each head center in the standard benchmarks are publicly available. Given a training set, we augment it by randomly cropping 9 patches from each image. Each patch is 1=4 size of the original image. All patches are used to train our model SaCNN. We train the model using the stochastic gradient descent (SGD) optimizer. The learning rate starts from 1e-6 and decays to 1e-8 with multistep policy. Momentum is 0.9 and batch size is 1, we train 250 epochs in total.

We evaluate the performance via the mean absolute error (MAE) and mean square error (MSE) commonly used in previous works [START_REF] Zhang | Cross-scene crowd counting via deep convolutional neural networks[END_REF][START_REF] Zhang | Singleimage crowd counting via multi-column convolutional neural network[END_REF][START_REF] Sam | Switching convolutional neural network for crowd counting[END_REF][START_REF] Boominathan | Crowdnet: a deep convolutional network for dense crowd counting[END_REF][START_REF] Onoro-Rubio | Towards perspective-free object counting with deep learning[END_REF][START_REF] Wang | Deep people counting in extremely dense crowds[END_REF]:

MAE = 1 N N X i=1 jF Y Y i j; MSE = 1 N N X i=1 p (F Y Y i ) 2 : (4)
One can refer to (3) for notations F Y and Y i . Small MAE and MSE indicate good performance.

Results on ShanghaiTech

Ablation study. We report an ablation study to offer the justification of our SaCNN in multi-scale and multi-task setup. Referring to Sec. Multi-task ablation test. We introduce a relative count loss (rcl) to the above scale-adaptive model to improve the network generalization ability on crowd scenes with few pedestrians. We denote by SaCNN(w/o cl) the scaleadaptive model without count loss and SaCNN(rcl) with relative count loss. It can be seen from Table 2 that, compared to SaCNN(w/o cl), SaCNN(rcl) decreases both MAE and MSE on PartA and PartB.

To justify the relative count loss over the absolute count loss (acl), we train another model SaCNN(acl) following [START_REF] Zhang | Cross-scene crowd counting via deep convolutional neural networks[END_REF], where they train a multi-task network by alter- nating between training on the density map loss and the absolute count loss. The result in Table . 2 shows that adding the absolute loss however impairs the performance. This is because the absolute count loss varies drastically among crowd images. In the following experiments, we use SaCNN to signify our best model SaCNN(rcl). We shall also show the significant improvement of adding rcl on SmartCity dataset (Sec. 4.6).

Comparison to state-of-the-art. We compare our best model SaCNN with state-of-the-art [START_REF] Zhang | Cross-scene crowd counting via deep convolutional neural networks[END_REF][START_REF] Zhang | Singleimage crowd counting via multi-column convolutional neural network[END_REF][START_REF] Sam | Switching convolutional neural network for crowd counting[END_REF] on both PartA and PartB (Table 3). Our method achieves the best MAE: 86.8 and 16.2 on PartA and PartB. Compared to [START_REF] Sam | Switching convolutional neural network for crowd counting[END_REF], SaCNN achieves 3.6 point decrease in MAE on PartA and 5.4 point on PartB; 7.6 point decrease in MSE on PartB and a comparable MSE (second best) on PartA. SaCNN requires less computation compared to [START_REF] Sam | Switching convolutional neural network for crowd counting[END_REF], where they split the test image into patches and employ both a classification and a regression network to test each patch. At test time SaCNN is 2 times faster than [START_REF] Sam | Switching convolutional neural network for crowd counting[END_REF] (293ms vs. 580ms per image).

Fig. 6 shows some examples on both PartA and PartB.

WorldExpo'10 S1 S2 S3 S4 S5 Avg. Zhang et al. [START_REF] Zhang | Cross-scene crowd counting via deep convolutional neural networks[END_REF] 9.8 14.1 14.3 22.2 3.7 12.9 Zhang et al. [START_REF] Zhang | Singleimage crowd counting via multi-column convolutional neural network[END_REF] 3.4 20.6 12.9 13.0 8.1 11.6 Sam et al. [START_REF] Sam | Switching convolutional neural network for crowd counting[END_REF] 4. The estimated density maps are visually similar to the crowd distributions in real images. We give the predicted number and the real pedestrian number under the density maps and real images, respectively. The estimated pedestrian numbers are close to the real numbers.

Results on WorldExpo'10

Referring to [START_REF] Zhang | Cross-scene crowd counting via deep convolutional neural networks[END_REF], training and test are both conducted within the ROI provided for each scene. MAE is reported for each test scene and averaged to evaluate the overall performance. We compare our SaCNN with other state-of-theart in Table 4. Notations i.e. (GT w/o perspective) and (GT with perspective) signify the selection of in [START_REF] Boominathan | Crowdnet: a deep convolutional network for dense crowd counting[END_REF]. [START_REF] Zhang | Cross-scene crowd counting via deep convolutional neural networks[END_REF][START_REF] Zhang | Singleimage crowd counting via multi-column convolutional neural network[END_REF] compute the as a ratio of the perspective value at certain pixel. [START_REF] Sam | Switching convolutional neural network for crowd counting[END_REF] however reports a better result without using perspective values. We provide both results with and w/o perspectives. It can be seen that except on S4, SaCNN (GT with perspective) is inferior to SaCNN (GT w/o perspective) on all the remaining scenes. SaCNN(GT w/o perspective) produces the best MAE on S1, S2 and S5: 2.6, 13.5 and 3.3. The average MAE of SaCNN across scenes outperforms [START_REF] Sam | Switching convolutional neural network for crowd counting[END_REF] by 0.9 point and reaches the best 8.5.

Results on UCF CC 50

We compare our method with seven existing methods on UCF CC 50 [START_REF] Zhang | Cross-scene crowd counting via deep convolutional neural networks[END_REF][START_REF] Zhang | Singleimage crowd counting via multi-column convolutional neural network[END_REF][START_REF] Sam | Switching convolutional neural network for crowd counting[END_REF]12,[START_REF] Idrees | Multi-source multi-scale counting in extremely dense crowd images[END_REF][START_REF] Boominathan | Crowdnet: a deep convolutional network for dense crowd counting[END_REF][START_REF] Onoro-Rubio | Towards perspective-free object counting with deep learning[END_REF] in Table 5. [12] proposed a density regression model to regress the density map rather than the pedestrian number in crowd counting. [START_REF] Idrees | Multi-source multi-scale counting in extremely dense crowd images[END_REF] average pedestrian number 7.4. Adding the relative count loss has significantly improved the network generalization on very sparse crowd scenes.

Overall, our results are not perfect, and we believe this makes the dataset a challenging task for future works.

