DMCA
Variational Methods in Image Matching and Motion Extraction in Level set and PDE Based Reconstruction Methods: Applications to Inverse Problems and Image Processing
BibTeX
@MISC{Rumpf_variationalmethods,
author = {Martin Rumpf},
title = {Variational Methods in Image Matching and Motion Extraction in Level set and PDE Based Reconstruction Methods: Applications to Inverse Problems and Image Processing},
year = {}
}
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Abstract
Abstract. In this chapter we are concerned with variational methods in image analysis. Special attention is paid on free discontinuity approaches of Mumford Shah type and their application in segmentation, matching and motion analysis. We study combined approaches, where one simultaneously relaxes a functional with respect to multiple unknowns. Examples are the simultaneously extraction of edges in two different images for joint image segmentation and image registration or the joint estimation of motion, moving object, and object intensity map. In these approaches the identification of one of the unknowns improves the capability to extract the other as well. Hence, combined methods turn out to be very powerful approaches. Indeed, fundamental tasks in image processing are highly interdependent: Registration of image morphology significantly benefits from previous denoising and structure segmentation. On the other hand, combined information of different image modalities makes shape segmentation significantly more robust. Furthermore, robustness in motion extraction of shapes can be significantly enhanced via a coupling with the detection of edge surfaces in space time and a corresponding feature sensitive space time smoothing. Furthermore, one of the key tools throughout most of the methods to be presented is nonlinear elasticity based on hyperelastic and polyconvex energy functional. Based on first principles from continuum mechanics this allows a flexible description of shape correspondences and in many cased enables to establish existence results and one-to-one mapping properties. Numerical experiments underline the robustness of the presented methods and show applications on medical images and biological experimental data. This chapter is based on a couple of recent articles [8,49,29,30,63] published
Keyphrases
variational method motion extraction image processing image matching reconstruction method level set structure segmentation many cased enables combined approach existence result object intensity map motion analysis different image modality nonlinear elasticity mumford shah type fundamental task polyconvex energy functional key tool edge surface numerical experiment image registration powerful approach free discontinuity approach shape segmentation show application joint image segmentation joint estimation image morphology medical image special attention different image continuum mechanic image analysis biological experimental data shape correspondence one-to-one mapping property corresponding feature sensitive space time recent article space time simultaneously extraction first principle flexible description
