Segmentation and simulation of objects represented in images using physical principles

Abstract

The main goals of the present work are to automatically extract the contour of anobject and to simulate its deformation using a physical approach. In this work, to segment anobject represented in an image, an initial contour is manually defined for it that will thenautomatically evolve until it reaches the border of the desired object. In this approach, thecontour is modelled by a physical formulation using the finite element method, and itstemporal evolution to the desired final contour is driven by internal and external forces. Theinternal forces are defined by the intrinsic characteristics of the material adopted for thephysical model and the interrelation between its nodes. The external forces are determined infunction of the image features most suitable for the object to be segmented. To build thephysical model of the contour used in the segmentation process, the isoparametric finiteelement proposed by Sclaroff is adopted, and to obtain its evolution towards the object borderthe methodology presented by Nastar is used, that consists in solving the dynamic equilibriumequation between two consecutive instants.To simulate the deformation between two different instances of an object, after they each havetheir contours properly modelled, modal analysis, complemented with global optimizationtechniques, is employed to establish the correspondence between their nodes (data points).After this matching phase, the displacements field between the two contours is simulatedusing the dynamic equilibrium equation that balances the internal forces defined by thephysical model, and the external forces determined by the distance between the two contours.