Regression v.s. detection

In this section we compare our regressed-based method SaCNN with a detection-based method YOLO9000 [START_REF] Redmon | Yolo9000: better, faster, stronger[END_REF]. There are no bounding box annotations available for crowd counting datasets, and it is often not feasible to annotate every pedestrian head with a bounding box in dense crowds (see Fig. 7). Thus, we train a pedestrian detector on COCO dataset [START_REF] Lin | Microsoft coco: Common objects in context[END_REF] following YOLO9000 with human annotations available. We also annotate the pedestrian head bounding boxes in COCO and train a head detector. We test both detectors on ShanghaiTech PartA and PartB, as well as SmartCity. The crowd scenes in these datasets vary from very sparse to very dense (see Table 1). Since the crowd images are taken from high angles, detectors trained from COCO might not generalize well on them. We thus always report the better result over the two detectors on crowd images. Results are shown in Table 7. In the detection context, a good detection is measured by the intersection-over-union (IoU) between the detected bounding box and the ground truth bounding box; the threshold for confidence score (cs) is set to be high, e.g. cs > 0:5. In the crowd counting context, a good prediction is measured via the difference between the estimated count and the ground truth count; having a lower threshold e.g. cs > 0:05 ends up with a bigger prediction. A bigger prediction however reflects a lower MAE/MSE in the crowd counting as YOLO tends to miss small objects in general in images. We illustrate both results with YOLO9000 cs > 0:05 and cs > 0:5 in Table 7: our SaCNN is significantly better than YOLO9000 on ShanghaiTech PartA and PartB; but on SmartCity it is a bit inferior to YOLO9000. Overall, we argue that the strength of our regression-based SaCNN is to provide a monolithic approach that performs close to or above the state-of-the-art on a wide range of datasets, from sparse to dense. For the very sparse case a detection-based method might be superior, but it would not perform well in the dense case. It is not clear how to combine a head detector and a density based approach, and this can be our future work.

We illustrate some examples in Fig. 7. Pedestrian crowds in the three samples range from very sparse to very dense. We illustrate the results of both pedestrian and head detectors. Using a small threshold for confidence score produces big prediction, but the bounding boxes are not always accurate (e.g. first row: PDcs > 0:05). In general, YOLO9000 is good at detecting big objects in sparse crowds and is bad with small objects in dense crowds. In contrast, SaCNN can generalize very well from very spare to very dense case. 7. Comparison between YOLO9000 [START_REF] Redmon | Yolo9000: better, faster, stronger[END_REF] and SaCNN. cs denotes the confidence score. For ShanghaiTech PartA and ParB we report the pedestrian detection results, while for SmartCity we report the head detection result.

Conclusion

In this paper we propose a scale-adaptive convolutional neural network (SaCNN) to automatically estimate the density maps and pedestrian numbers of crowd images. It concatenates multiple feature maps of different scales to produce a strong scale-adaptive crowd counter for each image; it introduces a multi-task loss including a relative count loss to improve the network generalization on crowd scenes with few pedestrians. The proposed method can easily adapt to pedestrians of different scales and perspectives. Extensive experiments on standard crowd counting benchmarks demonstrate the efficiency and effectiveness of the proposed method over the state-of-the-art.

We know that the pedestrian sizes vary in according to the perspective changes in crowd images; while the multiple feature maps in SaCNN fire on pedestrians of different sizes. In future work, we want to directly embed the perspective information as a weighting layer into SaCNN. It will produce different weights to combine the feature map outputs at every pixel depending on the perspectives.

Figure 1 .

 1 Figure 1. Top: crowd images. Bottom: ground truth density maps.

Figure 2 .

 2 Figure2. The structure of the proposed scale-adaptive convolutional neural network (SaCNN) for crowd counting. MP: max pooling layer; DeConv: deconvolutional layer; GT: ground truth. We build a single backbone network with a single filter size. We combine the feature maps of multiple layers to adapt the network to the changes in pedestrian scale and perspective. Multi-scale layers share the same low-level parameters and feature representations, which results in fewer parameters, fewer training data required, and faster training. We introduce two loss functions to jointly optimize the model: one is density map loss, the other is relative count loss. The relative count loss helps to reduce the variance of the prediction errors and improve the network generalization on very sparse crowd scenes.

  density map is computed by convolving this delta function using a Gaussian kernel normalized to sum to one:(1) where is the total head number. The sum of the density map is equivalent to the total number of pedestrians in an image. Parameter setting follows[START_REF] Zhang | Singleimage crowd counting via multi-column convolutional neural network[END_REF][START_REF] Sam | Switching convolutional neural network for crowd counting[END_REF][START_REF] Boominathan | Crowdnet: a deep convolutional network for dense crowd counting[END_REF].

Figure 3 .

 3 Figure 3. (a) single-scale model; (b) two-scale model. MP: max pooling layer of stride 1. The outputs of the networks are the density maps (blue-yellow heatmaps) and head counts (yellow cubes). p-conv denotes convolutional layer.

Figure 4 .

 4 Figure 4. Examples for the SmartCity dataset. They consist of both indoor and outdoor scenes with few pedestrians.

Figure 5 .

 5 Figure 5. Multi-scale ablation test on ShanghaiTech dataset. The MAE and MSE are clearly decreased from single-scale to twoscale and scale-adaptive model.

Figure 6 .

 6 Figure 6. Result on ShanghaiTech dataset. Top: PartA; Bottom: PartB. We present six test images and their estimated density maps on the right. Ground truth and the estimated pedestrian numbers are beneath the real images and the corresponding density maps, respectively.

  4 15.7 10.0 11.0 5.9 9.4 SaCNN (GT with perspective) 4.4 26.3 16.8 9.0 4.9 12.3 SaCNN (GT w/o perspective) 2.6 13.5 10.6 12.5 3.3 8.5 Table 4. Comparison of SaCNN with other state-of-the-art on WorldExpo'10 dataset. MAE is reported for each test scene and averaged in the end.

Figure 7 .

 7 Figure 7. Comparison between YOLO9000 [22] and SaCNN. PD: pedestrian detector; HD: head detector; cs confidence score. The numbers below the real images (first column) are the ground truth. Numbers below other images are the estimated pedestrian counts.

Figure 8 .

 8 Figure 8. Comparison of SaCNN and SaCNN(w/o cl). The numbers below the real images are the ground truth. The second column denotes the density maps produced by SaCNN(w/o cl) while the third column is produced by SaCNN. Numbers below the density maps are the corresponding estimated pedestrian counts.

Table 2 .

 2 Multi-task ablation test of SaCNN on ShanghaiTech dataset. cl is short for count loss; acl denotes the absolute count loss while rcl denotes the relative count loss proposed in this paper.

	ShanghaiTech	PartA	PartB
	Method	MAE MSE MAE MSE
	Zhang et al. [33] 181.8 277.7 32.0 49.8
	Zhang et al. [34] 110.2 173.2 26.4 41.3
	Sam et al. [26] 90.4 135.0 21.6 33.4
	SaCNN	86.8 139.2 16.2 25.8

Table 3 .

 3 Comparison of SaCNN with other state-of-the-art on ShanghaiTech dataset.

http://github.com/miao0913/SaCNN-CrowdCounting-Tencent Youtu

We used the published model from[START_REF] Zhang | Singleimage crowd counting via multi-column convolutional neural network[END_REF] and trained the model for[START_REF] Sam | Switching convolutional neural network for crowd counting[END_REF] using their released code.

Acknowledgement. We thank Holger Caesar for his careful proofreading.

