{"title": "Synergistic Face Detection and Pose Estimation with Energy-Based Models", "book": "Advances in Neural Information Processing Systems", "page_first": 1017, "page_last": 1024, "abstract": null, "full_text": " Synergistic Face Detection and Pose Estimation\n with Energy-Based Models\n\n\n\n Margarita Osadchy Matthew L. Miller Yann Le Cun\n NEC Labs America NEC Labs America The Courant Institute\n Princeton NJ 08540 Princeton NJ 08540 New York University\n rita@osadchy.net mlm@nec-labs.com yann@cs.nyu.edu\n\n\n\n\n Abstract\n\n We describe a novel method for real-time, simultaneous multi-view face\n detection and facial pose estimation. The method employs a convolu-\n tional network to map face images to points on a manifold, parametrized\n by pose, and non-face images to points far from that manifold. This\n network is trained by optimizing a loss function of three variables: im-\n age, pose, and face/non-face label. We test the resulting system, in a\n single configuration, on three standard data sets one for frontal pose,\n one for rotated faces, and one for profiles and find that its performance\n on each set is comparable to previous multi-view face detectors that can\n only handle one form of pose variation. We also show experimentally\n that the system's accuracy on both face detection and pose estimation is\n improved by training for the two tasks together.\n\n\n1 Introduction\n\nThe detection of human faces in natural images and videos is a key component in a wide\nvariety of applications of human-computer interaction, search and indexing, security, and\nsurveillance. Many real-world applications would profit from multi-view detectors that can\ndetect faces under a wide range of poses: looking left or right (yaw axis), up or down (pitch\naxis), or tilting left or right (roll axis).\n\nIn this paper we describe a novel method that not only detects faces independently of their\nposes, but simultaneously estimates those poses. The system is highly-reliable, runs at near\nreal time (5 frames per second on standard hardware), and is robust against variations in\nyaw (90), roll (45), and pitch (60).\n\nThe method is motivated by the idea that multi-view face detection and pose estimation are\nso closely related that they should not be performed separately. The tasks are related in the\nsense that they must be robust against the same sorts of variation: skin color, glasses, facial\nhair, lighting, scale, expressions, etc. We suspect that, when trained together, each task can\nserve as an inductive bias for the other, yielding better generalization or requiring fewer\ntraining examples [2].\n\nTo exploit the synergy between these two tasks, we train a convolutional network to map\nface images to points on a face manifold, and non-face images to points far away from\nthat manifold. The manifold is parameterized by facial pose. Conceptually, we can view\nthe pose parameter as a latent variable that can be inferred through an energy-minimization\nprocess [4]. To train the machine we derive a new type of discriminative loss function that\nis tailored to such detection tasks.\n\n\f\nPrevious Work: Learning-based approaches to face detection abound, including real-time\nmethods [16], and approaches based on convolutional networks [15, 3]. Most multi-view\nsystems take a view-based approach, which involves building separate detectors for differ-\nent views and either applying them in parallel [10, 14, 13, 7] or using a pose estimator to\nselect a detector [5]. Another approach is to estimate and correct in-plane rotations before\napplying a single pose-specific detector [12]. Closer to our approach is that of [8], in which\na number of Support Vector Regressors are trained to approximate smooth functions, each\nof which has a maximum for a face at a particular pose. Another machine is trained to con-\nvert the resulting values to estimates of poses, and a third is trained to convert the values\ninto a face/non-face score. The resulting system is very slow.