Shape Representation and Registration using Vector Distance Functions

Abstract

This paper introduces a new method for shape registration by matching vector distance functions. The vector distance function representation is more flexible than the conventional signed distance map since it enables us to better control the shapes registration process by using more general transformations. Based on this model, a variational frame work is proposed for the global and local registration of shapes which does not need any point correspondences. The optimization criterion can handle efficiently the estimation of the global registration parameters. A closed form solution is provided to handle an incremental free form deformation model for covering the local deformations. This is an advantage over the gradient descent optimization whichis biased towards the initialization and is more time consuming. Results of real shapes registration will be demonstrated to show the efficiency of the proposed approach with small and large global/local deformations.

Similarity Registration for Shapes Based on Signed Distance Functions

“…More recent work tends towards using SDF (SDF-based) (e.g. see [1], [4], [8] and [9]). These SDF-based algorithms usually minimize the distance between the SDFs iteratively for instance by using a gradient descent algorithm.…”

Modeling small objects under uncertainties : novel algorithms and applications.

“…These contours are then co-registered using the Proct;Istes method; the contour boundary points are obtained and used for registration. The Level sets approach (e.g., [40]) eliminates sources of errors that can arise with manual annotation in which only placing the seed point or points in the region of the nodule centroid is/are manually performed. Also, the elasticity of this variational approach addresses the issue of shape variations that can arise and handles these changes accordingly.…”

Shape analysis of the corpus callosum of autistic and normal subjects in neuroimaging.

“…Results of shape registration on the corpus callosum using the Abdelmunim and Farag Algorithm [38]. Rigid registration/alignment on the left and elastic registration is on the right.…”

“…We will focus our survey here to methods based on level sets; the mathematical developments of these approaches are very involved and well described in the PhD dissertations of two CVIP Lab graduates, Dr. Hossam Abdemunim and Dr. Rachid Fahmi (e.g., [39][41]). The segmentation and the registration approaches of Abdelmunium and Farag [38] and Fahmi and Farag [40] have been used in this thesis. We will highlight some standard approaches for registration in the computer vision and biomedical imaging literature which is of particular interest to the research in this thesis; specifically, the Mutual Information approach for intensity registration, ICP algorithm for rigid registration and the Procrustus technique for shape registration.…”

“…The energy function will be: Figure 9: Illustration of group shape registration using vector level set function [38].…”