Vicky Kalogeiton
email: vicky.kalogeiton@ed.ac.uk

Vittorio Ferrari

Cordelia Schmid
email: cordelia.schmid@inria.fr

Analysing domain shift factors between videos and images for object detection

Keywords: object detection, domain adaptation, video and image analysis. !

Object detection is one of the most important challenges in computer vision. Object detectors are usually trained on bounding-boxes from still images. Recently, video has been used as an alternative source of data. Yet, for a given test domain (image or video), the performance of the detector depends on the domain it was trained on. In this paper, we examine the reasons behind this performance gap. We define and evaluate different domain shift factors: spatial location accuracy, appearance diversity, image quality and aspect distribution. We examine the impact of these factors by comparing performance before and after factoring them out. The results show that all four factors affect the performance of the detectors and their combined effect explains nearly the whole performance gap.

INTRODUCTION

O BJECT class detection is a central problem in computer vision. Object detectors are usually trained on still images. Traditionally, training an object detector requires gathering a large, diverse set of still images, in which objects are manually annotated by a bounding-box [START_REF] Dalal | Histogram of Oriented Gradients for human detection[END_REF], [START_REF] Felzenszwalb | Object detection with discriminatively trained part based models[END_REF], [START_REF] Girshick | Rich feature hierarchies for accurate object detection and semantic segmentation[END_REF], [START_REF] Malisiewicz | Ensemble of exemplar-svms for object detection and beyond[END_REF], [START_REF] Uijlings | Selective search for object recognition[END_REF], [START_REF] Viola | Rapid object detection using a boosted cascade of simple features[END_REF], [START_REF] Wang | Regionlets for generic object detection[END_REF]. This manual annotation task can be very time consuming and expensive. This led the computer vision community to trying to reduce the amount of supervision necessary to train an object detector, typically down to just a binary label indicating whether the object is present or not [START_REF] Chum | An exemplar model for learning object classes[END_REF], [START_REF] Cinbis | Multi-fold MIL training for weakly supervised object localization[END_REF], [START_REF] Deselaers | Weakly supervised localization and learning with generic knowledge[END_REF], [START_REF] Fergus | Object class recognition by unsupervised scale-invariant learning[END_REF], [START_REF] Pandey | Scene recognition and weakly supervised object localization with deformable part-based models[END_REF], [START_REF] Siva | Looking beyond the image: Unsupervised learning for object saliency and detection[END_REF], [36], [START_REF] Siva | In defence of negative mining for annotating weakly labeled data[END_REF], [START_REF] Song | On learning to localize objects with minimal supervision[END_REF], [START_REF] Wang | Video action detection with relational dynamic-poselets[END_REF]. However, learning a detector with weak supervision is very challenging and current performance is still well below fully supervised methods [START_REF] Cinbis | Multi-fold MIL training for weakly supervised object localization[END_REF], [START_REF] Song | On learning to localize objects with minimal supervision[END_REF], [START_REF] Wang | Video action detection with relational dynamic-poselets[END_REF].

Video can be used as an alternative rich source of data. As opposed to still images, video provides several advantages: (a) motion enables to automatically segment the object from the background [31], replacing the need for manually drawing bounding-boxes; (b) a single video often shows multiple views of an object; and (c) multiple deformation and articulation states (e.g. for animal classes). Recent work [START_REF] Kim | Joint summarization of large sets of web images and videos for storyline reconstruction[END_REF], [START_REF] Leistner | Improving classifiers with weakly-related videos[END_REF], [START_REF] Prest | Learning object class detectors from weakly annotated video[END_REF], [START_REF] Sharma | Efficient detector adaptation for object detection in a video[END_REF], [39], [START_REF] Tang | Discriminative segment annotation in weakly labeled video[END_REF] started to exploit both sources of data for object detection, by transferring information extracted from the video domain to the still images domain, or vice versa. Hence, these works operate in a domain adaptation setting [START_REF] Duan | Visual event recognition in videos by learning from web data[END_REF], [START_REF] Gopalan | Unsupervised adaptation across domain shifts by generating intermediate data representations[END_REF], [START_REF] Pan | A survey on transfer learning[END_REF].

Several approaches for object detection exist, in which the source domain is video and the target domain is still images [START_REF] Leistner | Improving classifiers with weakly-related videos[END_REF], [START_REF] Prest | Learning object class detectors from weakly annotated video[END_REF], [START_REF] Tang | Discriminative segment annotation in weakly labeled video[END_REF]. Leistner et al. [START_REF] Leistner | Improving classifiers with weakly-related videos[END_REF] use patches extracted from unlabelled videos to regularize the learning of a random forest detector on still images. Prest et al. [START_REF] Prest | Learning object class detectors from weakly annotated video[END_REF] and Tang et al. [START_REF] Tang | Discriminative segment annotation in weakly labeled video[END_REF] present weakly supervised techniques for automatically annotating spatiotemporal segments on objects in videos tagged as containing a given class. These are then used to train object detectors. However, the experiments in [START_REF] Prest | Learning object class detectors from weakly annotated video[END_REF] show that training object detectors on still images outperforms training on video frames.

Other works such as [START_REF] Sharma | Efficient detector adaptation for object detection in a video[END_REF], [39] use still images as source domain and video frames as target domain. Tang et al. [39] introduce a self-paced domain adaptation algorithm to iteratively adapt an object detector from labeled images to unlabeled videos. Sharma and Nevatia [START_REF] Sharma | Efficient detector adaptation for object detection in a video[END_REF] propose an on-line adaptation method, which adapts a detector trained off-line on images to a test video. They show that the performance of the detector on videos can be significantly improved by this adaptation, as the initial image training samples and the video test samples can be very different.

The above works show that when testing on a target domain, there is a significant performance gap between training on this domain or on a different one. This is due to the different nature of the two domains. In this paper, we explore the differences between still images and video frames for training and testing an object detector. We consider several domain shift factors that make still images different from video frames. To the best of our knowledge, we are the first to analyze with a structured protocol such domain shift factors so as to reveal the source of the performance gap.

We carry out our investigation on two image-video dataset pairs. The first pair is PASCAL VOC 2007 [START_REF] Everingham | The PASCAL Visual Object Classes Challenge[END_REF] (images) and YouTube-Objects [START_REF] Prest | Learning object class detectors from weakly annotated video[END_REF] (video). Both datasets in the second pair come from ILSVRC 2015 [START_REF]Imagenet large scale visual recognition challenge (ilsvrc)[END_REF], [START_REF] Russakovsky | ImageNet Large Scale Visual Recognition Challenge[END_REF], i.e. from the 'object detection in images' and 'object detection in video' tracks of the challenge, respectively. We identify and analyse five kinds of domain shift factors that make still images different from video frames (sec. 3). The first is the spatial location accuracy of the training samples (sec. 3.1). As most previous experiments on training detectors from video were done in a weakly supervised setting, one might wonder whether much of the performance gap is due to the poor quality of automatically generated bounding-boxes. In contrast, still image detectors are typically trained from manually drawn bounding-boxes. The second factor we consider is the appearance diversity of the training samples within a domain (sec. 3.2). Video differs from still images in that frames are temporally correlated. Frames close in time often contain near identical samples of the same object, whereas in still image datasets such repetition happens rarely. This is an intrinsic difference in the medium, and leads to this often overlooked factor. The next factor is image quality (sec. 3.3), which includes level of blur, color accuracy and contrast, radial distortion, exposure range, compression artifacts, lighting conditions etc. In this paper, we consider Gaussian blur and motion blur, since we empirically found that level of blur is one of the most important differences between video and still images. The fourth factor is the distribution over aspects, i.e. the type of object samples in the training sets (sec. 3.4). As the space of possible samples for an object class is very large, each dataset covers it only partially [START_REF] Torralba | Unbiased look at dataset bias[END_REF], with its own specific bias. For example, horses jumping over hurdles might appear in one dataset but not in another. Hence, an important factor is the differences in the aspect distributions between the two domains. Finally, we consider object size and camera framing issues (sec. 3.5). Photographers and videographers might follow different approaches when capturing an object, e.g. in images the objects tend to be fully in focus, while videos might have objects coming in and out of the frame. Also the distance at which objects are captured might be different. Hence, we considered the distribution of object size, aspect-ratio, and truncation by the image frame as a last factor.

