Seminars

We describe a new region descriptor and apply it to two problems, object detection and texture classification. The covariance of d-features, e.g., the three-dimensional color vector, the norm of first and second derivatives of intensity with respect to x and y, etc., characterizes a region of interest. We describe a fast method for computation of covariances based on integral images. The idea presented here is more general than the image sums or histograms, which were already published before, and with a series of integral images the covariances are obtained by a
few arithmetic operations. Covariance matrices do not lie on Euclidean space, therefore we use a distance metric involving generalized eigenvalues which also follows from the Lie group structure of positive definite matrices. Feature matching is a simple nearest neighbor search under the distance metric and performed extremely rapidly using the integral images. The performance of the covariance features is superior to other methods, as it is shown, and large rotations and illumination changes are also absorbed by the covariance matrix.

Paper Link: http://www.merl.com/papers/docs/TR2005-111.pdf

Given a signal, we represent it in another system, typically a basis, where its characteristics are more readily apparent in the transform coefficients. However, these representations are typically nonredundant, and thus corruption or loss of transform coefficients can be serious.In comes redundancy; we build a safety net into our representation so that we can avoid those disasters. The redundant counterpart of a basis is called a frame [no one seems to know why they are called frames,perhaps because of the bounds in (25)?]. It is generally acknowledged (at least in the signal processing and harmonic analysis communities) that frames were born in 1952 in the paper by Duffin and Schaeffer [32]. Despite being over half a century old, frames gained popularity only in the last decade, due mostly to the work of the three wavelet pioneers—Daubechies, Grossman, and Meyer.

Paper Link: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4286567&tag=1

The attention paid to matrix manifolds has grown considerably in the computer vision community in recent years. There are a wide range of important applications including face recognition, action recognition, clustering, visual tracking, and motion grouping and segmentation. The increased popularity of matrix manifolds is due partly to the need to characterize image features in non-Euclidean spaces. Matrix manifolds provide rigorous formulations allowing patterns to be naturally expressed and classified in a particular
parameter space. This paper gives an overview of common matrix manifolds employed in computer vision and presents a summary of related applications. Researchers in computer vision should find this survey beneficial due to the overview of matrix manifolds, the discussion as well as the collective references.

Locally Linear embedding (LLE) is a popular dimension reduction method. In this paper, we systematically improve the two main steps of LLE: (A) learning the graph weights W, and (B) learning the embedding Y. We propose a sparse nonnegative W learning algorithm. We propose a weighted formulation for learning Y and show the results are identical to normalized cuts spectral clustering. We further propose to iterate the two steps in LLE repeatedly to improve the results. Extensive experiment results show that iterative LLE algorithm significantly improves both classification and clustering results.

Paper Link : http://arxiv.org/ftp/arxiv/papers/1206/1206.6463.pdf