\n\n\n2 Integrating face detection and pose estimation\n\nTo exploit the posited synergy between face detection and pose estimation, we must design\na system that integrates the solutions to the two problems. We hope to obtain better results\non both tasks, so this should not be a mere cascaded system in which the answer to one\nproblem is used to assist in solving the other. Both answers must be derived from one\nunderlying analysis of the input, and both tasks must be trained together.\n\nOur approach is to build a trainable system that can map raw images X to points in a\nlow-dimensional space. In that space, we pre-define a face manifold F (Z) that we para-\nmeterize by the pose Z. We train the system to map face images with known poses to the\ncorresponding points on the manifold. We also train it to map non-face images to points far\naway from the manifold. Proximity to the manifold then tells us whether or not an image\nis a face, and projection to the manifold yields an estimate of the pose.\n\nParameterizing the Face Manifold: We will now describe the details of the parameter-\nizations of the face manifold. Let's start with the simplest case of one pose parameter\nZ = , representing, say, yaw. If we want to preserve the natural topology and geometry\nof the problem, the face manifold under yaw variations in the interval [-90, 90] should\nbe a half circle (with constant curvature). We embed this half-circle in a three-dimensional\nspace using three equally-spaced shifted cosines.\n \n Fi() = cos( - i); i = 1, 2, 3; = [- , ] (1)\n 2 2\nWhen we run the network on an image X, it outputs a vector G(X) with three components\nthat can be decoded analytically into corresponding pose angle:\n 3 G\n = arctan i=1 i(X ) cos(i)\n 3 (2)\n G\n i=1 i(X ) sin(i)\n\nThe point on the manifold closest to G(X) is just F ().\n\nThe same idea can be applied to any number of pose parameters. Let us consider the set\nof all faces with yaw in [-90, 90] and roll in [-45, 45]. In an abstract way, this set is\nisomorphic to a portion of the surface of a sphere. Consequently, we encode the pose with\nthe product of the cosines of the two angles:\n Fij(, ) = cos( - i) cos( - j); i, j = 1, 2, 3; (3)\nFor convenience we rescale the roll angles to the range of [-90, 90]. With these parame-\nterizations, the manifold has constant curvature, which ensures that the effect of errors will\nbe the same regardless of pose. Given nine components of the network's output Gij(X),\nwe compute the corresponding pose angles as follows:\n cc = G G\n ij ij (X ) cos(i) cos(j ); cs = ij ij (X ) cos(i) sin(j )\n sc = G G\n ij ij (X ) sin(i) cos(j ); ss = ij ij (X ) sin(i) sin(j ) (4)\n = 0.5(atan2(cs + sc, cc - ss) + atan2(sc - cs, cc + ss))\n = 0.5(atan2(cs + sc, cc - ss) - atan2(sc - cs, cc + ss))\nNote that the dimension of the face manifold is much lower than that of the embedding\nspace. This gives ample space to represent non-faces away from the manifold.\n\n\f\n3 Learning Machine\n\nTo build a learning machine for the proposed approach we refer to the Minimum Energy\nMachine framework described in [4].\n\nEnergy Minimization Framework: We can view our system as a scalar-value function\nEW (Y, Z, X), where X and Z are as defined above, Y is a binary label (Y = 1 for face,\nY = 0 for a non-face), and W is a parameter vector subject to learning. EW (Y, Z, X)\ncan be interpreted as an energy function that measures the degree of compatibility between\nX, Z, Y . If X is a face with pose Z, then we want: EW (1, Z, X) EW (0, Z , X) for\nany pose Z , and EW (1, Z , X) EW (1, Z, X) for any pose Z = Z.\n\nOperating the machine consists in clamping X to the observed value (the image), and\nfinding the values of Z and Y that minimize EW (Y, Z, X):\n\n (Y , Z) = argminY {Y }, Z{Z}EW (Y, Z, X) (5)\n\nwhere {Y } = {0, 1} and {Z} = [-90, 90][-45, 45] for yaw and roll variables. Although\nthis inference process can be viewed probabilistically as finding the most likely configu-\nration of Y and Z according to a model that attributes high probabilities to low-energy\nconfigurations (e.g. a Gibbs distribution), we view it as a non probabilistic decision mak-\ning process. In other words, we make no assumption as to the finiteness of integrals over\n{Y }and {Z}that would be necessary for a properly normalized probabilistic model. This\ngives us considerable flexibility in the choice of the internal architecture of EW (Y, Z, X).