We proceed by examining and evaluating each domain shift factor in turn, following the same structure: (1) we introduce a metric to quantify the factor in each domain; (2) we modify the training set of each domain so that they are more similar in terms of this metric, effectively cancelling out the factor; (3) we examine the impact of this equalization on the performance of the object detector. As we found no difference in object size and camera framing between the two datasets (sec. 3.5), we carry out this procedure for the first four factors.

We consider the performance gap, i.e. the difference in performance of a detector trained on video frames or on still images (on a fixed test set consisting of still images). We examine the evolution of the performance gap as the training sets get progressively equalized by the procedure above. We also repeat the study in the reverse direction, i.e. where the test set is fixed to video frames. The results show that all factors affect detection performance and that cancelling them out helps bridging the performance gap. We perform experiments on two popular object detection models [START_REF] Felzenszwalb | Object detection with discriminatively trained part based models[END_REF], [START_REF] Girshick | Rich feature hierarchies for accurate object detection and semantic segmentation[END_REF]. While these are very different, our results hold for both, suggesting that our findings apply to object detection in general. Moreover, the results follow the same trends on both dataset pairs we considered, showing that the domain shift factors we examine are relevant in general, and the effects we observe are not specific to a particular dataset.

DATASETS AND PROTOCOL

In this section and the next we focus on the first dataset pair (i.e. PASCAL VOC 2007 and YouTube-Objects). Results on the second pair (ILSVRC 2015) are reported in sec. 4. For still images, we use PASCAL VOC 2007 [START_REF] Everingham | The PASCAL Visual Object Classes Challenge[END_REF], one of the most widely used datasets for object detection. For video frames we employ YouTube-Objects [START_REF] Prest | Learning object class detectors from weakly annotated video[END_REF], which is one of the largest available video datasets with bounding-box annotations on multiple classes. It has 10 classes from PASCAL VOC 2007, which enables studying image-video domain differences. We train two modern object detectors [START_REF] Girshick | Rich feature hierarchies for accurate object detection and semantic segmentation[END_REF], [START_REF] Girshick | Discriminatively trained deformable part models[END_REF] with annotated instances either from still images or from video frames and test them on both domains. In this fashion, we can observe how the performance of a detector depends on the domain it is trained from.

Datasets

Still images (VOC). Out of the 20 classes in PASCAL VOC 2007, we use the 10 which have moving objects, in order to have the same ones as in YouTube-Objects. Each object instance of these classes is annotated with a bounding-box in both training and test sets. Tab. 1 shows dataset statistics.

Video frames (YTO). The YouTube-Objects dataset [START_REF] Prest | Learning object class detectors from weakly annotated video[END_REF] contains videos collected from YouTube for 10 classes of moving objects. While it consists of 155 videos and over 720, 152 frames, only 1, 258 of them are annotated with a bounding-box around an object instance (3× fewer than in VOC). Instead, we would like to have a comparable number of annotations in both datasets. This would exclude differences in performance due to differences in the size of the training sets. Hence, we annotate many additional bounding-boxes on frames from YouTube-Objects. We first split the videos into disjoint training and test sets. In order to avoid any bias between training and test set, frames from the same video belong only to one set. Then, for both sets, we uniformly sample a constant number of frames in each shot, so that the total number of YTO training samples is roughly equal to the number of VOC training samples. For the training set, we annotate one object instance per frame. For the test set, we annotate all instances. The total number of annotated samples is 6, 973 (obtained from 6, 087 frames). Fig. 1 shows some annotated frames. The additional annotations are available on-line at http://calvin.inf.ed.ac.uk/datasets/youtube-objects-dataset/.

Equalizing the number of samples per class. For each class, we equalize the number of training samples exactly, by randomly sub-sampling the larger of the two training sets. The final number of equalized training samples is 3, 907 in total over the 10 classes (see column 'equalized' in tab. 1). Only these equalized training sets will be used in the remainder of the paper. We refer to them to as trainVOC and trainYTO for still images and video frames, respectively.

Protocol

Recall that we want to train object detectors either from still images or from video frames and then test them on both domains.

Each training set contains samples from one domain only. For a class, the positive training set contains annotated samples of this class, while the negative set contains images of all other classes. When testing on still images, we use the complete PASCAL VOC 2007 test set (tab. 1; this includes also images without instances of our 10 classes). When testing on video, we use a test set of 1, 781 images with 2, 667 objects instances in total (tab. 1). We refer to them as testVOC and testYTO, respectively. We measure performance using the PASCAL VOC protocol. A detection is correct if its intersection-over-union overlap with a ground-truth bounding-box is > 0.5 [START_REF] Everingham | The PASCAL Visual Object Classes Challenge[END_REF]. The performance for a class is Average Precision (AP) on the test set, and the overall performance is captured by the mean AP over all classes (mAP).

We experiment using two modern object detectors: the Deformable Part Model (DPM) [START_REF] Felzenszwalb | Object detection with discriminatively trained part based models[END_REF], [START_REF] Girshick | Discriminatively trained deformable part models[END_REF] and the Regions with Convolutional Neural Networks (R-CNN) [START_REF] Girshick | Rich feature hierarchies for accurate object detection and semantic segmentation[END_REF]. DPM models an object class by a mixture of components, each composed of a root HOG template [START_REF] Dalal | Histogram of Oriented Gradients for human detection[END_REF] and a collection of part templates arranged in a deformable configuration. This detector was the state-of-the-art reference for several years, until the arrival of CNN-based models. R-CNN [START_REF] Girshick | Rich feature hierarchies for accurate object detection and semantic segmentation[END_REF] is the current leading object detector. Candidate regions are obtained by selective search [START_REF] Uijlings | Selective search for object recognition[END_REF] and described with convolutional neural networks features (CNNs) extracted with Caffe [START_REF] Jia | Caffe: An open source convolutional architecture for fast feature embedding[END_REF], [START_REF] Jia | Caffe: Convolutional architecture for fast feature embedding[END_REF]. A linear SVM is then trained to separate positive and negative training regions (with hard negative mining to handle the large number of negative regions [START_REF] Dalal | Histogram of Oriented Gradients for human detection[END_REF], [START_REF] Girshick | Rich feature hierarchies for accurate object detection and semantic segmentation[END_REF], [START_REF] Girshick | Discriminatively trained deformable part models[END_REF]). In this paper, we use as features the 7 th layer of the CNN model trained on the ILSVRC12 classification challenge [START_REF] Krizhevsky | Imagenet classification with deep convolutional neural networks[END_REF], as provided by [START_REF] Girshick | Rich feature hierarchies for accurate object detection and semantic segmentation[END_REF]. We do not fine-tune the CNN for object detection, so that the features are not biased to a particular dataset. This enables to measure domain shift factors more cleanly.

DOMAIN SHIFT FACTORS

In this section we analyse the difference between VOC and YTO according to four factors: spatial location accuracy, appearance diversity, image quality and aspect distribution. We examine each factor by following the same procedure: (1: measurement) We introduce a metric to quantify the factor in each domain. (2: equalization) We present a way to make the training sets of the two domains more similar in terms of this metric. (3: impact) We compare the performance of object detectors trained from each domain before and after the equalization step. This enables to measure if, and by how much, equalization reduces the performance gap due to training on different domains.

As we apply the procedure above to each factor in sequence, we observe the evolution of the performance gap as the two domains are gradually equalized. As we have two test sets (one per domain) we monitor the evolution of two performance gaps in parallel.

