Free boundary methods and non-scattering phenomena.

We study a question arising in inverse scattering theory: given a penetrable obstacle, does there exist an incident wave that does not scatter? We show that every penetrable obstacle with real-analytic boundary admits such an incident wave. At zero frequency, we use quadrature domains to show that there are also obstacles with inward cusps having this property. In the converse direction, under a nonvanishing condition for the incident wave, we show that there is a dichotomy for boundary points of any penetrable obstacle having this property: either the boundary is regular, or the complement of the obstacle has to be very thin near the point.

Automatic dynamic texture segmentation using local descriptors and optical flow.

A dynamic texture (DT) is an extension of the texture to the temporal domain. How to segment a DT is a challenging problem. In this paper, we address the problem of segmenting a DT into disjoint regions.

A new convexity measure based on a probabilistic interpretation of images.

In this paper, we present a novel convexity measure for object shape analysis. The proposed method is based on the idea of generating pairs of points from a set and measuring the probability that a point dividing the corresponding line segments belongs to the same set. The measure is directly applicable to image functions representing shapes and also to gray-scale images which approximate image binarizations.

Affine invariant pattern recognition using Multiscale Autoconvolution.

This paper presents a new affine invariant image transform called Multiscale Autoconvolution (MSA). The proposed transform is based on a probabilistic interpretation of the image function. The method is directly applicable to isolated objects and does not require extraction of boundaries or interest points, and the computational load is significantly reduced using the Fast Fourier Transform.