UCF CC 50 MAE MSE Lempitsky et al. [12] 493.4 487. [START_REF] Boominathan | Crowdnet: a deep convolutional network for dense crowd counting[END_REF] Idrees et al. [START_REF] Idrees | Multi-source multi-scale counting in extremely dense crowd images[END_REF] 419.5 541.6 Zhang et al. [START_REF] Zhang | Cross-scene crowd counting via deep convolutional neural networks[END_REF] 467.0 498.5 Boominathan et al. [START_REF] Boominathan | Crowdnet: a deep convolutional network for dense crowd counting[END_REF] 452.5 -Zhang et al. [START_REF] Zhang | Singleimage crowd counting via multi-column convolutional neural network[END_REF] 377.6 509.1 Onoro et al. [START_REF] Onoro-Rubio | Towards perspective-free object counting with deep learning[END_REF] 333.7 425.3 Sam et al. [START_REF] Sam | Switching convolutional neural network for crowd counting[END_REF] 318.1 439.2 SaCNN 314.9 424.8 used multi-source features to estimate crowd count while [START_REF] Boominathan | Crowdnet: a deep convolutional network for dense crowd counting[END_REF] used a multi-column CNN with one column initialized by VGG net [START_REF] Simonyan | Very deep convolutional networks for large-scale image recognition[END_REF]. [START_REF] Onoro-Rubio | Towards perspective-free object counting with deep learning[END_REF] adopted a custom CNN network trained separately on each scale; fully connected layers are used to fuse the maps from each of the CNN trained on a particular scale.

Our method achieves the best MAE 314.9 and MSE 424.8 compared to the state-of-the-art. The smallest MSE indicating the lowest variance of our prediction across the dataset.

Results on SmartCity

For SmartCity there are too few pedestrians to train a model. We employ the model trained on ShanghaiTech PartB and test it on SmartCity. Crowd scenes in Shang-haiTech PartB are outdoors and relatively sparse while in SmartCity they are both indoor and outdoor scenes with few pedestrians (7.4 on average, see Table . 1 and Fig. 4). Referring to the multi-task ablation test on ShanghaiTech (Sec. 4.3), we test both SaCNN(w/o cl) and SaCNN in Table . 6 to show how much improvement is achieved by SaCNN over SaCNN(w/o cl). By adding the relative count loss in the network, the MAE and MSE clearly drops 9.2 and 11.8 points, respectively. Fig. 8 illustrates some test examples. The density map produced by SaCNN is sparser compared to that of SaCNN(w/o cl); it is more likely to fire on the real pedestrians. While the result of SaCNN(w/o cl) reflects more subtle details of the image which are unrelated to pedestrians (e.g. the third row).

In Table 6 we also test [START_REF] Zhang | Singleimage crowd counting via multi-column convolutional neural network[END_REF][START_REF] Sam | Switching convolutional neural network for crowd counting[END_REF] 2 : both are trained on PartB and perform poorly on SmartCity; the MAE are 40.0 and 23.4, respectively. Our best MAE is 8.6 close to the


Marta Perez
email: marta.perezmiguel@esi-group.com

Adrien Scheuer
email: adrien.scheuer@ec-nantes.fr

Emmanuelle Abisset-Chavanne
email: emmanuelle.abisset-chavanne@ec-nantes.fr

Amine Ammar
email: amine.ammar@ensam.eu

Francisco Chinesta
email: francisco.chinesta@ensam.eu

Roland Keunings
email: roland.keunings@uclouvain.be

On the multi-scale description of micro-structured fluids composed of aggregating rods

Keywords: Aggregate, Cluster, Jeffery's equation, Non-ellipsoidal particles, Concentrated suspensions, Multiscale modelling

When addressing the flow of concentrated suspensions composed of rods, dense clusters are observed. Thus the adequate modelling and simulation of such a flow requires addressing the kinematics of these dense clusters and their impact on the flow in which they are immersed. In a former work we addressed a first modelling framework of these clusters, assumed so dense that they were considered rigid and their kinematics (flow-induced rotation) were totally defined by a symmetric tensor c with unit trace representing the cluster conformation. Then, the rigid nature of the clusters was relaxed, assuming them deformable, and a model giving the evolution of both the cluster shape and its microstructural orientation descriptor (the so-called shape and orientation tensors) was proposed. This paper compares the predictions coming

from those models with finer-scale discrete simulations inspired of molecular dynamics modeling.

Introduction

Suspensions involving rods are described at three different scales. At the microscopic scale, the motion of each rod is tracked using Jeffery's equation [START_REF] Jeffery | The motion of ellipsoidal particles immersed in a viscous fluid[END_REF] and their impact on the fluid rheology evaluated from one of the available models [START_REF] Petrie | The rheology of fibre suspensions[END_REF] [24] [START_REF] Batchelor | The stress system in a suspension of force-free particles[END_REF] [23] [START_REF] Hinch | The effect of Brownian motion on the rheological properties of a suspension of non-spherical particles[END_REF] [26] [START_REF] Hinch | Constitutive equations in suspension mechanics. Part II[END_REF]. At the mesoscopic scale, the individuality of particles is replaced by a distribution function giving the probability of finding a particle at a given position and time and having a given orientation. At that scale, usual physical coordinates (space and time) are complemented with some conformational coordinates [START_REF] Doi | The Theory of Polymer Dynamics[END_REF] [START_REF] Bird | Dynamic of polymeric liquid[END_REF] (in the present case the orientation described by the unit vector p) in order to retain the main fluid features. Finally, at the macroscopic scale, only the moments of the distribution function are retained -the so-called orientation tensors -whose time evolution only involves the physical coordinates.

Moving from the microscopic to the mesoscopic scale is motivated by the computational complexity that the consideration of large population of interacting particles entails (as well as the particles-fluid interactions). In turn, mesoscopic descriptions are confronted to issues related to their multidimensional character, and the associated inability of most experienced discretization techniques to address their simulation. For circumventing the curse of dimensionality, several techniques exist: (i) most of them are based on the used of computational particles [START_REF] Öttinger | Smart polymers in finite element calculation[END_REF] [10] [START_REF] Wapperom | Numerical simulation of branched polymer melts in transient complex flows using pom-pom models[END_REF] [START_REF] Chinesta | On the solution of the Fokker-Planck equation in steady recirculating flows involving short fibre suspensions[END_REF] [17] [18]; (ii) other procedures consider standard discretization techniques with adapted approximations [START_REF] Lozinski | A fast solver for Fokker-Planck equation applied to viscoelastic flows calculations: 2D FENE model[END_REF] [11]; (iii) finally a third group consists of the use of separated representations proposed some years ago by the authors, with as main ingredient the so-called Proper Generalized Decomposition [START_REF] Ammar | A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids[END_REF] [6] [START_REF] Mokdad | On the simulation of kinetic theory models of complex fluids using the Fokker-Planck approach[END_REF] [14] [START_REF] Chinesta | The Proper Generalized Decomposition for advanced numerical simulations[END_REF]. At the macroscopic scale, the equations governing the time evolution of the distribution moments usually involve closure approximations whose impact on the results is unpredictable [START_REF] Keunings | On the Peterlin approximation for finitely extensible dumbells[END_REF] [START_REF] Chiba | On the fiber orientation in steady recirculating flows involving short fibers suspensions[END_REF].