Spatial location accuracy

There are several methods to automatically segment objects from the background in video frames by exploiting spatio-temporal continuity [START_REF] Brox | Object segmentation by long term analysis of point trajectories[END_REF], [START_REF] Lee | Key-segments for video object segmentation[END_REF], [31], [START_REF] Prest | Learning object class detectors from weakly annotated video[END_REF]. We evaluate two methods: (PRE) the method of [START_REF] Prest | Learning object class detectors from weakly annotated video[END_REF], which extends the motion segmentation algorithm [START_REF] Brox | Object segmentation by long term analysis of point trajectories[END_REF] to joint co-localization over all videos of an object class; and (FVS) the fast video segmentation method of [31], which operates on individual videos. Both methods automatically generate bounding-boxes for all video frames. We sample as many bounding-boxes as there are in the trainVOC and trainYTO sets by following the approach in [START_REF] Prest | Learning object class detectors from weakly annotated video[END_REF]. In the first step we quantify the quality of each bounding-box, based on its objectness probability [START_REF] Alexe | Measuring the objectness of image windows[END_REF] and the amount of contact with the image border (boxes with high contact typically contain background). In the second step we randomly sample bounding-boxes according to their quality (treating the quality values for all samples as a multinomial distribution). In this way, we obtain the PRE and FVS training sets.

this section, we use the trainVOC set for still images. For video frames, we use the PRE and FVS training sets and we measure their accuracy with respect to the ground-truth annotations (sec. 3.1: Measurement). We also use the trainYTO set, in order to improve video training data to match the perfect spatial support of still images (sec. 3.1: Equalization). Finally, we train object detectors from each training set and test them on testVOC and testYTO. In this way, we can quantify the impact of the different levels of spatial location accuracy on performance (sec. 3.1: Impact).

Measurement. We measure the accuracy of bounding-boxes by CorLoc: the percentage of bounding-boxes that satisfy the PAS-CAL VOC criterion [START_REF] Everingham | The PASCAL Visual Object Classes (VOC) Challenge[END_REF] (IoU > 50%). Bounding-boxes delivered by the PRE method have 24.0% CorLoc, while FVS brings 54.3% CorLoc. This shows that FVS can automatically produce good bounding-boxes in about half the frames, which is considerably better than the older method [START_REF] Prest | Learning object class detectors from weakly annotated video[END_REF] (fig. 3). However, this is worse than having all frames correctly annotated (as it is the case with manual ground-truth).

Equalization. The equalization step enhances the quality of the bounding-boxes in video frames, gradually moving from the worst to perfect annotations. We match the perfect location accuracy of the still image trainVOC set by using ground-truth bounding-boxes for the video frames (trainYTO set).

Impact. For video frames we train object detectors for each of the three levels of spatial support: starting with poor automatic annotations (PRE), then moving to better ones (FVS), and finally using ground-truth bounding-boxes (trainYTO). For still images we train detectors from the trainVOC set (ground-truth boundingboxes). We test on the testVOC and testYTO sets. Fig. 2 reports the performance for both detectors (DPM, R-CNN) and test sets.

When testing on still images (testVOC), the mAP of training from video continuously improves when using more and more accurate spatial support (fig. 2a,c). However, the performance of training on trainVOC is still considerably superior even to training on trainYTO with perfect ground-truth annotations. These results show that the imperfect spatial location accuracy of training samples produced by automatic video segmentation methods can only explain part of the gap. This is surprising, as we expected that using perfect annotations would close the gap much more. Quantitatively, for DPM the gap goes from 15.7% to 11.8% when going from training on the weakest automatic segmentation (PRE) to ground-truth bounding-boxes (trainYTO). The result is analog for R-CNN, with the gap going from 27.3% when using PRE, to 18.5% when using trainYTO. These results imply that we cannot get detectors learned from video to perform very well on still images even with great future progress on video segmentation, and in fact not even by manually annotating frames. Moreover, this also suggests there are other significant causes that produce the leftover gap. Testing on videos (testYTO) reveals a similar trend: more accurate spatial support on video frames leads to better performance (fig. 2b,d). Interestingly, training from videos here performs better than training from still images (when both are ground-truth annotated). This shows we are confronted with a real domain adaptation problem, where it is always better to train on the test domain. Again results hold for both detectors, but the 'reverse gap' left after equalizing spatial location accuracy is smaller than on testVOC: 5.9% mAP for DPM and 3.6% for R-CNN.

Appearance diversity

Video is intrinsically different from still images in that frames are temporally correlated. Frames that are close in time often contain near identical samples of the same object (top row of fig. 4. In still images such repetition happens rarely and typically samples that look very similar co-occur in the same image (bottom row of fig. 4). We first measure the appearance diversity of training sets (sec. 3.2: Measurement). Then we modify them to equalize their appearance diversity (sec. 3.2: Equalization). Finally, we observe the impact of this equalization on the performances of object detectors (sec. 3.2: Impact). In the spirit of our progressive equalization mission, here we use the trainYTO and trainVOC sets, which have ground-truth annotations. In this way, we focus on differences due to appearance diversity alone and not due to spatial support. Measurement. To measure appearance diversity within a training set, we manually group near-identical training samples, i.e. samples of identical objects in very similar viewing conditions (e.g. viewpoint and degrees of occlusion, fig. 4). This results in a set of groups, each containing near-identical samples (fig. 5). We quantify appearance diversity by the number of groups, i.e. the number of unique samples in the training set.

As shown in tab. 2, trainYTO has only half the number of unique samples than trainVOC, despite them having exactly the same total number of samples (tab. 1). This shows that half of the video samples (51%) are repeated, while almost all (97%) still image samples are unique. This reveals a considerable difference in appearance diversity between the two domains.

Equalization. We equalize appearance diversity by resampling each training set so that: (1) it contains only unique samples; and (2) the size of the training sets is the same in the two domains. We achieve first goal by randomly picking one sample per group, and the second by randomly subsampling the larger of the two training sets (i.e. VOC). This procedure is applied for each class Equalizing appearance diversity reduces the performance gap when testing on VOC down to 8.1% mAP for DPM and 15.0% mAP for R-CNN. Notably, this bridges the gap for both detectors by about the same amount (3.5% -3.7%). When testing on YTO the equalization has the opposite effect and increases the gap by about 3% to 8.8% mAP for DPM and 5.7% for R-CNN. This is expected, as the process handicaps trainVOC down to the level of diversity of trainYTO, without harming trainYTO.

Image quality

We examine the image quality factor while working on the Unique Samples training sets, which have the same size, accuracy of spatial support, and level of appearance diversity. In this way, all those factors will not cause any performance difference.

Measurement. We measure the image quality of a training sample by its gradient energy, as in [START_REF] Prest | Learning object class detectors from weakly annotated video[END_REF]. This computes the sum of the gradient magnitudes in the HOG cells of an object boundingbox, normalized by its size (computed using the implementation of [START_REF] Felzenszwalb | Object detection with discriminatively trained part based models[END_REF]). The gradient energy averaged over all classes is 4.4 for trainVOC Unique Samples and 3.2 for trainYTO Unique Samples. This is because video frames suffer from compression artefacts, motion blur, and low color contrast.