\n\nOur energy function for a face EW (1, Z, X) is defined as the distance between the point\nproduced by the network GW (X) and the point with pose Z on the manifold F (Z):\n\n EW (1, Z, X) = GW (X) - F (Z) (6)\n\nThe energy function for a non-face EW (0, Z, X) is equal to a constant T that we can\ninterpret as a threshold (it is independent of Z and X). The complete energy function is:\n\n EW (Y, Z, X) = Y GW (X) - F (Z) + (1 - Y )T (7)\n\nThe architecture of the machine is depicted in Figure 1. Operating this machine (find-\ning the output label and pose with the smallest energy) comes down to first finding:\nZ = argminZ{Z}||GW (X) - F (Z)||, and then comparing this minimum distance,\n GW (X) - F (Z) , to the threshold T . If it smaller than T , then X is classified as a face,\notherwise X is classified as a non-face. This decision is implemented in the architecture as\na switch, that depends upon the binary variable Y .\n\nConvolutional Network: We employ a Convolutional Network as the basic architecture for\nthe GW (X) image-to-face-space mapping function. Convolutional networks [6] are \"end-\nto-end\" trainable system that can operate on raw pixel images and learn low-level features\nand high-level representation in an integrated fashion. Convolutional nets are advantageous\nbecause they easily learn the types of shift-invariant local features that are relevant to image\nrecognition; and more importantly, they can be replicated over large images (swept over\nevery location) at a fraction of the cost of replicating more traditional classifiers [6]. This\nis a considerable advantage for building real-time systems.\n\nWe employ a network architecture similar to LeNet5 [6]. The difference is in the number\nof maps. In our architecture we have 8 feature maps in the bottom convolutional and\nsubsampling layers and 20 maps in the next two layers. The last layer has 9 outputs to\nencode two pose parameters.\n\nTraining with a Discriminative Loss Function for Detection: We define the loss function\nas follows:\n 1 1\n L(W ) = L L\n |S 1(W, Zi, X i) + 0(W, X i) (8)\n 1| |S\n iS 0|\n 1 iS0\n\n\f\n Figure 1: Architecture of the Minimum Energy Machine.\n\nwhere S1is the set of training faces, S0the set of non-faces, L1(W, Zi, Xi) and L0(W, Xi)\nare loss functions for a face sample (with a known pose) and non-face, respectively1.\n\nThe loss L(W ) should be designed so that its minimization for a particular positive training\nsample (Xi, Zi, 1), will make EW (1, Zi, Xi) < EW (Y, Z, Xi) for Y = Y i or Z = Zi.\nTo satisfy this, it is sufficient to make EW (1, Zi, Xi) < EW (0, Z, Xi). For a particu-\nlar negative training sample (Xi, 0), minimizing the loss should make EW (1, Z, Xi) >\nEW (0, Z, Xi) = T for any Z. To satisfy this, it is sufficient to make EW (1, Z, Xi) > T .\n\nLet W be the current parameter value, and W be the parameter value after an update\ncaused by a single sample. To cause the machine to achieve the desired behavior, we need\nthe parameter update to decrease the difference between the energy of the desired label and\nthe energy of the undesired label. In our case, since EW (0, Z, X) = T is constant, the\nfollowing condition on the update is sufficient to ensure the desired behavior:\n\nCondition 1. for a face example (X, Z, 1), we must have: EW (1, Z, X) < EW (1, Z, X)\nFor a non-face example (X, 1), we must have: EW (1, Z, X) > EW (1, Z, X)\n\nWe choose the following forms for L1 and L0:\n\n L1(W, 1, Z, X) = EW (1, Z, X)2; L0(W, 0, X) = K exp[-E(1, Z, X)] (9)\n\nwhere K is a positive constant.\n\nNext we show that minimizing (9) with an incremental gradient-based algorithm will satisfy\ncondition 1. With gradient-based optimization algorithms, the parameter update formula\nis of the form: W = W - W = -A L\n W . where A is a judiciously chosen symmetric\npositive semi-definite matrix, and is a small positive constant.