Paper Info
Title
Statistical M-Estimation and Consistency in Large Deformable Models for Image Warping
Abstract
The problem of defining appropriate distances between shapes or images and modeling the variability of natural images by group transformations is at the heart of modern image analysis. A current trend is the study of probabilistic and statistical aspects of deformation models, and the development of consistent statistical procedure for the estimation of template images. In this paper, we consider a set of images randomly warped from a mean template which has to be recovered. For this, we define an appropriate statistical parametric model to generate random diffeomorphic deformations in two-dimensions. Then, we focus on the problem of estimating the mean pattern when the images are observed with noise. This problem is challenging both from a theoretical and a practical point of view. M-estimation theory enables us to build an estimator defined as a minimizer of a well-tailored empirical criterion. We prove the convergence of this estimator and propose a gradient descent algorithm to compute this M-estimator in practice. Simulations of template extraction and an application to image clustering and classification are also provided.
Year
DOI
Venue
2009
10.1007/s10851-009-0146-1
Journal of Mathematical Imaging and Vision
Keywords
Field
DocType
Image warping,Template extraction,Random diffeomorphism,Large deformable models,M-estimation,Asymptotic statistics,Clustering
Convergence (routing),Artificial intelligence,Probabilistic logic,Cluster analysis,Diffeomorphism,Computer vision,Mathematical optimization,Gradient descent,Parametric model,Image warping,Pattern recognition,Mathematics,Estimator
Journal
Volume
Issue
ISSN
34
3
0924-9907
Citations 
PageRank 
References 
9
0.72
13
Authors
3
Name
Order
Citations
PageRank
Jérémie Bigot1495.38
Sébastien Gadat2504.37
Jean-Michel Loubes34311.63