Equalization. We equalize the gradient energy by blurring the VOC samples, so as to match the energy of the YTO samples. We consider two different ways to blur a sample: Gaussian blur and motion blur. For Gaussian blur we apply an isotropic Gaussian filter with standard deviation σ. For Motion blur we apply a box filter of length K along the horizontal direction (as most camera motion in YouTube videos is horizontal). The motion blurred value g (m, n) of a pixel (m, n) is given by:

g (m, n) = 1 K K-1 i=0 f (m -i, n).
We set the parameter of the blur filter (σ and K) separately for each class, so that the average gradient energy of the blurred VOC samples equals that of the YTO samples. We find the exact parameter values using a bisection search algorithm (as an indication, the average values are σ = 1.35, K = 8.4). This procedure leads to the new training sets 'trainVOC Gaussian Blurred Unique Samples' and 'trainVOC Motion Blurred Unique Samples'. For uniformity, we also apply the same blur filters to the negative training sets. Fig. 7 shows the effect of the blur filters on a VOC training image. Impact. We train object detectors from either of the two trainVOC blurred Unique Samples sets. Fig. 2 reports results for both detection models and test sets. Note how results do not change when training from YTO, as this equalization process does not affect video training data. When testing on VOC, performance drops considerably when using blurred training samples, especially for R-CNN. On both detection models, the effect is more pronounced for motion blur than for Gaussian blur. This is likely because motion blur rarely happens naturally in still images, and so it is almost entirely absent in testVOC, making the equalization process distort the training set further away from the test set statistics. This also reveals that motion blur is a more important domain difference between VOC and YTO than Gaussian blur. Testing on YTO shows an interesting phenomenon: using blurred training samples has a much smaller effect. This is normal as testYTO is already naturally blurred, and therefore blurring the training set does not lose much relevant information.

Equalizing image quality with Gaussian blur reduces the performance gap when testing on VOC down to 7.0% mAP for DPM and 8.1% for R-CNN. Motion blur makes the gap even smaller, to 5.1% for DPM and 6.3% for R-CNN. The amount of gap bridged for R-CNN is remarkably large (8.7% mAP). When testing on YTO, Gaussian blur leaves the gap essentially unchanged for both detectors, while motion blur widens the gap for R-CNN by a small amount of 2.7%, reaching 8.4% mAP. Given that motion blur better represents the relevant image quality difference between the two domains, in the following we work only with motion blurred training sets.

Aspect distribution

As the last factor, we consider the distribution over aspects, i.e. the type of object samples in the training sets. Differences can be due to biases in the distribution of viewpoints, subclasses, articulation and occlusion patterns. As the space of possible samples for an object class is very large, any given dataset invariably samples it in a limited way, with its own specific bias [START_REF] Torralba | Unbiased look at dataset bias[END_REF]. Fig. 6 illustrates this point by showing all training samples of the class 'horse' from both domains. The distributions differ considerably and overlap only partially. Horses jumping over hurdles appear in trainVOC but not in trainYTO, while the latter has more horses running free in the countryside (more examples in fig. 8). We work here with the most equalized training sets, i.e. trainVOC Motion Blurred Unique Samples and trainYTO Unique Samples. These have the same size, accuracy of spatial support, level of appearance diversity, and image quality.

Measurement. We refer to the two training sets as A = x A 1 , . . . , x A n for VOC, and B = x B 1 , . . . , x B n for YTO. Measuring the difference in distributions of a source and a target domain is not a new task. Hoffman et al. [START_REF] Hoffman | Asymmetric and category invariant feature transformations for domain adaptation[END_REF] learn a similarity function by performing feature transformations. Duan et al. [START_REF] Duan | Domain transfer multiple kernel learning[END_REF] measure the distribution mismatch based on the distance between the mean values of the two domains, referred to as Maximum Mean Discrepancy [START_REF] Borgwardt | Integrating structured biological data by kernel maximum mean discrepancy[END_REF]. Here, we measure the difference in the aspect distributions of the two training sets with the symmetrized Kullback-Leibler (KL) divergence

d KL (A, B) = n i=1 fA x A i ln fA x A i fB x B i + fB x B i ln fB x B i fA x A i where fs (x s ) = 1 n n i=1 K (x s -x s i ; h) , s ∈ {A, B}
is a kernel density estimator fit to sample set s; K ( • ; h) is the isotropic Gaussian kernel with standard deviation h (automatically set based on the standard deviation of the sample set [START_REF]Kernel density estimation toolbox for matlab (kde toolbox)[END_REF]). For ease of visualization and computational efficiency, we reduce the dimensionality of the CNN features to 2D, using the algorithm of [START_REF] Van Der Maaten | Visualizing data using t-sne[END_REF] (as done by [START_REF] Donahue | Decaf: A deep convolutional activation feature for generic visual recognition[END_REF], [START_REF] Jia | Caffe: Convolutional architecture for fast feature embedding[END_REF]).

The KL divergence between the two training sets, averaged over all classes, is 5. [START_REF] Krizhevsky | Imagenet classification with deep convolutional neural networks[END_REF]. This shows that the difference in aspect distribution is quite big, given that the KL divergence averaged over all classes between trainVOC and testVOC is 1.24.

Equalization. We equalize the aspect distributions by subsampling the two training sets such that the subsets have a similar aspect distribution, i.e. a small d KL . More precisely, we want to find the largest subsets A ⊂ A and B ⊂ B which have a small enough d KL to be considered equally distributed: d KL ( A, B) < . We approximate this optimization by a greedy forward selection algorithm that starts from A = B = ∅, and iteratively adds the pairs of samples with the smallest Euclidean distance. We stop growing the subsets when d KL exceeds .

Fig. 6 (right) illustrates the evolution of d KL ( A, B) during this process for the class 'horse'. We use a small = 0.1 in all experiments 1 . For the horse class, this selects 70 samples from each set, which is just after the horizontal portion of the curve in fig. 6, when the distributions start to differ significantly, see samples along the curve. Fig. 6 (left) depicts a selected pair of samples, which lies in the region where the distributions overlap. This pair shows samples with similar aspects, whereas distant samples typically show very different aspects.

This procedure constructs the new training sets "trainVOC Motion Blurred Unique Samples and Aspects" and "trainYTO Unique Samples and Aspects". These sets contain 551 samples each (about 1/4 of all samples left after equalizing the previous domain shift factors).

Impact. We train object detectors from the aspect-distribution equalized sample sets. Results for R-CNN on both test sets are reported in fig. 2c,d (we do not perform this equalization process for DPM, as it does not work on a simple feature space where we can easily measure distances, due to its movable parts). When testing on VOC, the performance of training from YTO is barely affected by the equalization process, despite having 4× fewer training samples. Instead, the mAP of training from VOC drops considerably. This can be explained by the fact that the equalization process returns the intersection of the distributions of the two training sets. The video training set only loses samples with aspects not occurring in the trainVOC distribution, and hence unlikely to be in the test set. Instead, the VOC training set is losing many aspects that do occur in the test set. Testing on YTO corroborates this interpretation by displaying the inverse behavior: the Equalizing the aspect distributions when testing on VOC, brings the performance down to just 2.0% mAP, closing it by 4.3%. When testing on YTO, the equalization has an even greater effect: it bridges the gap by 6.9% mAP, reducing to just 1.5%.

The results show that aspects play an important role. Performance depends considerably on the training set containing aspects appearing in the test set, and this matters more than the size of the training set. The results also show that the aspect distributions in trainVOC and trainYTO are quite different, a dataset bias phenomenon analog to that observed by [START_REF] Torralba | Unbiased look at dataset bias[END_REF] when studying the differences between still image datasets. Our findings provide a guideline for practitioners trying to enrich still image training sets with video data (or vice-versa): it is more important to carefully consider which data samples to add, rather than simply trying to add a large number of them.

Other factors

In addition to the four domain shift factors we studied in sec. 3.1 to 3.2, we also considered other factors, which we summarize here. However, when measuring these other factors, we did not observe any significant differences between the VOC and YTO, and so we did not proceed to the equalization and impact steps.

Object size and aspect-ratio. The average size of ground-truth bounding-boxes in trainVOC, relative to the size of the image, is 0.26. For trainYTO it is nearly the same (0.25). Similarly, the average aspect-ratio (width-over-height) is 1.48 for trainVOC vs 1.53 for trainYTO.

Camera framing. We look for differences in the way objects are framed by the camera. Potentially, YTO might have more objects coming in and out of the frame. Each VOC instance is annotated by a tag marking it as either normal, truncated (partially out of the image frame), or difficult (very small, very dark, or heavily occluded) [START_REF] Everingham | The PASCAL Visual Object Classes Challenge[END_REF]. In order to measure camera framing for trainYTO, we annotated all its instances with the same tags. Both trainVOC and trainYTO have about the same proportion of truncated instances (35.8% in trainVOC, 33.2% in trainYTO). We exclude instances marked as difficult from trainVOC, as they are not taken into account in the PASCAL VOC 2007 either. Only 0.3% of the trainYTO set are difficult instances, again leading to about the same percentage. All other instances are normal (i.e. about 65% in both trainVOC and trainYTO).

