Segmentation and simulation of the deformation of objects represented in images using physical principles

Abstract

The goal of this work is to automatically extract the contour of an object and to simulate its deformation using a physical approach. In this work, to segment an object represented in an image, an initial contour is manually defined for it that will then automatically evolve until it equals the border of the desired object. In our approach, the contour is modelled by physical formulation, using the Finite Elements Method (FEM), and its temporal evolution to the desired final contour is driven by internal forces, defined by the intrinsic material characteristics adopted for the physically model built and the interrelation between its nodes, and external forces, determined in function of the image features that are most representative of the object to be segmented. To build the physical model of the contour used in the segmentation process, we adopted the isoparametric finite element proposed by Sclaroff, and to obtain its evolution towards the object border is used the methodology presented by Nastar that consists in solving the dynamic equilibrium equation between two consecutive instants. As for the simulation of the deformation of an object into another one, or between two different instances of one object, after the initial and final contours have been properly modelled, again using FEM, modal analysis complemented with global optimization technique are employed to establish correspondences between their nodes (data points). After the matching phase, the displacements field between the two contours is simulated using the dynamic equilibrium equation. Our approach seems to be very satisfactory in the segmentation of objects represented in images as well as to simulate the deformation involved between two images. Moreover, it is governed by physically principles, and so the results are coherent with expected behaviour of the objects modelled.