In this work, we consider the problem of modeling the dynamic structure of human activities in the attributes space. A video sequence is first represented in a semantic feature space, where each feature encodes the probability of occurrence of an activity attribute at a given time. A generative model, denoted the binary dynamic system (BDS), is proposed to learn both the distribution and dynamics of different activities in this space. The BDS is a non-linear dynamic system, which extends both the binary principal component analysis (PCA) and classical linear dynamic systems (LDS), by combining binary observation variables with a hidden Gauss-Markov state process. In this way, it integrates the representation power of semantic modeling with the ability of dynamic systems to capture the temporal structure of time-varying processes. An algorithm for learning BDS parameters, inspired by a popular LDS learning method from dynamic textures, is proposed. A similarity measure between BDSs, which generalizes the Binet-Cauchy kernel for LDS, is then introduced and used to design activity classifiers. The proposed method is shown to outperform similar classifiers derived from the kernel dynamic system (KDS) and state-of-the-art approaches for dynamics-based or attribute-based action recognition.

The problem of multiclass boosting is considered. A new framework,based on multi-dimensional codewords and predictors is introduced. The optimal set of codewords is derived, and a margin enforcing loss proposed. The resulting risk is minimized by gradient descent on a multidimensional functional space. Two algorithms are proposed: 1) CD-MCBoost, based on coordinate descent, updates one predictor component at a time, 2) GD-MCBoost, based on gradient descent, updates all components jointly. The algorithms differ in the weak learners that they support but are both shown to be 1) Bayes consistent, 2) margin enforcing, and 3) convergent to the global minimum of the risk. They also reduce to AdaBoost when there are only two classes. Experiments show that both methods outperform previous multiclass boosting approaches on a number of datasets.

We propose maximum covariance unfolding (MCU), a manifold learning algorithm for simultaneous dimensionality reduction of data from different input modalities. Given high dimensional inputs from two different but naturally aligned sources, MCU computes a common low dimensional embedding that maximizes the cross-modal (inter-source) correlations while preserving the local (intra-source) distances. In this paper, we explore two applications of MCU. First we use MCU to analyze EEG-fMRI data, where an important goal is to visualize the fMRI voxels that are most strongly correlated with changes in EEG traces. To perform this visualization, we augment MCU with an additional step for metric learning in the high dimensional voxel space. Second, we use MCU to perform cross-modal retrieval of matched image and text samples from Wikipedia. To manage large applications of MCU, we develop a fast implementation based on ideas from spectral graph theory. These ideas transform the original problem for MCU, one of semidefinite programming, into a simpler problem in semidefinite quadratic linear programming.

The problem of controlling the margin of a classifier is studied. A detailed analytical study is presented on how properties of the classification risk, such as its optimal link and minimum risk functions, are related to the shape of the loss, and its margin enforcing properties. It is shown that for a class of risks, denoted canonical risks, asymptotic Bayes consistency is compatible with simple analytical relationships between these functions. These enable a precise characterization of the loss for a popular class of link functions. It is shown that, when the risk is in canonical form and the link is inverse sigmoidal, the margin properties of the loss are determined by a single parameter. Novel families of Bayes consistent loss functions, of variable margin, are derived. These families are then used to design boosting style algorithms with explicit control of the classification margin. The new algorithms generalize well established approaches, such as LogitBoost. Experimental results show that the proposed variable margin losses outperform the fixed margin counterparts used by existing algorithms. Finally, it is shown that best performance can be achieved by cross-validating the margin parameter.

The determination of dominant orientation at a given image location is formulated as a decision-theoretic question. This leads to a novel measure for the dominance of a given orientation $\theta$, which is similar to that used by SIFT. It is then shown that the new measure can be computed with a network that implements the sequence of operations of the standard neurophysiological model of V1. The measure can thus be seen as a biologically plausible version of SIFT, and is denoted as bioSIFT. The network units are shown to exhibit trademark properties of V1 neurons, such as cross-orientation suppression, sparseness and independence. The connection between SIFT and biological vision provides a justification for the success of SIFT-like features and reinforces the importance of contrast normalization in computer vision. We illustrate this by replacing the Gabor units of an HMAX network with the new bioSIFT units. This is shown to lead to significant gains for classification tasks, leading to state-of-the-art performance among biologically inspired network models and performance competitive with the best non-biological object recognition systems.