EXPERIMENTS ON ILSVRC 2015

We repeat here our analysis on another dataset pair, to verify that our findings are general. Both datasets in this pair come from the ImageNet Large Scale Visual Recognition Challenge (ILSVRC We do not examine the spatial location accuracy factor, since we start from perfect spatial support (groundtruth bounding-boxes). For the appearance diversity factor, 96.6% of the samples in trainIMG are unique, whereas only 61.6% trainVID samples are unique, analog to what observed on the PASCAL VOC -YouTube-Objects dataset pair. We apply the equalization procedure of sec. 3.2, obtaining two new training sets, each containing 7, 902 unique samples. For image quality, the gradient energy averaged over all classes is 4.4 for the unique samples in IMG (identical to VOC) and 3.0 for those in VID (i.e. blurrier than YTO). By applying the Gaussian blur filter of sec. 3.3 on the image samples, we equalize their blur level to match the VID samples. For aspect distribution, the KL divergence between the two training sets, averaged over all classes, is 7.52. We apply the aspect distribution equalization procedure of sec. 3.4, resulting in the two final training sets, each containing 3, 446 samples. Fig. 9 shows the evolution of the performance of the R-CNN detector on the test sets after canceling out each domain shift factor in turn. Generally, we observe the same trend as in the VOC-YTO pair, i.e. the gap is initially rather substantial, and it is gradually reduced by our equalization steps. The final gap after all steps is below 1.5% mAP on both test sets.

When looking closer, some differences to the VOC-YTO results appear. When testing on images, the appearance diversity factor leaves the gap unchanged. This is due to the larger number of training samples in ILSVRC IMG, compared to VOC (4× more). Even after removing about 40% of the unique training samples from ILSVRC IMG in order to match the number of unique samples in ILSVRC VID, there are still enough samples left to train good detectors. Interestingly, when testing on images, the image quality factor closes the gap by a large margin. This is due to ILSVRC VID being blurrier than YTO, so the image quality equalization applies a stronger blur to ILSVRC IMG than to VOC. The aspect distribution factor bridges the performance gaps for both domains, in line with what observed on VOC-YTO. This confirms the important impact that the aspects contained in a training set have on performance at test time.

CONCLUSIONS

We analyzed several domain shift factors between still images and video frames for object detection. This is the first study that addresses with a systematic experimental protocol such an important task. We believe our conclusions are valuable in promoting and guiding future research. We thoroughly explored 4 domain shift factors and their impact on the performance two modern object detectors [START_REF] Felzenszwalb | Object detection with discriminatively trained part based models[END_REF], [START_REF] Girshick | Rich feature hierarchies for accurate object detection and semantic segmentation[END_REF]. We showed that by progressively cancelling out these factors we gradually closed the performance gap between training on the test domain and training on the other domain.

Given that data is becoming abundant, it is important to decide which data to annotate so as to create better object detectors. Our experiments lead to several useful findings, especially relevant when trying to train detectors from video to perform well on image test sets: (1) training from videos with ground-truth boundingannotation still produces a worse detector than when training from still images. Hence, future research on video segmentation cannot solve problem on its own; (2) blur has a strong impact on the performance gap; hence, deblurring algorithms might be an avenue for removing this factor; (3) the appearance diversity and aspect distribution of a training set is much more important than the number of training samples it contains. For good performance one should collect a broad range of videos showing all aspects expected to appear in the test set.

Fig. 1 .

 1 Fig. 1. Example YTO frames with ground-truth bounding-boxes.

Fig. 2 .

 2 Fig. 2. Impact of the domain shift factors when training on VOC and YTO for two detectors DPM (top row (a) and (b)) and R-CNN (bottom row (c) and (d)) and for two test sets VOC (left column) and YTO (right column).

Fig. 3 .

 3 Fig. 3. Example bounding-boxes produced by PRE [32] (red), FVS [31] (blue), and ground-truth annotations (green).

Fig. 4 .

 4 Fig. 4. (top row) YTO dataset: Frames in the same shot that contain near identical samples of an object. (bottom row) VOC dataset: Example of near identical samples in the same image.

Fig. 5 .

 5 Fig.5. Three example groups of near-identical samples in trainYTO. We display a subset of the frames for each group.

  separately. This leads to the new training sets 'trainVOC Unique Samples' and 'trainYTO Samples', each containing 2, 201 unique samples (tab. 2, column 'Equalized Unique Samples').Impact. We train object detectors from the equalized unique sample sets only. Fig. 2 reports results for both detection models and test sets. When testing on VOC, the mAP of training from still images decreases significantly when going from using all training samples (trainVOC) to trainVOC Unique Samples, as about half of the unique training samples are removed. Instead, the mAP of training from video remains almost constant, as only duplicate samples are removed. Testing on YTO produces similar effects, with the unique sample equalization procedure leaving the performance of training from YTO almost unchanged, but significantly reducing that of training from VOC. These results reveal that indeed near identical samples do not bring any extra information, and only artificially inflate the apparent size of a training set. Hence, these findings suggest that one should pool training samples out of a large set of diverse videos, sampling very few frames from each shot.

Fig. 7 .

 7 Fig. 7. Video frame, VOC training image, Gaussian and motion blurred VOC training images.TABLE 2 Appearance diversity equalization. Statistics of the groups: number of groups, ratio: number of groups / number of ground-truth samples and number of equalized unique samples.

Fig. 6 .

 6 Fig. 6. (Left) 2D visualization of the trainYTO Unique Samples (red) and trainVOC Motion Blurred Unique Samples (green) for the 'horse' class in R-CNN feature space. Circles indicate the samples selected by our equalization technique of sec. 3.4: Equalization. (Right) evolution of d KL as more and more sample pairs are added by our algorithm. The two distributions are very similar at the beginning and start to diverge later. At the = 0.1 threshold, 70 samples from each set are selected (left). This number is driven by and changes from class to class.

Fig. 8 .

 8 Fig. 8. Top row: Aspects common to both VOC (green) and YTO (red). Bottom row: Red: aspects occurring only in YTO. YouTube users often film their own pets doing funny things, such as jumping, rolling and going on a skateboard. Green: aspects occurring only in VOC. Chicken and birds flying are common in VOC, but do not appear in YTO. performance of training on VOC remains essentially unchanged, whereas that of training on YTO worsens substantially.Equalizing the aspect distributions when testing on VOC, brings the performance down to just 2.0% mAP, closing it by 4.3%. When testing on YTO, the equalization has an even greater effect: it bridges the gap by 6.9% mAP, reducing to just 1.5%.The results show that aspects play an important role. Performance depends considerably on the training set containing aspects appearing in the test set, and this matters more than the size of the training set. The results also show that the aspect distributions in trainVOC and trainYTO are quite different, a dataset bias phenomenon analog to that observed by[START_REF] Torralba | Unbiased look at dataset bias[END_REF] when studying the differences between still image datasets. Our findings provide a guideline for practitioners trying to enrich still image training sets with video data (or vice-versa): it is more important to carefully consider which data samples to add, rather than simply trying to add a large number of them.

4 N

 4 detector for the test set ILSVRC IMG Training set ILSVRC VID Training set ILSVRC IMG

Fig. 9 .