In [3], the flow model of a suspension composed of rods was established, in the dilute and semi-dilute regimes by considering nine structural bricks, three at each scale (microscopic, mesoscopic and macroscopic). These three key bricks are: (i) the considered conformational variable, (ii) the equation governing its time evolution and (iii) its contribution to the suspension stress.

When the concentration increases, particles tend to aggregate [33] [34] [35] creating a new microstructure with an intermediate scale. Indeed, instead of having rods dispersed into a fluid matrix, the flowing system is composed of dense rod aggregates immersed into the fluid matrix.

A first attempt to describe such flowing systems has been proposed in [3]. There, it was assumed that these dense clusters of rods are and remain rigid enough to evolve as a rigid solid leading to a cluster flow-induced kinematics depending on a single conformation tensor [3]. The main results will be summarized in Section 2. This framework was extended [START_REF] Binetruy | Flows in polymers, reinforced polymers and composites. A multi-scale approach[END_REF] by considering the flow-induced motion and deformation of deformable aggregates, in which orientation and shape time evolutions are described by using two conformation tensors. The corresponding model is also summarized in Section 2.

The present work only addresses the cluster kinematics, rheology will be addressed in a future work, because it requires formulating the behaviour within a generalized continuum framework, as considered when addressing other media with internal structure [2,19,[START_REF] Eremeyev | Foundations of micropolar mechanics[END_REF][START_REF] Pietraszkiewicz | On natural strain measures of the nonlinear micropolar continuum[END_REF].

While in the case of rigid cluster we could validate the model using the existing analogy between tri-dumbbells and ellipsoids, in the case of deformable clusters, the flow-induced deformation will be validated by comparing the model predictions with direct numerical simulations inspired by molecular dynamics -MD -descriptions, including rods and their interactions.

After this introduction, Section 2 revisits the description of rigid and deformable clusters composed of rods. Then in order to validate the predictions Section 3 proposed a finer-scale discrete description inspired of moleculardynamics simulations. Finally Section 4 presents and discusses some numerical results.

Revisiting description of rigid and deformable clusters composed of rods

This section summarizes the main elements involved in the modeling of rigid and deformable clusters, deeply described in [3] and [START_REF] Binetruy | Flows in polymers, reinforced polymers and composites. A multi-scale approach[END_REF] respectively.

Rigid clusters

Let consider a 3D rigid cluster, sketched in Fig. 1, consisting of N/2 rods R j of length 2L j . Each rod R j is assumed containing two beads at its ends on which hydrodynamic forces apply. Thus, the cluster contains N beads B i , i = 1, • • • , N. The location of each bead B i with respect to the cluster center of gravity G is represented by S i q i , where q i is the unit vector pointing from G to B i .

Brownian effects are neglected and only hydrodynamic forces, assumed acting at each bead, are retained. Thus, on each bead located at position S i q i (Fig. 1) acts a force F i proportional to the difference between the velocity of the unperturbed flow at the bead location and the velocity of the bead itself:

F i = ξ (V 0 + ∇v • q i S i -V G -qi S i ), ( 1
)
where ξ is the friction coefficient, v the flow velocity field, V 0 the fluid velocity at the cluster centre of gravity G and V G the velocity of the cluster center of gravity itself. The equilibrium neglecting inertia terms implies

0 = i=N i=1 F i = N (V 0 -V G ) + ∇v • i=N i=1 S i q i - i=N i=1 S i qi , (2)
where both sums in Eq. ( 2) vanish, the first one as a direct consequence of the definition of the center of gravity, and the second because the cluster is assumed rigid. Thus, Eq. (2) becomes

V 0 = V G , (3)
implying that the cluster center of gravity is moving with the fluid velocity at that position. The torque created by the forces applied on bead B i is given by

M i = S i q i × F i , (4)
whose resultant must also vanish:

i=N i=1 M i = 0. (5)
By developing the balance of torques (the interested reader can refer to [3]), it finally results:

ω = (I -c) -1 • ( : (∇v • c)) , ( 6
)
where ω represents the cluster angular velocity and c is the conformation tensor defined from

c = i=N i=1 S 2 i q i ⊗ q i i=N i=1 S 2 i . ( 7
)
An extremely important consequence of this analysis is that rigid clusters composed of rods having the same conformation tensor c rotate at the same angular velocity.

As the conformation tensor c is symmetric and positive definite, it has real eigenvalues and eigenvectors. In 3D, the three mutually perpendicular eigenvectors will be denoted by u 1 , u 2 and u 3 , with the associated eigenvalues τ 1 , τ 2 and τ 3 respectively. Imagine a rigid cluster composed of three rods oriented in directions u 1 , u 2 and u 3 with respective lengths √ τ 1 , √ τ 2 and √ τ 3 . The conformation tensor of such a three-rod cluster coincides with c and then both tensors have the same rotary velocity. Thus in [3] it has been proven the link between a rigid cluster composed of three mutually orthogonal rods and the Jeffery's triaxial-ellipsoid.

Deformable clusters

In the case of deformable clusters, two types of forces were assumed acting on each bead of a generic rod R (of length 2L) [START_REF] Binetruy | Flows in polymers, reinforced polymers and composites. A multi-scale approach[END_REF].

One, F H i , is due to the fluid-rod friction once again modelled as

F H i = ξ (v i 0 + ∇v • p i L -v i G -ṗi L) ( 8 )
where the superscript "H" refers to its hydrodynamic nature, v i 0 is the fluid velocity (assumed unperturbed by the presence of the cluster) at the rod R i centre of gravity G i and v i G the velocity of the rod R i centre of gravity G i . The other one, F C i , is due to the rods entanglements. That force is assumed scaling with the difference between the rigid motion velocity (the one that the bead would have if the cluster would be rigid) v R B i and the real one v i G + ṗi L. As proven in the previous section, the bead velocity when assuming the cluster rigid reads:

v R B i = V G + W • S i q i = V 0 + W • r i + W • p i L, (9)
where the fact that V G = V 0 was taken into account. In the previous equation r i is the vector connecting the cluster centre of gravity G to the rod centre of gravity G i , i.e. r i = G i -G and tensor W derives from the rigid rotary velocity ω given by Eq. ( 6) from

W • p i = ω × p i , ∀p i . ( 10
)
Thus, the contribution to the bead force due to collective effects (a sort of mean field) when considering the generic rod R i reads:

F C i = μ (V 0 + W • r i + W • p i L -v i G -ṗi L), ( 11
)
and the net force acting on the bead located at

G i + p i L is given by F i (G i + p i L) = F H i (G i + p i L) + F C i (G i + p i L).
The linear momentum balance, neglecting inertia effects, allows us to obtain the velocity of the rods centre of gravity [START_REF] Binetruy | Flows in polymers, reinforced polymers and composites. A multi-scale approach[END_REF]

v i G = V 0 + ξ ξ + μ ∇v • r i + μ ξ + μ W • r i . ( 12
)
Now, the angular momentum balance leads to the rods rotary velocity (the interested reader can refer to [START_REF] Binetruy | Flows in polymers, reinforced polymers and composites. A multi-scale approach[END_REF] for he exhaustive derivation)

ṗi = ξ ξ + μ ṗJ i + μ ξ + μ W • p i = ξ ξ + μ ṗJ i + μ ξ + μ ṗR i , ( 13
)
where ṗJ i represents the orientation evolution of a rod in absence of collective effects (dilute regime described by the Jeffery's equation) and ṗR i the one of a rod in a rigid cluster.

