We study the problem of supervised learning for both binary and multiclass classification from a unified geometric perspective. In particular, we propose a geometric regularization technique to find the submanifold corresponding to an estimator of the class probability P(y|\vec x). The regularization term measures the volume of this submanifold, based on the intuition that overfitting produces rapid local oscillations and hence large volume of the estimator. This technique can be applied to regularize any classification function that satisfies two requirements: firstly, an estimator of the class probability can be obtained; secondly, first and second derivatives of the class probability estimator can be calculated. In experiments, we apply our regularization technique to standard loss functions for classification, our RBF-based implementation compares favorably to widely used regularization methods for both binary and multiclass classification.

This paper proposes a fast online multi-target tracking method, called motion agreement algorithm, which dynamically selects stable object regions to track. The appearance of each object, here pedestrians, is represented by multiple local patches. For each patch, the algorithm computes a local estimate of the direction of motion. By fusion of the agreements between a global estimate of the object motion and each local estimate, the algorithm identifies the object stable regions and enables robust tracking. The proposed patch-based appearance model was integrated into an efficient online tracking system that uses bipartite matching for data association. The experiments on recent pedestrian tracking benchmark sequences show that the proposed method achieves competitive results compared to state-of-the-art methods, including several offline tracking techniques.

We propose a randomized ensemble algorithm to model the time-varying appearance of an object for visual tracking. In contrast with previous online methods for updating classifier ensembles in tracking-by-detection, the weight vector that combines weak classifiers is treated as a random variable and the posterior distribution for the weight vector is estimated in a Bayesian manner. In essence, the weight vector is treated as a distribution that reflects the confidence among the weak classifiers used to construct and adapt the classifier ensemble. The resulting formulation models the time-varying discriminative ability among weak classifiers so that the ensembled strong classifier can adapt to the varying appearance, backgrounds, and occlusions. The formulation is tested in a tracking-by-detection implementation. Experiments on 28 challenging benchmark videos demonstrate that the proposed method can achieve results comparable to and often better than those of state-of-the-art approaches.

We present a novel framework for multiple object tracking in which the problems of object detection and data association are expressed by a single objective function. The framework follows the Lagrange dual decomposition strategy, taking advantage of the often complementary nature of the two subproblems. Our coupling formulation avoids the problem of error propagation from which traditional “detection-tracking approaches” to multiple object tracking suffer. We also eschew common heuristics such as “nonmaximum suppression” of hypotheses by modeling the joint image likelihood as opposed to applying independent likelihood assumptions. Our coupling algorithm is guaranteed to converge and can handle partial or even complete occlusions. Furthermore, our method does not have any severe scalability issues but can process hundreds of frames at the same time. Our experiments involve challenging, notably distinct datasets and demonstrate that our method can achieve results comparable to those of state-of-art approaches, even without a heavily trained object detector.

This paper proposes novel algorithms that use network-flow and set-cover techniques to perform occlusion reasoning for a large number of small, moving objects in single or multiple views. We designed a track-linking framework for reasoning about short-term and long-term occlusions. We introduce a two-stage network-flow process to automatically construct a “track graph” that describes the track merging and splitting events caused by occlusion. To explain short-term occlusions, when local information is sufficient to distinguish objects, the process links trajectory segments through a series of optimal bipartite-graph matches. To resolve long-term occlusions, when global information is needed to characterize objects, the linking process computes a logarithmic approximation solution to the set cover problem. If multiple views are available, our method builds a track graph, independently for each view, and then simultaneously links track segments from each graph, solving a joint set cover problem for which a logarithmic approximation also exists. Through experiments on different datasets, we show that our proposed linear and integer optimization techniques make the track graph a particularly useful tool for tracking large groups of individuals in images.

We propose a multi-object multi-camera framework for tracking large numbers of tightly-spaced objects that rapidly move in three dimensions. We formulate the problem of finding correspondences across multiple views as a multidimensional assignment problem and use a greedy randomized adaptive search procedure to solve this NP-hard problem efficiently. To account for occlusions, we relax the one-to-one constraint that one measurement corresponds to one object and iteratively solve the relaxed assignment problem. After correspondences are established, object trajectories are estimated by stereoscopic reconstruction using an epipolar-neighborhood search. We embedded our method into a tracker-to-tracker multi-view fusion system that not only obtains the three-dimensional trajectories of closely-moving objects but also accurately settles track uncertainties that could not be resolved from single views due to occlusion. We conducted experiments to validate our greedy assignment procedure and our technique to recover from occlusions. We successfully track hundreds of flying bats and provide an analysis of their group behavior based on 150 reconstructed 3D trajectories.