\n\nFor Y = 1 (face): An update step will change the parameter by W = -A EW (1,Z,X)2 =\n W\n-2EW (1, Z, X)A EW (1,Z,X)\n W . To first order (for small values of ), the resulting change\nin EW (1, Z, X) is given by:\n E T T\n W (1, Z, X ) E E\n W = -2E W (1, Z, X ) A W (1, Z, X ) < 0\n W W (1, Z, X ) W W\n\nbecause EW (1, Z, X) > 0 (it's a distance), and the quadratic form is positive. Therefore\nEW (1, Z, X) < EW (1, Z, X).\n\n 1Although face samples whose pose is unknown can easily be accommodated, we will not discuss\nthis possibility here.\n\n\f\n 100 100\n\n\n 95 95\n\n\n 90 90\n\n\n 85 85\n\n\n 80 80\n\n\n 75 75\n\n\n 70 70\n\n\n 65 65\n\n Percentage of faces detected 60 \n Pose + detection 60 \n Pose + detection\n\n Detection only\n Pose only\n \n 55 Percentage of yaws correctly estimated 55\n\n 50 50\n 0 2 4 6 8 10 12 14 16 18 20 0 5 10 15 20 25 30\n False positive rate Yaw-error tolerance (degrees)\n\n\n\nFigure 2: Synergy test. Left: ROC curves for the pose-plus-detection and detection-only networks.\nRight: frequency with which the pose-plus-detection and pose-only networks correctly estimated the\nyaws within various error tolerances.\n\nFor Y = 0 (non-face): An update step will change the parameter by W =\n-A K exp[-E(1,Z,X)] = K exp[-E\n W W (1, Z, X )] EW (1,Z,X)\n W . To first order (for small\nvalues of ), the resulting change in EW (1, Z, X) is given by:\n\n E T T\n W (1, Z, X ) E E\n W = K exp[-E W (1, Z , X ) A W (1, Z , X ) > 0\n W W (1, Z , X )] W W\n\nTherefore EW (1, Z, X) > EW (1, Z, X).\n\nRunning the Machine: Our detection system works on grayscale images and it applies\n \nthe network to each image at a range of scales, stepping by a factor of 2. The network\nis replicated over the image at each scale, stepping by 4 pixels in x and y (this step size\nis a consequence of having two, 2x2 subsampling layers). At each scale and location,\nthe network outputs are compared to the closest point on the manifold, and the system\ncollects a list of all instances closer than our detection threshold. Finally, after examining\nall scales, the system identifies groups of overlapping detections in the list and discards all\nbut the strongest (closest to the manifold) from each group. No attempt is made to combine\ndetections or apply any voting scheme. We have implemented the system in C. The system\ncan detect, locate, and estimate the pose of faces that are between 40 and 250 pixels high\nin a 640 480 image at roughly 5 frames per second on a 2.4GHz Pentium 4.\n\n\n4 Experiments and results\n\nUsing the above architecture, we built a detector to locate faces and estimate two pose\nparameters: yaw from left to right profile, and in-plane rotation from -45 to 45 degrees.\nThe machine was trained to be robust against pitch variation.\n\nIn this section, we first describe the training regimen for this network, and then give the\nresults of two sets of experiments. The first set of experiments tests whether training for\nthe two tasks together improves performance on both. The second set allows comparisons\nbetween our system and other published multi-view detectors.\n\nTraining: Our training set consisted of 52, 850, 32x32-pixel faces from natural images\ncollected at NEC Labs and hand annotated with appropriate facial poses (see [9] for a\ndescription of how the annotation was done). These faces were selected from a much\nlarger annotated set to yield a roughly uniform distribution of poses from left profile to right\nprofile, with as much variation in pitch as we could obtain. Our initial negative training data\nconsisted of 52, 850 image patches chosen randomly from non-face areas of a variety of\nimages. For our second set of tests, we replaced half of these with image patches obtained\nby running the initial version of the detector on our training images and collecting false\ndetections. Each training image was used 5 times during training, with random variations\n\n\f\n 100 100\n\n\n 95 95\n\n\n 90 90\n\n\n 85 85\n\n\n 80 80\n\n\n 75 75\n\n\n 70 70\n\n\n 65 65\n Frontal\n Percentage of faces detected 60 \n Rotated in plane 60 \n In-plane rotation\n Profile Yaw \n 55 Percentage of poses correctly estimated 55\n\n 50 50\n 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 5 10 15 20 25 30\n False positives per image Pose-error tolerance (degrees)\n\n\n\nFigure 3: Results on standard data sets. Left: ROC curves for our detector on the three data\nsets. The x axis is the average number of false positives per image over all three sets, so each point\ncorresponds to a single detection threshold. Right: frequency with which yaw and roll are estimated\nwithin various error tolerances.