6,011 research outputs found
On the consistency of Fr\'echet means in deformable models for curve and image analysis
A new class of statistical deformable models is introduced to study
high-dimensional curves or images. In addition to the standard measurement
error term, these deformable models include an extra error term modeling the
individual variations in intensity around a mean pattern. It is shown that an
appropriate tool for statistical inference in such models is the notion of
sample Fr\'echet means, which leads to estimators of the deformation parameters
and the mean pattern. The main contribution of this paper is to study how the
behavior of these estimators depends on the number n of design points and the
number J of observed curves (or images). Numerical experiments are given to
illustrate the finite sample performances of the procedure
Construction of Bayesian Deformable Models via Stochastic Approximation Algorithm: A Convergence Study
The problem of the definition and the estimation of generative models based
on deformable templates from raw data is of particular importance for modelling
non aligned data affected by various types of geometrical variability. This is
especially true in shape modelling in the computer vision community or in
probabilistic atlas building for Computational Anatomy (CA). A first coherent
statistical framework modelling the geometrical variability as hidden variables
has been given by Allassonni\`ere, Amit and Trouv\'e (JRSS 2006). Setting the
problem in a Bayesian context they proved the consistency of the MAP estimator
and provided a simple iterative deterministic algorithm with an EM flavour
leading to some reasonable approximations of the MAP estimator under low noise
conditions. In this paper we present a stochastic algorithm for approximating
the MAP estimator in the spirit of the SAEM algorithm. We prove its convergence
to a critical point of the observed likelihood with an illustration on images
of handwritten digits
Statistical M-Estimation and Consistency in Large Deformable Models for Image Warping
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
Speeding up active mesh segmentation by local termination of nodes.
This article outlines a procedure for speeding up segmentation of images using active mesh systems. Active meshes and other deformable models are very popular in image segmentation due to their ability to capture weak or missing boundary information; however, where strong edges exist, computations are still done after mesh nodes have settled on the boundary. This can lead to extra computational time whilst the system continues to deform completed regions of the mesh. We propose a local termination procedure, reducing these unnecessary computations and speeding up segmentation time with minimal loss of quality
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