This thesis addresses two problems in content-based video analysis: the segmentation of a 2D rigid moving object; and the inference of 3D rigid structure. In Part I, we consider motion segmentation. Existing methods often fail to detect the motions of low textured regions and regions moving against low contrast background. We describe an algorithm to segment low textured moving objects that mov...

Power corrections to differential cross sections near a kinematic threshold are analysed by Dressed Gluon Exponentiation. Exploiting the factorization property of soft and collinear radiation, the dominant radiative corrections in the threshold region are resummed, yielding a renormalization-scale-invariant expression for the Sudakov exponent. The interplay between Sudakov logs and renormalons ...

The corona factorization property is a property with connections to extension theory, K-theory and the structure of C *-algebras. This paper is a short survey of the subject, together with some new results and open questions.

The corona factorization property is a property with connections to extension theory, K-theory and the structure of C *-algebras. This paper is a short survey of the subject, together with some new results and open questions.

We review the combinatorial structure of perturbative quantum field theory with emphasis given to the decomposition of graphs into primitive ones. The consequences in terms of unique factorization of Dyson– Schwinger equations into Euler products are discussed.

Microblog that provides us a new communication and information sharing platform has been growing exponentially since it emerged just a few years ago. To microblog users, recommending followees who can serve as high quality information sources is a competitive service. To address this problem, in this paper we propose a matrix factorization model with structural regularization to improve the acc...

Given a sparse symmetric positive definite matrix AAT and an associated sparse Cholesky factorization LDLT or LLT, we develop sparse techniques for obtaining the new factorization associated with either adding a column to A or deleting a column from A. Our techniques are based on an analysis and manipulation of the underlying graph structure and on ideas of Gill et al. [Math. Comp., 28 (1974), ...

Tomasi and Kanade [1] introduced the factorization method for recovering 3D structure from 2D video. In their formulation, the 3D shape and 3D motion are computed by using an SVD to approximate a matrix that is rank 3 in a noiseless situation. In this paper we reformulate the problem using the fact that the x and y coordinates of each feature are known from their projection onto the image plane...

Several factorization techniques have been proposed for tackling the Structure from Motion problem. Most of them provide a good solution, while the amount of missing data is within an acceptable ratio. Focussing on this problem, we propose an incremental multiresolution scheme able to deal with a high rate of missing data, as well as noisy data. It is based on an iterative approach that applies...

Complex symmetric matrices whose real and imaginary parts are positive definite are shown to have a growth factor bounded by 2 for LU factorization. This result adds to the classes of matrix for which it is known to be safe not to pivot in LU factorization. Block LDLT factorization with the pivoting strategy of Bunch and Kaufman is also considered, and it is shown that for such matrices only 1×...