In this work, we propose a novel node splitting method for regression trees and incorporate it into the regression forest framework. Unlike traditional binary splitting, where the splitting rule is selected from a predefined set of binary splitting rules via trial-and-error, the proposed node splitting method first finds clusters of the training data which at least locally minimize the empirical loss without considering the input space. Then splitting rules which preserve the found clusters as much as possible are determined by casting the problem into a classification problem. Consequently, our new node splitting method enjoys more freedom in choosing the splitting rules, resulting in more efficient tree structures. In addition to the Euclidean target space, we present a variant which can naturally deal with a circular target space by the proper use of circular statistics. We apply the regression forest employing our node splitting to head pose estimation (Euclidean target space) and car direction estimation (circular target space) and demonstrate that the proposed method significantly outperforms state-of-the-art methods (38.5% and 22.5% error reduction respectively).

Recognizing group activities is challenging due to the difficulties in isolating individual entities, finding the respective roles played by the individuals and representing the complex interactions among the participants. Individual actions and group activities in videos can be represented in a common framework as they share the following common feature: both are composed of a set of low-level features describing motions, e.g., optical flow for each pixel or a trajectory for each feature point, according to a set of composition constraints in both temporal and spatial dimensions. In this paper, we present a unified model to assess the similarity between two given individual or group activities. Our approach avoids explicit extraction of individual actors, identifying and representing the inter-person interactions. With the proposed approach, retrieval from a video database can be performed through Query-by-Example; and activities can be recognized by querying videos containing known activities. The suggested video matching process can be performed in an unsupervised manner. We demonstrate the performance of our approach by recognizing a set of human actions and football plays.

We present a two-stage approach for learning dictionaries for object classification tasks based on the principle of information maximization. The proposed method seeks a dictionary that is compact, discriminative, and generative. In the first stage, dictionary atoms are selected from an initial dictionary by maximizing the mutual information measure on dictionary compactness, discrimination and reconstruction. In the second stage, the selected dictionary atoms are updated for improved reconstructive and discriminative power using a simple gradient ascent algorithm on mutual information. Experiments using real datasets demonstrate the effectiveness of our approach for image classification tasks.

In this paper, we consider the 'Precis' problem of sampling K representative yet diverse data points from a large dataset. This problem arises frequently in applications such as video and document summarization, exploratory data analysis, and pre-filtering. We formulate a general theory which encompasses not just traditional techniques devised for vector spaces, but also non-Euclidean manifolds, thereby enabling these techniques to shapes, human activities, textures and many other image and video based datasets. We propose intrinsic manifold measures for measuring the quality of a selection of points with respect to their representative power, and their diversity. We then propose efficient algorithms to optimize the cost function using a novel annealing-based iterative alternation algorithm. The proposed formulation is applicable to manifolds of known geometry as well as to manifolds whose geometry needs to be estimated from samples. Experimental results show the strength and generality of the proposed approach.

Matrix factorization in the presence of missing data is at the core of many computer vision problems such as structure from motion (SfM), non-rigid SfM and photometric stereo. We formulate the problem of matrix factorization with missing data as a low-rank semidefinite program (LRSDP) with the advantage that: $1)$ an efficient quasi-Newton implementation of the LRSDP enables us to solve large-scale factorization problems, and $2)$ additional constraints such as ortho-normality, required in orthographic SfM, can be directly incorporated in the new formulation. Our empirical evaluations suggest that, under the conditions of matrix completion theory, the proposed algorithm finds the optimal solution, and also requires fewer observations compared to the current state-of-the-art algorithms. We further demonstrate the effectiveness of the proposed algorithm in solving the affine SfM problem, non-rigid SfM and photometric stereo problems.

A combined neural network and rule-based approach is suggested as a general framework for pattern recognition. This approach enables unsupervised andsupervised learning, respectively, while providing probability estimates for the output classes. The probability maps are utilized for higher level analysis such as a feedback for smoothing over the output label mapsand the identification of unknown patterns (pattern "discovery"). The suggested approach is presented and demonstrated in the texture - analysis task. A correct classification rate in the 90 percentile is achieved for both unstructured and structured natural texture mosaics. The advantages ofthe probabilistic approach to pattern analysis are demonstrated.

A combined neural network and rule-based approach is suggested as a general framework for pattern recognition. This approach enables unsupervised and supervised learning, respectively, while providing probability estimates for the output classes. The probability maps are utilized for higher level analysis such as a feedback for smoothing over the output label maps and the identification of unknown patterns (pattern "discovery"). The suggested approach is presented and demonstrated in the texture - analysis task. A correct classification rate in the 90 percentile is achieved for both unstructured and structured natural texture mosaics. The advantages of the probabilistic approach to pattern analysis are demonstrated.