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

Relevance Vector Machines For Multivariate Calibration Purposes

The introduction of support vector regression (SVR) and least square support vector machines (LS-SVM) methods for regression purposes in the field of chemometrics has provided advantageous alternatives to the existing linear and nonlinear multivariate calibration (MVC) approaches. Relevance vector machines (RVMs) claim the advantages attributed to all the SVM-based methods over many other regression methods. Additionally, it also exhibits advantages over the standard SVM-based ones since: it is not necessary to estimate the error/margin trade-off parameter C and the insensitivity parameter ε in regression tasks, it is applicable to arbitrary basis functions, the algorithm gives probability estimates seamlessly and offer, additionally, excellent sparseness capabilities, which can result in a simple and robust model for the estimation of different properties. This paper presents the use of RVMs as a nonlinearMVC method capable of dealing with ill-posed problems. To study its behavior, three different chemometric benchmark datasets are considered, including both linear and non-linear solutions. RVM was compared with other calibration approaches reported in the literature. Although RVM performance is comparable with the best results obtained by LS-SVM, the final model achieved is sparser, so the prediction process is faster. Taking into account the other advantages attributed to RVMs, it can be concluded that this technique can be seen as a very promising option to solve nonlinear problems in MVC. Copyright © 2008 JohnWiley & Sons, Ltd.2211-12686694Swierenga, H., (2000) Robust multivariate calibration models in vibrational spectroscopic applications, , Ph.D. Thesis, University of NijmegenHageman, J.A., Streppel, M., Wehrens, R., Bydens, L.M.C., Wave length selection with Tabu search (2003) J. 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