 9 Fig. 9. Impact of the domain shift factors when training on ILSVRC IMG and VID for the R-CNN detector.

[ 2 ]

 2 ), i.e. from the object detection in images (IMG) and in videos (VID) tracks of the challenge. We consider the same 10 object classes as in the previous sections. Data and protocol. The ILSVRC IMG dataset contains 60k training images (train60k) and 20k validation images, fully annotated with bounding-boxes on all instances of 200 object classes. We split the validation set into val1 and val2 as in[START_REF] Girshick | Rich feature hierarchies for accurate object detection and semantic segmentation[END_REF]. For training, we use train60k+val1, resulting in 13, 335 bounding-boxes for our 10 classes (8, 021 images). For testing we use val2, which comprises 5, 310 bounding-boxes (3, 362 images). The ILSVRC VID dataset contains 3, 862 training and 555 validation video snippets, which we use for training and testing respectively. The snippets are manually annotated with bounding-boxes for 30 object classes. For our 10 classes, the training set has 2, 198 snippets, totalling 292, 199 bounding-boxes in 212, 643 frames. The validation set, used as test set, has 332 snippets, with 134, 432 bounding-boxes in 87, 715 frames. We apply the equalization procedure of sec. 2.1 to have the same number of training samples in each domain. This results in 13, 335 training samples and 3, 362 test images per domain. We refer to the two training sets as trainIMG and trainVID. Following the protocol of sec. 2.2, we train an R-CNN detector either from still images or from video frames, then test it on both domains, and finally measure performance by mAP on the test set. Domain shift factors. We analyze 3 out of the 4 domain shift factors from sec. 3.

TABLE 1

 1 Number of object samples in the training and test sets for image (VOC) and video (YTO) domains.

			Training			Test
	Classname	Number of object samples	Number of object samples
		VOC YTO Equalized	VOC	YTO
	aeroplane	306	415	306	285	180
	bird	486	359	359	459	162
	boat	290	357	290	263	233
	car	1250	915	915	1201	605
	cat	376	326	326	358	165
	cow	259	321	259	244	315
	dog	510	454	454	489	173
	horse	362	427	362	348	463
	motorbike	339	360	339	325	213
	train	297	372	297	282	158
	total	4475	4306	3907	4254	2667

TABLE 2

 2 Appearance diversity equalization. Statistics of the groups: number of groups, ratio: number of groups / number of ground-truth samples and number of equalized unique samples.

	Classname	Number of groups YTO VOC	Ratio YTO VOC Unique Samples Equalized
	aeroplane	244	268	0.59	0.88	244
	bird	123	452	0.34	0.93	123
	boat	138	275	0.39	0.95	138
	car	310	1221	0.34	0.98	310
	cat	249	376	0.76	1.00	249
	cow	90	252	0.28	0.97	90
	dog	295	507	0.65	0.99	295
	horse	286	358	0.67	0.99	286
	motorbike	243	337	0.68	0.99	243
	train	223	294	0.60	0.99	223
	avg	220	434	0.51	0.97	220

40.1 31.0 40.2 31.0 29.3 26.8 27.4 % mAP of the R-CNN detector for the test set ILSVRC IMG 33.1 27.4 32.2 25.8 32.2 24.9 % mAP of the R-CNN detector for the test set I 31.1 31.0 31.0 29.3 26.8 27.4

									33.1
								33.1 33.1	33.1	32.2
	1.1	31.0		31.0			31.1	33.1 31.0	32.2 32.2	31.0	32.2 3 32.2
									32.2
	31.0 31.0	31.0 31.0	31.1 31.1			31.1 31.0 31.0	31.0 31.0 31.0	31.0
	31.0		31.0	31.1	29.3		31.0	31.0	29.3
		29.3 29.3						29.3 29.3	29.3
				29.3			26.8 27.4	27.4 29.3
				26.8 27.4 26.8 27.4 26.8 27.4	27.4 27.4	27.4	27.4 25.8 25.8 26.8 27.4 26.8 2 26.8
							33.1		25.8
	initial	appearance diversity	motion blur	initial	aspects appearance diversity initial	appearance motion blur
	initial appearance diversity appearance diversity motion blur pearance diversity motion blur initial initial motion blur aspects aspects appearance diversity aspects initial initial initial appearance diversity initial appearance diversity appeara appearance diversity mot motion blur motion blur aspects appearance diversity motion blur aspects
	appearance diversity	motion blur	initial	aspects appearance diversity initial	appearance diversity motion blur	as

27.4 32.2 25.8 32.2 26.7 29.8 28.7 % mAP of the R-CNN detector for the test set ILSVRC VID

	40.2
	31.0	31.0
		29.3
		intial	appearance diversity	blur	aspects

26.8 27.4 he R-CNN detector for the test set ILSVRC IMG 33.1 27.4 32.2 25.8 32.2 24.9 24.5 24.9 % mAP of the R-CNN detector for the test set ILSVRC VID 31.1 40.1 40.2 31.0 29.3 26.8 27.4 % mAP of the R-CNN detector for the test set ILSVRC IMG

	Training set ILSVRC VID
	Training set ILSVRC IMG

Note the need for this parameter, otherwise d KL ( A, B) = 0 is achieved by picking 0 samples from each set.

ACKNOWLEDGMENTS

We gratefully acknowledge the ERC projects VisCul and ALLE-GRO.


L Thevenard

S A Hussain

H J Von Bardeleben

M Bernard

A Lemaître

C Gourdon

High domain wall velocities in in-plane magnetized (Ga,Mn)(As,P) layers

Keywords: numbers: 75.50.Pp, 75.60.Ch, 75.78.Fg

Field-induced domain wall (DW) propagation was evidenced in unpatterned layers of in-plane magnetized Ga1-xMnxAs1-yPy using Kerr microscopy. Both stationary and precessional regimes were observed, and domain wall velocities of up to 500 m s -1 were measured, of the order of magnitude of those observed on in-plane magnetized metals. Taking advantage of the strain-dependent magneto-crystalline anisotropy in this dilute magnetic semiconductor, both out-of-plane and inplane anisotropies were adjusted by varying the manganese and phosphorus concentrations. We demonstrate that these anisotropies are a critical parameter to obtain large velocities. These results are interpreted in the framework of the one-dimensional model for domain wall propagation.

Spintronics has spurred a renewed interest in in-plane magnetized materials, with soft ferromagnets being used in novel shift-register memories based on magnetic domain wall propagation (DWP) 1,2 . To be viable, these devices require an excellent knowledge of the physics governing the DW velocity and structure, via the micromagnetic parameters of the material. Among them, the magnetic anisotropy -shape or magneto-crystallinegoverns the canting of the magnetization within the domain wall, which propels it forward [START_REF] Thiaville | Spin Dynamics in Confined Magnetic Structures III[END_REF] . Nanostructuring the devices was thus a substantial progress as it induces shape anisotropy [START_REF] Moriya | [END_REF]5 and somewhat simplifies the theoretical treatment of the problem [START_REF] Thiaville | Spin Dynamics in Confined Magnetic Structures III[END_REF] . However, confinement also introduces edge roughness that is complex to model, and imposes a sample design for a desired DW velocity behavior (such as the maximum velocity, or the maximum field giving a stationary configuration of the DW). Past experiments have studied at length the effects of shape anisotropy on the DW velocity in metals [START_REF] Moriya | [END_REF]5 , but no exploration has been done of the powerful lever that is magneto-crystalline anisotropy. This was mostly due to the difficulty to tune it over a broad range in metals, and to the technical issues linked to measuring high DW velocities at fields higher than a few Oersteds 6 .

In this context, we believe dilute magnetic semiconductors (DMS) to be ideally suited materials for these studies. In particular the model material GaMnAs, and its Phosphorus substituted compound offer obvious advantages: micromagnetic parameters that can be tuned during 7 or after the growth 8 , and weak DW pinning permitting the observation of intrinsic flow regimes for field-driven DW propagation in out-of-plane magnetized layers 9 . DWP studies on in-plane magnetized GaMnAs layers have been limited to observations of the magnetic after-effect in the creep regime 10 , and transport measurements of low DW velocities in micron-wide stripes 11 . In this geometry, the interplay between magnetic anisotropies and DWP could not be studied. Working on unpatterned layers and tuning the magnetic anisotropies in GaMnAs(P) alloys would however provide unprecedented understanding and control of the field dependence of the velocity. Moreover these layers should be well suited to achieve high DW velocities because of large DW width 12 , as expected from the well-known onedimensional (1D) model 13,14 for DW propagation.