It can be noticed that when ξ μ hydrodynamic effects are preponderant and the rod kinematics is governed by the Jeffery's equation, i.e. ṗi ≈ ṗJ i . In the opposite case, μ ξ, the cluster is too rigid and the rods adopt the velocity dictated by the rigid cluster kinematics ṗi ≈ ṗR i . The main macroscopic descriptors of a deformable cluster are its shape and its microstructure.

Macroscopic description: clusters inertia and shape

Integrating the position of the center of gravity of each rod composing the cluster from Eq. ( 12), it is natural to obtain the cluster inertia and shape.

The cluster inertia tensor S is defined from a continuous description of the cluster: the rods individuality is replaced by a distribution function ψ r (r) and then integrated:

S = S r ⊗ r ψ r (r) dr. ( 14
)
Its time evolution, according to [START_REF] Binetruy | Flows in polymers, reinforced polymers and composites. A multi-scale approach[END_REF] results

Ṡ = ξ ξ + μ ∇v • S + S • (∇v) T + μ ξ + μ (W • S -S • W) . ( 15
)
The trace of S gives an information on the cluster size. A normalized inertia tensor -called shape tensor s -can be defined as:

s = S Tr(S) . ( 16
)

Macroscopic description: orientation

Now, if the orientation of the rods of a deformable cluster is assumed to be given by the orientation distribution ψ p (p), the time derivative of its second order moment ȧ yields [START_REF] Binetruy | Flows in polymers, reinforced polymers and composites. A multi-scale approach[END_REF]:

ȧ = ξ ξ + μ ȧJ + μ ξ + μ ȧR , ( 17
)
whose objectivity was proved in [START_REF] Chinesta | From single-scale to two-scales kinetic theory descriptions of rods suspensions[END_REF], and where ȧJ and ȧR are given by

ȧJ = ∇v • a + a • (∇v) T -2 A : D ȧR = W • a + a • W T , ( 18
)
with A the fourth order orientation tensor expressed from the second order one by considering any of the numerous closure relations proposed in the literature [4] [START_REF] Dupret | Modelling the flow of fibre suspensions in narrow gaps[END_REF] [31] [START_REF] Pruliere | Recirculating flows involving short fiber suspensions: Numerical difficulties and efficient advanced micro-macro solvers[END_REF].

It has just been proven that the conformation of a deformable cluster is defined from both the orientation tensor a and the inertia tensor S. The evolution of both tensors makes use of tensor W that depends itself on the conformation tensor c. Tensor c is very close to tensor S; the first is defined from the vectors joining the cluster centre of gravity with each rod bead, whereas the second one involves vectors joining the cluster centre of gravity with the rods centre of gravity. If the length of the rods are very small compared to the cluster size, both tensors are very close and consequently tensor W can be evaluated by using s instead of c. In [START_REF] Binetruy | Flows in polymers, reinforced polymers and composites. A multi-scale approach[END_REF] the following expression was obtained:

c = S + L 2 a Tr(S) + L 2 , ( 19
)
that as soon as L 2 Tr(S) leads to c ≈ s.

Fine-scale discrete simulation

In order to compute the reference solution of a moving cluster suspending in a fluid flow, we proceed to a direct numerical simulation based on a molecular dynamics representation of the entangled rods composing a dense cluster. This modeling approach is based on the following assumptions: (i) each of the R rods consists of a set of P r connected particles (the total number of particles in the system being P); (ii) particles interactions are described from appropriate potentials, in particular the Lennard-Jones potential V LJ used to describe the inter-particles interactions (and consequently ensuring inter-rods interaction), and two other potential, V E and V B , used to describe the rod elongation and bending respectively, see Fig. 2. Thus the total potential reads where j refers to the rods R j , R(i) to the rod to which particle i belongs, and indexes i and k are related to particles P i and P k . Index j in potentials V E i,i+1;j and V B i-1,i,i+1;j indicates that particle P i belongs to rod R j . The Lennard-Jones potential reads

V = R j=1 P r -1 i=1 V E i,i+1;j + R j=1 P r -1 i=2 V B i-1,i,i+1;j + P i=1 P k>i k / ∈R(i) V LJ i,k (20)
V LJ i,k = 4ε σ d ik 12 - σ d ik 6 , ( 21
)
with d ik = ||x kx i || the distance between particles P i and P k , located at positions x i and x k respectively, and and σ the two usual parameters involved in the Lennard-Jones potential. The elongation potential is given by

V E i,i+1 = K E 2 1 - d ij d eq 2 , ( 22
)
where d eq is the equilibrium distance between two particles, distance at which the potential reaches its minimum (and consequently the associated force vanishes). In the previous expression K E reflects the potential intensity. The bending potential between three successive particles belonging to the same fibre reads

V B i-1,i,i+1 = K B 2 (θ i-1,i,i+1 -θ eq ) 2 , ( 23
)
where θ i-1,i,i+1 is the angle defined by vectors joining particles i -1, i and i, i + 1 with θ eq the angle at equilibrium. In our study we consider without loss of generality θ eq = 0. Again, the potential intensity is described from K B .

Force applying at each particle results from the potential derivative according to

F I i = - ∂V ∂x i . ( 24
)
The other force acting on each particle is the one related to the fluid drag F D i . Let v(x) be the fluid velocity at position x, assumed unperturbed by the rods presence, the drag force reads

F D i = ξ(v(x i ) -ẋi ), ( 25
)
where ẋi denotes the velocity of particle P i .

The linear momentum balance involving particle P i reads

F i = F D i + F I i = ma i , ( 26
)
with the particle acceleration

a i = d ẋi dt = d 2 x i dt 2 . A second order time integration scheme is considered, consisting of ⎧ ⎨ ⎩ a n+1 i = F n i m x n+1 i = x n i + ẋn i Δt + 1 2 a i (t)(Δt) 2 ẋn+1 i = ẋn i + 1 2 a n i + a n+1 i Δt , ( 27
)
where the superscript n refers to the time step, t n = nΔt. Prior to proceed with the time integration, equations are rewritten in dimensionless form, by considering as characteristic variables the length : σ the energy : ε the mass : m the velocity : ε/m the acceleration : ε/(mσ) the time : σ m/ε that allows writing the dimensionless model in which for the sake of clarity we do not change the notation for designating the dimensionless variables.