\n \nin scale (from x 2 to x(1 + 2)), in-plane rotation (45), brightness (20), contrast\n(from 0.8 to 1.3).\n\nTo train the network, we made 9 passes through this data, though it mostly converged after\nabout the first 6 passes. Training was performed using LUSH [1], and the total training\ntime was about 26 hours on a 2Ghz Pentium 4. At the end of training, the network had\nconverged to an equal error rate of 5% on the training data and 6% on a separate test set of\n90,000 images.\n\nSynergy tests: The goal of the synergy test was to verify that both face detection and pose\nestimation benefit from learning and running in parallel. To test this claim we built three\nnetworks with almost identical architectures, but trained to perform different tasks. The\nfirst one was trained for simultaneous face detection and pose estimation (combined), the\nsecond was trained for detection only and the third for pose estimation only. The \"detection\nonly\" network had only one output for indicating whether or not its input was a face. The\n\"pose only\" network was identical to the combined network, but trained on faces only (no\nnegative examples). Figure 2 shows the results of running these networks on our 10,000\ntest images. In both these graphs, we see that the pose-plus-detection network had better\nperformance, confirming that training for each task benefits the other.\n\nStandard data sets: There is no standard data set that tests all the poses our system is\ndesigned to detect. There are, however, data sets that have been used to test more restricted\nface detectors, each set focusing on a particular variation in pose. By testing a single\ndetector with all of these sets, we can compare our performance against published systems.\nAs far as we know, we are the first to publish results for a single detector on all these data\nsets. The details of these sets are described below:\n MIT+CMU [14, 11] 130 images for testing frontal face detectors. We count 517 faces\nin this set, but the standard tests only use a subset of 507 faces, because 10 faces are in\nthe wrong pose or otherwise not suitable for the test. (Note: about 2% of the faces in the\nstandard subset are badly-drawn cartoons, which we do not intend our system to detect.\nNevertheless, we include them in the results we report.)\n TILTED [12] 50 images of frontal faces with in-plane rotations. 223 faces out of 225\nare in the standard subset. (Note: about 20% of the faces in the standard subset are outside\nof the 45 rotation range for which our system is designed. Again, we still include these\nin our results.)\n PROFILE [13] 208 images of faces in profile. There seems to be some disagreement\nabout the number of faces in the standard set of annotations: [13] reports using 347 faces\nof the 462 that we found, [5] reports using 355, and we found 353 annotations. However,\nthese discrepencies should not significantly effect the reported results.\n\nWe counted a face as being detected if 1) at least one detection lay within a circle centered\non the midpoint between the eyes, with a radius equal to 1.25 times the distance from that\npoint to the midpoint of the mouth, and 2) that detection came at a scale within a factor of\n\n\f\nFigure 4: Some example face detections. Each white box shows the location of a detected face. The\nangle of each box indicates the estimated in-plane rotation. The black crosshairs within each box\nindicate the estimated yaw.