The problem of optimal and automatic design of a detector cascade is considered. A novel mathematical model is introduced for a cascaded detector. This model is analytically tractable, leads to recursive computation, and accounts for both classification and complexity. A boosting algorithm, FCBoost, is proposed for fully automated cascade design. It exploits the new cascade model, minimizes a Lagrangian cost that accounts for both classification risk and complexity. It searches the space of cascade configurations to automatically determine the optimal number of stages and their predictors, and is compatible with bootstrapping of negative examples and cost sensitive learning. Experiments show that the resulting cascades have state-of-the-art performance in various computer vision problems.

The machine learning problem of classifier design is studied from the perspective of probability elicitation, in statistics. This shows that the standard approach of proceeding from the specification of a loss, to the minimization of conditional risk is overly restrictive. It is shown that a better alternative is to start from the specification of a functional form for the minimum conditional risk, and derive the loss function. This has various consequences of practical interest, such as showing that 1) the widely adopted practice of relying on convex loss functions is unnecessary, and 2) many new losses can be derived for classification problems. These points are illustrated by the derivation of a new loss which is not convex, but does not compromise the computational tractability of classifier design, and is robust to the contamination of data with outliers. A new boosting algorithm, SavageBoost, is derived for the minimization of this loss. Experimental results show that it is indeed less sensitive to outliers than conventional methods, such as Ada, Real, or LogitBoost, and converges in fewer iterations.

The classical hypothesis, that bottom-up saliency is a center-surround process, is combined with a more recent hypothesis that all saliency decisions are optimal in a decision-theoretic sense. The combined hypothesis is denoted as discriminant center-surround saliency, and the corresponding optimal saliency architecture is derived. This architecture equates the saliency of each image location to the discriminant power of a set of features with respect to the classification problem that opposes stimuli at center and surround, at that location. It is shown that the resulting saliency detector makes accurate quantitative predictions for various aspects of the psychophysics of human saliency, including non-linear properties beyond the reach of previous saliency models. Furthermore, it is shown that discriminant center-surround saliency can be easily generalized to various stimulus modalities (such as color, orientation and motion), and provides optimal solutions for many other saliency problems of interest for computer vision. Optimal solutions, under this hypothesis, are derived for a number of the former (including static natural images, dense motion fields, and even dynamic textures), and applied to a number of the latter (the prediction of human eye fixations, motion-based saliency in the presence of ego-motion, and motion-based saliency in the presence of highly dynamic backgrounds). In result, discriminant saliency is shown to predict eye fixations better than previous models, and produce background subtraction algorithms that outperform the state-of-the-art in computer vision.

A dynamic texture is a video model that treats a video as a sample from a spatiotemporal stochastic process, specifically a linear dynamical system. One problem associated with the dynamic texture is that it cannot model video where there are multiple regions of distinct motion. In this work, we introduce the layered dynamic texture model, which addresses this problem. We also introduce a variant of the model, and present the EM algorithm for learning each of the models. Finally, we demonstrate the efficacy of the proposed model for the tasks of segmentation and synthesis of video.

A dynamic texture is a video model that treats a video as a sample from a spatiotemporal stochastic process, specifically a linear dynamical system. Oneproblem associated with the dynamic texture is that it cannot model video where there are multiple regions of distinct motion. In this work, we introduce the layered dynamic texture model, which addresses this problem. We also introduce a variant of the model, and present the EM algorithm for learning each of the models. Finally, we demonstrate the efficacy of the proposed model for the tasks of segmentation and synthesis ofvideo.