Thus, we obtain

⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ V i,j = 4 1 d ij 12 -1 d ij 6 V E i,i+1 = KE 2 1 - d ij d eq 2 V B i-1,i,i+1 = KB 2 (θ i-1,i,i+1 -θ eq ) 2 F I i = -∂V ∂x i F D i = ξ(v(x i ) -ẋi ) F i = a i , ( 28
)
where KE = K E ε , KB = K B ε , ξ = ξ √ εm/σ, with KB = 100, KE = 100 and the dimensionless equilibrium distance d eq = 2 1/6 . The applied flow consists of a simple shear flow with dimensionless shear rate γ = 5. Thus, at the microscopic scale, as soon as K E and K B are taken large enough to represent almost non-deformable rods, the model only contains one parameter that controls numerical simulations, ξ.

Numerical results

In this section, we first present numerical simulations to illustrate the behaviour of the proposed model, and then a comparison of the model with fine-scale direct simulations.

The equations governing the rate of change of the cluster orientation and inertia tensors, Eqs. ( 17) and ( 15) respectively, have similar expressions. They contain a term, the last one, that introduces the mean field effects, in particular the cluster rotation, scaling with tensor W that in turn depends on the cluster shape.

In order to better understand the underlying physics of those equations, we are considering both rigid and deformable clusters of different aspect ratio and evaluate the time evolution of their inertia tensor.

Firstly, Fig. 3 compares for two rigid clusters of different aspect ratio the time evolution of their inertia tensor S. As expected from our previous works [3], inertia tensor is simply rotated with a period that scales with the cluster aspect ration, i.e. the higher the cluster aspect ratio, the larger the rotation period. When examining the evolution of the trace of the inertial tensor over time, it can be noticed that it remains constant.

Secondly, Fig. 4 presents similar results but now for deformable cluster with the same initial aspect ratios. It can be noticed that inertial tensor remains periodic with a similar evolution of its period with respect to the cluster aspect ratio. Moreover, the cluster deformability results in a periodic evolution of the tensor trace, as Fig. 5 reveals. Thus, the cluster is stretched and then compressed during a complete rotation, while keeping its perfect periodicity. Moreover, as expected, the higher the cluster aspect ration, the larger the amplitude of the inertia tensor trace evolution.

Figure 6 compares now the model predictions with direct simulation. The applied flow and the considered inter-rods interaction potential almost guarantee the cluster integrity, that is, the cluster rotates while slightly deforming, but after a complete rotation the initial configuration is almost recovered. In this figure, it can be noticed that direct numerical simulation exhibits some amount of irreversible cluster deformation, with the consequent impact on the cluster rotary velocity and in its period of rotation, increasing as the cluster aspect ration enlarges. Both solutions are in good agreement.

Figure 7 compares, for the aggregate considered in Fig. 6, the prediction of the model for a deformable cluster with the prediction obtained by assuming the cluster is rigid. It can be noticed that as discussed above, cluster deformability induces a slight increase of the rotation period.

Figure 8 compares model prediction and direct simulation for larger shear rates (larger with respect the rods interaction preserving the aggregate integrity). The model prediction differs from direct simulation since the the applied shear rates produces cluster degradation, as evidenced in Fig. 9, where some rods detach from the cluster. This scenario compromises the validity of the proposed macroscopic model and defines the limit of its interval of validity.

Conclusions

In this work, a multiscale model of deformable clusters, based on the use of two tensors, the first associated to the global cluster shape and the second to the orientation of the rods composing is solved an its predictions compared with finer descriptions inspired from molecular dynamics. From both scale simulation it was proved that clusters deform while rotating, and it was found that the model almost captures the shape and orientation evolution. When the applied shear rate becomes too large, rods detach from the clusters and model predictions exhibit significant differences with respect to direct numerical simulations. Compliance with Ethical Standards. The authors declare that they have no conflict of interest.

Fig. 1

 1 Fig. 1 Rigid cluster composed of rods.

Fig. 2

 2 Fig. 2 Sketch of rods, particles and potentials

12 Fig. 3

 123 Fig. 3 Rigid clusters with different aspect ratio.

12 Fig. 4

 124 Fig. 4 Deformable clusters with different aspect ratio.

Fig. 5

 5 Fig. 5 Inertia tensor trace time evolution.

Fig. 6

 6 Fig. 6 Comparison of cluster orientation and inertia evolution: model prediction (dashed line) versus direct simulations.

Fig. 7

 7 Fig. 7 Comparison of cluster orientation and inertia evolution: deformable versus rigid cluster model.

Fig. 8

 8 Fig. 8 Comparison of cluster orientation and inertia evolution: model prediction (dashed line) versus direct simulations for larger applied shear rates.

Fig. 9

 9 Fig. 9 Aggregate conformation: (left) initial configuration and (right) configuration after a first rotation.


Philippe Dumas
email: dumas@univ-tln.fr

Franck Bulinge
email: bulinge@univ-tln.fr

Eric Boutin
email: boutin@univ-tln.fr

Éticas Dimensões

Em Colocações De Km

Profissionais

Ethical dimensions of KM in professional settings

Keywords: informação, administração, ética, qualidade, inteligência ETHICAL information, management, ethics, quality, intelligence

INTRODUCTION

Ethics may appear as a fashionable reflection topic. It is returning loudly in all sectors of the social life. Traditionally associated to sciences of the nature (bound to the human existence) or of matter (bound to the human survival), it invests today the field of sciences of the mind, of which makes part Knowledge Management. It is not indifferent. Knowledge Management and social studies in general now take such an importance that one realizes the dangers that they can carry and tries to canalize them on the path of the morals. Among hypotheses that explain this contemporary situation, one can mention the fear of a moral dead end to which leads that society of illusions (virtuality?), disenchantment, hyper relativism, atomization of knowledge and cultures, individualism, transformation of social ties, all based on the omnipotence and omnipresence of technology.

In this paper we shall adopt another view. Ethics is not a phenomenon of fashion, although the intensity of ethical debates seems linked to a fashion pattern. Concern for ethics is as old as mankind. As stated by Comte-Sponville (2001) [START_REF] Comte-Sponville | Dictionnaire philosophique[END_REF] , "ethics is a work, a process, a movement: it is the reflexive path for living, inasmuch as it tends to the good life, as the ancient Greeks said, or the least bad possible, and it is the only wisdom as a matter of fact." Therefore to treat the ethics of the development of information sciences and knowledge management is a permanent necessity to which this communication would like to contribute. It is partitioned in three; at first we recall the main concepts linked to an ethical reflection and the field of knowledge management; then we address a case study in which our job of KM professionals is confronted with ethical issues; we conclude by proposing a categorization of these issues and sketching out basics of ethical behavior.

CONCEPTUAL FRAMEWORK

Ethics

According to the Webster dictionary, "ethics is the part of philosophy that studies foundations of the morals ; it is the set of moral principles which are the basis of the someone's conduct". For A. Comte-Sponville (ibid., p219), in his Philosophical Dictionary, an ethics answers the question : "how to live ? ". "It is always particular to an individual or a group. It is an art of living : it often tends toward happiness and culminates in wisdom".