\n\n Data set TILTED PROFILE MIT+CMU\n False positives per image 4.42 26.90 .47 3.36 .50 1.28\n Our detector 90% 97% 67% 83% 83% 88%\n Jones & Viola [5] (tilted) 90% 95% x x\n Jones & Viola [5] (profile) x 70% 83% x\n Rowley et al [11] 89% 96% x x\n Schneiderman & Kanade [13] x 86% 93% x\n\nTable 1: Comparisons of our results with other multi-view detectors. Each column shows the detec-\ntion rates for a given average number of false positives per image (these rates correspond to those for\nwhich other authors have reported results). Results for real-time detectors are shown in bold. Note\nthat ours is the only single detector that can be tested on all data sets simultaneously.\n\n\ntwo of the correct scale for the face's size. We counted a detection as a false positive if it\ndid not lie within this range for any of the faces in the image, including those faces not in\nthe standard subset.\n\nThe left graph in Figure 3 shows ROC curves for our detector on the three data sets. Figure 4\nshows a few results on various poses. Table 1 shows our detection rates compared against\nother systems for which results were given on these data sets. The table shows that our\nresults on the TILTED and PROFILE sets are similar to those of the two Jones & Viola\ndetectors, and even approach those of the Rowley et al and Schneiderman & Kanade non-\nreal-time detectors. Those detectors, however, are not designed to handle all variations in\npose, and do not yield pose estimates.\n\nThe right side of Figure 3 shows our performance at pose estimation. To make this graph,\nwe fixed the detection threshold at a value that resulted in about 0.5 false positives per\nimage over all three data sets. We then compared the pose estimates for all detected faces\n(including those not in the standard subsets) against our manual pose annotations. Note that\nthis test is more difficult than typical tests of pose estimation systems, where faces are first\nlocalized by hand. When we hand-localize these faces, 89% of yaws and 100% of in-plane\nrotations are correctly estimated to within 15.\n\n\n5 Conclusion\n\nThe system we have presented here integrates detection and pose estimation by training\na convolutional network to map faces to points on a manifold, parameterized by pose,\nand non-faces to points far from the manifold. The network is trained by optimizing a loss\nfunction of three variables image, pose, and face/non-face label. When the three variables\nmatch, the energy function is trained to have a small value, when they do not match, it is\n\n\f\ntrained to have a large value.\n\nThis system has several desirable properties:\n The use of a convolutional network makes it fast. At typical webcam resolutions, it can\nprocess 5 frames per second on a 2.4Ghz Pentium 4.\n It is robust to a wide range of poses, including variations in yaw up to 90, in-plane\nrotation up to 45, and pitch up to 60. This has been verified with tests on three\nstandard data sets, each designed to test robustness against a single dimension of pose\nvariation.\n At the same time that it detects faces, it produces estimates of their pose. On the standard\ndata sets, the estimates of yaw and in-plane rotation are within 15 of manual estimates\nover 80% and 95% of the time, respectively.\n\nWe have shown experimentally that our system's accuracy at both pose estimation and face\ndetection is increased by training for the two tasks together.\n\n\nReferences\n\n [1] L. Bottou and Y. LeCun. The Lush Manual. http://lush.sf.net, 2002.\n\n [2] R. Caruana. Multitask learning. Machine Learning, 28:4175, 1997.\n\n [3] C. Garcia and M. Delakis. 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IEE Proc on Vision, Image, and Signal Processing, 141(4):245250, August 1994.\n\n[16] P. Viola and M. Jones. Rapid object detection using a boosted cascade of simple features. In\n Proceedings IEEE Conf. on Computer Vision and Pattern Recognition, pages 511518, 2001.\n\n\f\n", "award": [], "sourceid": 2638, "authors": [{"given_name": "Margarita", "family_name": "Osadchy", "institution": null}, {"given_name": "Matthew", "family_name": "Miller", "institution": null}, {"given_name": "Yann", "family_name": "Cun", "institution": null}]}