In this model, the field-induced propagation is expected to consist of a stationary linear regime, followed beyond the Walker field H W by a precessional regime. An interesting case occurs when samples exhibit both a strong perpendicular uniaxial magnetic anisotropy making the sample plane an easy plane (coefficient K ⊥ ) and a uniaxial in-plane anisotropy (coefficient K 0 ). In this configuration, the Walker field is expected to depend solely on K ⊥ and the DW width on K 0 . However, the maximum velocity in the stationary regime depends on the relative weight of both anisotropies [START_REF] Thiaville | Spin Dynamics in Confined Magnetic Structures III[END_REF] .

In this Letter, we evidence using longitudinal Kerr microscopy the propagation of DWs in the flow regimes, both stationary and precessional, in GaMnAs(P) layers with in-plane magnetization. DW velocities comparable to those found in Permalloy (Py), and over tenfold higher (up to 500 m s -1 ) than any recorded speeds in DMS are measured. Several samples are investigated to understand the impact of the different magnetic anisotropies on the DW dynamics, in particular on the maximum achievable velocities.

Four 50 nm thick (Ga 1-x Mn x )(As 1-y P y ) samples were studied. Their characteristics are given in Table I of-plane anisotropy coefficient

K ⊥ =µ 0 M 2 s /2-K 2⊥ -3 2 K 4// and a uniaxial in-plane anisotropy coefficient K 0 =K 2// - K 4// .
The strained lattice mismatch (lm) is defined as (a ⊥ -a sub )/a sub , where a ⊥ is the strained lattice parameter of the film parallel to the growth axis and a sub is the lattice parameter of the substrate. [Mn] ef f is defined as the concentration of magnetically active Mn atoms.

Phosphorus alloying has been shown to be well suited to tune the strain and the magnetic properties of the layers, through their dependence on the valence band structure 15,17 . Decreasing the phosphorus concentration from y ≈3.4 to 0% at constant [Mn] ef f =3.7% increases the strained lattice mismatch from 0 to 6890 ppm. The strain-induced uniaxial out-of-plane anisotropy constant (K ⊥ ) consecutively increases, with the uniaxial in-plane anisotropy constant (K 0 ) remaining low. Rising [Mn] ef f to 4.7% keeping y=0% further increases both in-plane and out-of-plane anisotropies (Table I). For all samples, the easy axis is expected from FMR to be along [1 10] at T ≥20 K and between -4 • and -13 • degrees away from [100] below.

Direct observation of the DW propagation was done by longitudinal Kerr microscopy using an LED source (λ=632nm), a high numerical aperture (0.4) objective and a deported aperture diaphragm [START_REF] Hubert | Magnetic domains[END_REF] . The set-up probes the horizontal component of the magnetization (Kerr axis). Two external coils surrounding the cryostat provide a homogeneous horizontal field H ext (minimum risetime 60µs). Inside the cryostat, a homemade set of micro-coils was designed to apply in-plane pulsed fields H pul of up to 42 mT (risetime 100 ns). Contrary to most DW propagation studies relying on transport measurements 11,[START_REF] Corodeanu | [END_REF] , this set-up permits the simultaneous imaging of the propagating domains with a large field of view and application of short field pulses (see Ref. 16 for experimental details).

In order to establish the optimum field orientation for the dynamic study, hysteresis loops were first obtained from Kerr microscopy images under a static field H ext applied at various angles. For T ≥ 20 K and H ext //[1 10] (easy axis) and along the Kerr axis, we observed square cycles for all samples, with coercive fields µ 0 H c roughly increasing with the strain-induced anisotropy K ⊥ . At T =0.2T c , µ 0 H c =0.9, 1.2 and 2 mT for resp. C3, B3, A3; µ 0 H c =2 mT for A4. For H ext //[100] and along the Kerr axis, the domains remained along [ 1 10]. The resulting contrast was about cos(π/4) times weaker than for H ext //[1 10], indicating that the magnetization within the domains remained aligned along the easy axis regardless of the field orientation. For the subsequent DWP study, the field was therefore aligned along the easy axis of the sample, as well as with the Kerr axis. This configuration led to the observation of 180 • charged DWs, as reported previously 20,21 . The layers were kept unpatterned to understand how the complex in-plane anisotropy of the material interplays with its uniaxial anisotropy in fieldinduced DW dynamics.

The DW velocity is measured by applying several field pulses, and measuring the DW displacement on snapshots taken in zero field between consecutive pulses 16 . Domains expanded anisotropically, along the easy axis direction. Figs. 1b,c show DW velocity measurements done on samples with the weakest out-of-plane uniaxial anisotropies of the [Mn] ef f =3.7% series, B3 and C3. Once the DWs depin around the coercive field, the velocity at 20/30 K rises quasi-linearly towards a peak of 186 m s -1 for B3 and ≈ 100 m s -1 for C3. It then decreases by up to 36% of its peak value. The behavior at 60 K is similar but nucleations prevent the observation of the velocity decrease after the peak (see Table I for velocity values at 60 K).

In order to test the influence of the perpendicular uniaxial anisotropy on the maximum velocity, the DW velocities of samples A4 and A3 (of higher K ⊥ ) were then measured for similar temperatures. For H pul just below the coercive field, very few domains nucleate and they adopt a wedge shape (Fig. 2b and Ref. 16) very reminiscent of the saw-tooth domains seen on in-plane magnetized Py 22 or Fe 23 . This profile efficiently reduces the magnetostatic energy cost of a 180 • charged DW. Such a shape could not be observed as clearly on samples B3, C3 because of the great number of nucleations, due to the much weaker K ⊥ . Once again, domains expanded very anisotropically along the easy axis. The v(H) data are shown in Figs. 1a and2a.

After depinning, the velocity first rises very steeply with a mobility (dv/dH) that increases with temperature. For sample A3 at T ≈0.2T C , the velocity then plateaus at v max =320 m s -1 above µ 0 H max =4.9 mT. At 7.6 mT, the velocity increases once again to reach a second plateau at 403 ms -1 (values of µ 0 H max and v max at 60 K in Table I). For sample A4 at T ≈0.2T C , there is only one clear velocity plateau of about 507 m s -1 reached at 7.8 mT (µ 0 H max , v max at 60 and 85 K in Table I). The 85 K curve goes up to 481 m s -1 before nucleations prevent further measurement. The DW velocities measured on this sample are to our knowledge the highest observed to this day on any DMS. Moreover, they are close to -if not higher than -typical DW velocities encountered on unpatterned 6 and patterned 24 Permalloy. The observed velocities are moreover much higher than those measured on out-of-plane magnetized GaM-nAs samples (field-25 or current-induced 26 propagation) where they could only be measured up to a few tens of m s -1 . DW velocities measured on planar GaMnAs micronwide stripes 11 were less than 0.1 m s -1 , very probably because the field was not applied along the easy axis which led to the formation of slower 90 • domain walls. Two main issues are raised up by the experiments presented above: the dependence of the maximum velocity on the magnetic anisotropy, and the different shapes of the v(H) curves between samples A4, A3 on the one hand, and B3, C3 on the other hand. Although the thickness of the layer (about 5 times the exchange length) and lack of DW confinement make a genuine 1D-type DW propagation unlikely 25,27 , this theory provides useful guidelines. In the case of simultaneous perpendicular and in-plane uniaxial anisotropies, it demonstrates the existence of a stationary solution for a propagating DW up to the Walker field H W =αK ⊥ /µ 0 M S , with α the Gilbert damping constant and M S the saturation magnetization. The maximum velocity in the stationary regime is then not necessarily the Walker velocity V W =γ∆ 0 µ 0 H W /α reached at Walker breakdown 3 , but rather

V max reached at H max =2H W (1 + κ) 1/4 √ 1+κ-1 κ < H W : V max = 2V W √ 1 + κ -1 κ (1)
In these equations, κ = K ⊥ /K 0 reflects the ratio of the two anisotropies 3 and ∆ 0 = Aexc K0 is the static DW width with A exc the exchange constant. This is completely equivalent to the case of weakly perpendicularly magnetized samples [START_REF] Hubert | Magnetic domains[END_REF] , for which the parameter equivalent to κ is 1/Q=µ 0 M 2 s /2K ⊥ . For our samples, the static DW width is then calculated to lie around ∆ 0 ≈ 50 nm, over 10 times wider than the DW width estimated experimentally in perpendicularly-magnetized GaMnAs(P) layers 7 . This estimated ∆ 0 is of the order of the widths measured for near-180 • DWs by high-resolution electron holography on 500 nm thick in-plane magnetized GaMnAs 12 .