Ethics includes the morals, that answers to the question : " what should I do ? ". Thus "moral commands, ethics recommends".

Morals

Taking the Webster, we will say that "morals is the set of conduct rules considered good in absolute way, or ensuing from a certain conception of life". A. Comte-Sponville (ibid., p389) specifies that "morals is the whole set of our duties that we impose to ourselves, independently of any expected reward or sanction". Morals is unprejudiced.

Deontology

Deontology refers to the good professional conduct. It sets forth principles of moral essence, but targeted on a particular public. The birth of a deontology indicates the state of a profession that reaches maturity and tries to make itself recognized. Starting from a nonwritten code, one arrives at an explicit and public formulation. The profession needs the experience of the day-to-day practice and of the influences that strive to dominate it, obviously economic influences, but as well as ideological and cultural ones. Physicians have experienced it since antiquity. Journalists since the beginning of the XIX° century. Internauts, information scientists, KM professionals are presently at their deontological stammers for at least two reasons. First, they are multifaceted professions, each one declining his/her/its version of the deontology (journalists, merchants, webmasters, documentalists, multimedia designers, programmers, etc.). Then, for lack of extensively admitted referents, charts and codes they sketch out are bound to evolve.

Codes of ethics and professional charts

In general, these were born among technicians and professionals themselves (for example Bill Gates in the United States, or Telecom engineers in France) worried of the drifts of their tool and of the bad press that have tendency to impede their diffusion. So, they propose various "charts of electronic edition" and the like while academics set forth "user charts".

The problem is that of the acceptance and the acceptability of these charts by the concerned parties, users, producers, transmitters of information. Ensues the question of their enforcement that cannot be assured by a moral pressure only, i.e. a form of individual ethics.

It has to be turned into law. However as one is going to see below, law is inevitably phased in time and space. Besides, law is an antinomic response to the search for liberty that dragged the so promising starting of the internet, including newsgroups, freedom of expression, free access to open source software, sharing of knowledge, diffusion of music, etc. But Anglo-Saxons (United States, Canada, Australia,…) are very fond of "home made" codes of ethics and, for instance, propose classes such as "Creating a Code of Ethics for Your Organization" (C. MacDonald, 2002) [START_REF] Macdonald | [END_REF] . In Latin countries, such an attitude is rarer. A recent survey of the Ifp 3 (2002) indicates that in French regional press, 18% only have an internal deontology Code written by journalists and 59% written by the editors and adopted by professionals.

Law

Law is posterior to ethics. The law applies "hic and nunc"; it is therefore timed and localized. On the contrary, online information is asynchronous and delocalized. In our opinion, the law can only place barriers against already listed behaviors. To legislate too much risks to block the development of our "information society"; not to legislate enough places the moral responsibility on appreciations (notably by the judge, but not solely) to the case by case, therefore on a certain arbitrary mixed with true laxity, as can be seen with recent sentences pronounced in the US for Microsoft case. It is interesting to note that the Anglo Saxons, that are rather adepts of the second way, i.e. laissez-faire, have, in this domain, greatly influenced the French administrative culture. The latter has made proof of a relative legislative restraint concerning internet and information management during these last years.

Nétiquettes

Curious phenomenon, the emergence of nétiquettes is a characteristic of the libertarian wind that blew on the generalization of the internet in years 80 in the United States. One doesn't know from where they come ; they spread out themselves by drag and stick. They don't make reference to any outside authority. They call to individual responsibility, thus forming an auspicious ground for the ulterior development of ethical concepts.

Merchant ethics

Whatever was the scientists' dream of a new frontier for intellectual freedom stemming from the technology of internet, it is now obvious that merchants are turning it into a commercial tool. Following the same process of emergence that we have described for engineers, merchants have felt the need for ethical charts. These generally deal with the protection of confidentiality, the respect of copyright and the security of transactions. It is at this price that the internauts could be attracted in the new virtual shopping malls. These prescriptions of merchant ethics are to be taken in account by the specialist of information, because whether he/she likes it or not, he/she has to insert him/herself in the economic process, even though the access or diffusion is free.

But those ethical moves by corporate business should not let us forget that capitalistic processes are also at work. They underlie economic development of the internet and they obey to the natural tendency towards more profits through more or less moral ways. D. Bollier (2002) [START_REF] Bollier | Silent theft: The Private Plunder of our Common wealth[END_REF] notes that "the struggle for control of the internet is a modern version of range war". Dealing with the fact that, although the internet infrastructure has been set up on public funding, big corporations are now fighting to privatize it, he comments: "It's almost human nature: if you're allowed the use of something for enough time, you begin to think you have a right on it, even that you own it." So is the internet, and also the airwaves on which data is flowing. He calls this process "a silent theft" and accuses Microsoft and the like to "enclose the Web experience within digital walls that resemble those of a shopping mall" without much concern for public service. This example shows that the same corporation can simultaneously sets forth ethical principles in its consumer communication and behave economically in a clearly non ethical mode.

Co-regulation and responsibility

This brief review of sources of an ethics of the informational activity brings us to adopt two principles to pursue our development. The first one is that of "co-regulation" of the internet. The second one is that of the individual responsibility.

Decreeing rules by the administrative or political authorities proved its limits, as well in practice as in theory, as well for their acceptability as for their applicability. The pure selfregulation is a libertarian dream that cannot achieve itself in global economy dominated by the United States. "A consensus currently clears himself in favor of a form of regulation of the internet by its own actors or « co-regulation », because the other means of regulation must be abandoned. Thus, apart from the fact the internet endures an overflow of applicable legislation rather than a supposed legal vacuum, any state regulation in the domain of the internet would present a certain number of inconveniences from the qualitative viewpoint.

The principal risks in elaborating ethical norms by the public powers are the lack of knowledge of the technique, the working and specificities of the internet. […] The coregulation doesn't mean the absence of regulation or the irresponsibleness of actors of the internet" (Beaussant, 2001, p83) [START_REF] Beaussant | La charte de l'internet a-t-elle encore un avenir ?[END_REF] .

On the contrary, responsibleness becomes a major stake, as indicates P. Brunet (2001) [START_REF] Brunet | L'éthique de la responsabilité individuelle dans la société de l'information[END_REF] , while concluding that "individual responsibility constitutes the ethical positioning of everybody facing technological change and the founding value of viable societies". We will put it to the heart of our findings.

KNOWLEDGE MANAGEMENT AT THE CROSSROAD OF ETHICS

Classically, KM is made of a series of procedures based on information manipulation which include (Quoniam, 1999) [START_REF] Quoniam | Intelligence competitive, enjeux et outils, lecture, Semanha de conhecimento[END_REF] :

• Information gathering in different format (internal and external, factual and textual, formal and informal) and from different sources (data bases, web, newsgroups, Cd-Rom, etc.); • Information structuring both in presentation and contents, manually or automatically;

• Information analysis in order to cope with the needs of the decision maker:

• Information evaluation in order to trace its origin and how it has been made available, especially in the field of competitive intelligence where disinformation is a current practice;

• Information recording with its issue of security and reliability of the data warehouse:

• Information retrieval so that the relevant information is provided out of the huge masses of data;

• Information intelligence which allow to elaborate refined information out of raw data, to understand the environment of decision making, to draw inferences, to trace relationship, to complement information from various sources, to select the right information for the right person, in other words calibrate information to the level of decision;

• Information valuation to really add value i.e. meaning in the professional setting by synthesizing, providing keen expertise of the domain, discovering opportunities and discerning those weak signals which normally escape bulk analysis;

• Information accessibility which deals with determining the right to access the contents of data bases and strategic data.

