Fundamentals of digital image processing
Fundamentals of digital image processing
The nature of statistical learning theory
The nature of statistical learning theory
Computational anatomy: an emerging discipline
Quarterly of Applied Mathematics - Special issue on current and future challenges in the applications of mathematics
MiniMax Methods for Image Reconstruction
MiniMax Methods for Image Reconstruction
Landmark Matching via Large Deformation Diffeomorphisms on the Sphere
Journal of Mathematical Imaging and Vision
A Statistical Approach to Large Deformation Diffeomorphisms
CVPRW '04 Proceedings of the 2004 Conference on Computer Vision and Pattern Recognition Workshop (CVPRW'04) Volume 12 - Volume 12
Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics
Foundations of Computational Mathematics
Image Statistics Based on Diffeomorphic Matching
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements
Journal of Mathematical Imaging and Vision
Large deformation diffeomorphisms with application to optic flow
Computer Vision and Image Understanding
POP: Patchwork of Parts Models for Object Recognition
International Journal of Computer Vision
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
Smoothing under Diffeomorphic Constraints with Homeomorphic Splines
SIAM Journal on Numerical Analysis
Image Morphing in Frequency Domain
Journal of Mathematical Imaging and Vision
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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.