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FEATURE PERFORMANCE COMPARISON FEATURE PERFORMANCE COMPARISON y SC is a training set of k-dimensional observations with labels S and C b C is a parameter vector representing content, while A S is a style-specific linear map mapping the content space onto the observation space EXPERIMENTS WITH THE MOBO DATABASE EXPERIMENTS WITH THE MOBO DATABASE ASYMMETRIC BILINEAR MODELS ASYMMETRIC BILINEAR MODELS USING BILINEAR MODELS FOR VIEW-INVARIANT ACTION AND IDENTITY RECOGNITION Fabio Cuzzolin, UCLA Vision Lab, University of California at Los Angeles USING BILINEAR MODELS FOR VIEW-INVARIANT ACTION AND IDENTITY RECOGNITION Fabio Cuzzolin, UCLA Vision Lab, University of California at Los Angeles INTERNATIONAL CONFERENCE ON COMPUTER VISION AND PATTERN RECOGNITION, CVPR 2006 New York University, NY, June 17-22 2006 the training set of sequences is used to learn a three-layer model the model can be used thereafter to estimate the content of new image sequences with known content but unknown style we want to recognize the identity of a walking person, no we want to recognize the identity of a walking person, no matter the viewpoint or the walking gait performed matter the viewpoint or the walking gait performed bilinear models can be used to describe datasets in bilinear models can be used to describe datasets in which each sequence possesses more than a single label which each sequence possesses more than a single label a three-layer model in which HMMs represent sequences a three-layer model in which HMMs represent sequences and are fed to a bilinear model is proposed to provide an and are fed to a bilinear model is proposed to provide an effective view- and action-invariant approach to gaitID effective view- and action-invariant approach to gaitID VIEW-INVARIANCE IN IDENTITY VIEW-INVARIANCE IN IDENTITY RECOGNITION FROM GAIT RECOGNITION FROM GAIT the problem: recognizing the identity of a person from the way he/she walks in a realistic setup, the person to identify would walk into the surveyed area from an arbitrary direction -> view-invariance view-invariance is a particular case of the style-invariance issue 3 view-invariant gaitID. Left: score as a function of the nuisance (action), test view 1. Right: score for the dataset of sequences of action ``slow", different test views. performance of the bilinear classifier in the ID vs action experiment as a function of the nuisance (view=1:5), averaged over all the possible choices of the test action. The average best-match performance of the bilinear classifier is shown in solid red, (minimum and maximum in magenta). The best-3 matches ratio is in dotted red. The average performance of the KL-nearest neighbor classifier is shown in solid black, minimum and maximum in blue. Pure chance is in dashed black. FEATURE EXTRACTION FROM SILHOUETTES FEATURE EXTRACTION FROM SILHOUETTES VIEW- AND ACTION-INVARIANT GAIT ID VIEW- AND ACTION-INVARIANT GAIT ID in the first layer features are extracted from the available silhouettes, by simply projecting their contour onto a family of lines passing through their center; in the second layer each feature sequence is fed to an HMM with a fixed number of states, yielding a dataset of Markov models; as the dynamics is the same for all sequences, they can be represented by the stacked C matrix of the HMM HIDDEN MARKOV MODELS HIDDEN MARKOV MODELS Left: ID-invariant action recognition using the bilinear classifier. The entire dataset is considered, regardless the viewpoint. The correct classification percentage is shown as a function of the test identity in black (for models using Lee's features) and red (contour projections). Related mean levels are drawn as dotted lines. Right: View- invariant action recognition. THREE-LAYER MODEL THREE-LAYER MODEL we chose the CMU Mobo database, in which 25 different people perform four different walking- related actions: walking slow, walking fast, walking along a slope, walking while carrying a ball. Cameras are more or less equally spaced around the treadmill. sequences in the Mobo database have three different labels: identity, action, and viewpoint; four series of tests in which we built bilinear models for different content and style labels: view-invariant gaitID, action-invariant gaitID, view-invariant action recognition, style-invariant action classification. comparison with two other approaches: baseline algorithm, and direct application of a nearest-neighbor NN classifier on the dataset of HMMs, using Kullback-Leibler. 2 consider a training set of sequences in which each sequence is associated with more than a single label; each motion can in fact be classified according to the person who performed it, the category of action performed (i.e. walking, reaching out, pointing, etc.), or (if the number of cameras is finite) the viewpoint from which the sequence is shot; multilinear and bilinear models can be seen as tools for separating ``style" and ``content" of the objects to classify. 1 an asymmetric bilinear model can learned from an observation sequence through the SVD of a stacked observation matrix y SC when new motions are acquired in which a known person is being seen walking from a different viewpoint (unknown style) an iterative EM procedure can be set up to classify the content (identity): E step: estimation of p(c|s), the prob. of the content given the current estimate of s; M step: estimation of the linear map for s. FROM VIEW-INVARIANCE TO STYLE-INVARIANCE FROM VIEW-INVARIANCE TO STYLE-INVARIANCE

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