All these steps of information processing in the KM professional setting imply the notion of qualitative rather than quantitative evaluation and subsequently are liable to ethical consideration, whether at the level of individual morals or with respect to legal constraints.

The key issues that we can immediately point out in relation with KM are summarized in the quality of information, which is the basis for decision, and its trustworthiness. These are at least as crucial as the traditional issues of privacy, intellectual property or security which are commonly invoked. We are going to see how this happen on a specific case study.

A CASE STUDY: HOW TO EXTRACT MEANINGFUL INFORMATION FROM NEWSGROUPS

Newsgroups are forums on the internet which allow any person connected to know the opinion of other internauts about a theme of discussion, and to give anybody or everybody his/her own opinion. They are places of casual and emergent information exchanges by a community of co-actors in a complex communication process. The themes, or centers of interest, are in the scientific domain as well as economic or societal ones that may interest professionals. These newsgroups are typically new outcomes of information technology and provide new ways of communication. Interesting enough is that they indirectly may provide a lot of information about people and the way they think about the theme of discussion, hence be the basis for new knowledge.

Incentives of actors that participate in newsgroups are varied and can cover the gratuitous practices of information exchanges, to interventions aiming at publicizing oneself, or intentions having for objective to launch campaigns of rumors or disinformation.

Exploiting the information of a newsgroup may yield either seizing emergent information opportunities that are located at the level of weak signals or avoiding the consequences that could provoke a rumor by deactivating it as early as it appears.

For these two reasons, the analysis of newsgroups and discussion forums is a component of a global approach to offensive and defensive watches. It concerns large corporations as well as small and middle sized enterprises. In professional setting, it especially answers the following issues:

• identification of experts of the domain;

• follow up of the image of an enterprise in a given newsgroup;

• the most upstream possible identification of a rumor;

It is the vigil on the informational risks. For example, corporations in oil or nuclear industries have direct interest to identify or to let identify opinion leaders in discussion groups linked to active environmentalists (boycott, demonstrations, etc.), to know who they are, what they are searching for, how and towards whom should these corporations communicate to deactivate a crisis.

An academic study was conducted at the University of Toulon by the Laboratory

LePont on the corpus of a French newsgroup activity (veille-abonnement@egroups.fr) during year 2001.

• 1343 questions have been posed by 630 different actors

• 3124 interventions in total; an intervention is a question or an answer.

• 653 actors have answered questions

• 1025 actors have posed or answered questions

The method for extracting weak signals from newsgroup can be summed up in a sequence of steps out of which we extract four typical.

1. to collect mail exchanges. Raw data are of the type illustrated in figure 1. Please note that all following figures are real printouts with reduced legibility so as to preserve anonymity of actors, one of the ethical issues of our case study.

CONCLUSION: HOW TO BEHAVE ETHICALLY AS KM PROFESSIONALS

We have seen in the first section that deontological rules and ethical principles are not lacking in our field, following the professional practices of journalists, documentalists, webmasters and other information professionals. Apparently the answers could be found easily in that professional corpus. However, the experience of our academic study has confronted our research team with actual ethical issues. We are at the core of practical ethical questions because several deontological principles were conflicting while the law is not yet established that would have drawn a clear delineation between what can be done and what shouldn't be done. We have deeply realized the importance of ethical concern when our study was unintentionally made accessible to the members of the newsgroup. Later, those have let known their reactions on the list and in private. We are going to elaborate on this case in order to arrive at some practical guidance.

It's not a surprise that watching newsgroups would raise divergent opinions. First, any kind of watching is more or less associated with intelligence in its military or criminal acceptation, even with eavesdropping. Hence not recommendable. Second, watching e-mails is controversial since mailing to the group may be taken as private mail as well as publication on a media. Hence the law is not helping at present. Third the use and interpretation of data are far from being methodologically established (for instance: what is the representativity of the sample?). Hence how to draw conclusions from such a study.

Following our accidental divulgation of raw data on the web, we have received a bunch of mails which we can classify in five categories summarized in the following assertions from the most negative to the most positive:

• threat of judiciary follow up for violation of the French law "Informatique et liberté"; • emotional reactions based on the fact that invisible colleges (i.e. the groupings shown in figure 3) were revealed;

• inefficiency of workgroup analysis due to the garbage contents of most messages;

• effectiveness of workgroup analysis to disclose weak signals and protect major interests (public or private) • deep comprehension of our approach as a by-product of our society of information in the direction of competitive intelligence;

• satisfaction to see in the open the kind of results that many corporations (especially the big ones) are routinely obtaining in the shadow.

The prominent finding is that a single issue in knowledge management produces a large variety of responses, based on ethical or legal values, from rejection to enthusiastic acceptance. Interestingly enough is to browse the background of the authors of those comments. Although not quantitatively established, it is clear that positive comments are coming from professionals that adopt an explicit ethics of usage of data and transparency, more or less linked to Scip (the Society of Competitive Intelligence Professionals).

Negative comments come from general public, fascinated enough by techniques and methods of competitive intelligence to take part in a newsgroup, but insecure enough to admit all the consequences of their participation.

As a conclusion, we would like to sketch out some guidelines for an ethical conduct in Knowledge management. We have seen that questions of morals are neither permanent nor universal; they are deeply embodied in the individual and his/her professional setting.

Practical issues are raised when they are in the middle of conflicting deontological rules. Most people agree on ethical values such as freedom, respect of the individual, ban on violence, etc.

Problems arise when those values are conflicting, e.g. for a professional, when free access to information may damage his/her institution.

Hence we return to our general reflection on Ethics in section 1: ethics is a continuous process; it is permanently both threatened and reinforced; it is a personal and social construct; it is not redeemable to simple rules and guidelines, contrary to what most managers and politicians would expect. We can set forth a theoretical viewpoint for ethics in our professional setting: since knowledge management is grounded in information processing, as shown in section 2, an invariant of our ethics is certainly the quality of information, and the confidence that can be attached to any piece of information. This specifically implies transparency and tracing the processes of information elaboration in a way similar to Iso quality certification which has induced consumers to accept and be confident in industrial products. If a higher level of professional ethics should be defined, meta-ethics should deal with happiness following Kant's heritage. In our technique geared society, the guarantor of ethical process is to transcend the technique and aim at human values.

Final word: be cautious with your communication on the internet; you might always be watched!

FIGURE 2 -FIGURE 2 -

 22 FIGURE 2 -Typical raw data from a newsgroup

FIGURE 3 -

 3 FIGURE 3 -Relational analysis