|Multiscale analysis of similarities between images on Riemannian manifolds and applications|
|Coloma Ballester, Dept de Tecnologies de la Informació i les Comunicacions of the Universitat Pompeu Fabra in Barcelona, Spain|
Image comparison is a main ingredient in many applications in image processing and computer vision such as object recognition, stereo vision, image interpolation, image denoising, exemplar-based image inpainting, among others. The purpose of this talk will be to give an overview of recent techniques allowing to define a multiscale comparison of images defined on Riemannian manifolds and its applications in image and video problems.
The image comparison problem will be formulated as the problem of comparing two patches (local neighborhoods) belonging to each image defined on a Riemannian manifold, which in turn can be defined by the image domain with a suitable metric depending on the image. We will derive from an axiomatic approach a set of multiscale similarity measures that appear as solutions of a degenerate PDE. We will single out some particular instances, in particular, we present a linear model to compare patches defined on two images in R^n endowed with an intrinsic metric which allows to compare them in an affine invariant manner. Besides its genericity, this linear model is selected by its computational feasibility, since it can be approximated leading to an algorithm that has the complexity of the usual patch comparison using a weighted Euclidean distance. We will show applications of this multiscale analysis of similarities to different problems such as interpolation, exemplar-based inpainting and stereo vision.
Coloma Ballester received the degree in Mathematics at the U. Autònoma de Barcelona, the Master "Mathématiques Appliquées à l'Ingénierie" at the U.Paris-IX in 1992 and the Ph.D. in Computer Science at the U. Illes Balears in 1995. After her PhD, she worked at UIB until 1997, and at the CNRS at IHP in Paris, in 1998. Since 1999 Coloma Ballester is an Associate Professor at the Department of Information and Communication Technologies, University Pompeu Fabra, Barcelona.Her research interests include image processing and computer vision. She is currently interested in depth computation, stereo vision and 3D reconstruction, motion estimation, video inpainting and stereo video inpainting, film post-production algorithms, shape recognition, geometric models, and in general in variational models for image processing and computer vision.