The resulting calculated v(H) curve of ideally propagating DWs is shown in Fig. 3a for various values of K 0 , K ⊥ . The dependence of the maximum velocity on the magnetic anisotropies can be understood as follows for transverse DWs. When the field is applied along the easy axis, the DW magnetization starts precessing around it and comes out of the plane by an angle φ. The resulting magnetostatic charges created at the surfaces of the layer create a demagnetizing field H demag : proportional to M s in soft in-plane magnetized materials such as Py, or to the uniaxial anisotropy field 2K ⊥ /µ 0 M s in the case of in-plane magnetization induced by magnetocrystalline anisotropy. It is the torque between H demag and the DW's magnetization that propels the DW forward with a velocity proportionnal to H demag and ∆(φ). As the applied field increases, so does φ, resulting in the progressive shrinking of the DW width from its static value, becoming:

∆(φ)= ∆0 √ 1+κsin 2 φ
. At small κ, this non-linearity is minor, and the mobility is linear up to Walker breakdown (κ=1 curve in Fig. 3a). As κ increases, the end of the stationary regime evolves into a broad plateau. Its amplitude rises with increasing outof-plane anisotropy coefficient K ⊥ (through its effect on H demag ), but also with decreasing in-plane anisotropy as this will broaden the DW, and increase the velocity. The 1/ √ K 0 dependence of the velocity is however weaker than the linear dependence on K ⊥ . In the case of κ ≫1, the expression of the maximum velocity can in fact be simplified to V ∞ max ≈ 2γ Ms √ A exc K ⊥ , evidencing once more the weaker influence of the uniaxial inplane anisotropy on the maximum speed. In Permalloy nanowires, the magnetic anisotropy mainly results from the shape of the wire, and typical κ are close to 1. In our samples on the contrary, κ=20-200 (Table I).

In the framework of this model, and taking into account that the DWs depin at a finite field (very close to the coercive field) two different experimental scenarios can occur as shown schematically in Fig. 3b: the DW propagation can meet the intrinsic regime either before (dashed line) or after (dotted line) the Walker field. We attribute samples A3, A4 to the first category, and samples B3, C3 to the second one.

For samples with very low anisotropy fields (B3, C3), the Walker field is expected to be quite small, and the DW velocity meets directly the precessional regime (dotted line in Fig. 3b), at which point the velocity decreases with field. An upper boundary for the damping constant can then be estimated from H W =αK ⊥ /µ 0 M S . Using the anisotropy coefficients determined by FMR and the experimental peak fields H max at different temperatures (Table I) then yields α max =0.02-0.04. This value is very much of the order found by variable-frequency FMR 28 , but ten times smaller than the one estimated from the ratio of stationary and precessional mobilities (µ stat , µ prec ) in out-of-plane magnetized GaMnAs 9 . Although this discrepancy has been pointed out before 29 , it may also originate from an incorrect evaluation of µ stat in these samples. Finally, calculating the field expected to give the maximum velocity at T ≈0.2T c gives: µ 0 H max =1.2 mT (1.5 mT) for sample C3 (B3). These are barely above their coercive fields µ 0 H c =0.9 mT (1.2 mT), which explains why the high velocity plateau is not seen at all.

For samples with higher anisotropy fields (A3, A4), it is the stationary regime that is reached after depinning (dashed line in Fig. 3b). This occurs at exceptionally high speeds (≈ 150 m s -1 for A3 and ≈ 300 m s -1 for A4) which contrasts strongly with the claims of Ref. 11 of a stationary regime reached by 8.10 -2 m s -1 . The expected saturation velocities calculated from Eq. (1) at T ≈0.2T c from the 1D model are indicated in Table I for samples A3 and A4. For this calculation, the exchange constant was taken as 3.10 -13 J m -1 for [Mn] ef f =4.7% (sample A4) and as 10 -13 J m -1 for [Mn] ef f =3.7% (sample A3), as estimated on perpendicularly magnetized samples of similar manganese content 7 . The experimentally determined velocities follow the predicted trend of increasing V max with perpendicular anisotropy K ⊥ , as well as the weaker influence of the in-plane anisotropies (Table I). However, the observed maximum velocities are underestimated by a factor of about 1.5, and the velocity plateaus are unexpected within this model. As evidenced repeatedly in both simulations 3 and experiments 30 , an abrupt change in velocity often results from a modification of the nature of the DW. A modification of the domain profile can indeed be seen on the domain images of samples A3 and A4 (Fig. 2b). The domain gradually loses its sawtooth shape and smoothens out with increasing field, or more exactly divides up into sawtooths of shorter period. These DW transformations could be the reason for the plateaus observed for samples A3 and A4. To summarize, the 1D model provides gives good qualitative trends, but underestimates the observed velocities, possibly due to a transformation of the DW profile. This work gives clear guidelines for designing high speed DW based devices. In particular, the largest DW velocities are found for 180 • charged DWs propagating along the easy axis, with layers exhibiting the largest out-of-plane anisotropy and a weak in-plane anisotropy, which corresponds to a large DW width. Lateral confinement of the DWs through nanostructuration of the layer is expected to have a further impact on the max-imum velocity since it will affect the uniaxial in-plane anisotropy, as already shown in GaMnAs 31 . In light of our results, this additional parameter would open a wide range of possibilities to control the DW dynamics in fieldor current-driven DW motion experiments.

We acknowledge C. Doré and S. Majrab for technical assistance. This work was performed in the framework of the MANGAS project (ANR 2010-BLANC-0424-02).

FIG. 1 .

 1 FIG. 1. Domain wall velocity versus applied field in the [Mn] ef f =3.7% series in order of decreasing lattice mismatch (slm) and uniaxial out-of-plane anisotropy. (a) A3, (b) B3, (c) C3. The lines are guides for the eyes.

FIG. 2 .

 2 FIG. 2. (a) Domain wall velocity for the [Mn] ef f =4.7% sample at T =25, 60 and 85 K. (b) Modification of the domain profile with increasing field.

FIG. 3 .

 3 FIG. 3. Computed 1D model v(H) curves with the vertical arrows indicating the position of the Walker field. (a) Varying in-plane (K0) and out-of-plane (K ⊥ ) anisotropies without pinning (following Ref. 3 with α=0.03, Aexc=10 -13 J m -1 , Ms=36 kA m -1 ). (b) Possible modifications to the v(H) curve when pinning is taken into account. The DW velocity may rejoin the intrinsic regime before Walker breakdown (dashed line) or afterwards (dotted line).

TABLE I

 I

	. Main characteristics of the samples 15 , with values at 0.2TC highlighted in bold: effective Mn concentration [Mn] ef f ,
	approximate phosphorus concentration [P], lattice mismatch (lm), Curie temperature TC and magnetic anisotropy coefficients 16 .
	Vmax is the maximum velocity expected in the stationary regime from the 1D model (Eq. (1) and Ref. 3). vmax(Hmax) is the
	maximum observed velocity. When 2 plateaus were observed, both values of maximum field/velocities are given.