Calculus of Variations and Geometric Measure Theory

A. C. G. Mennucci - S. Soatto - G. Sundaramoorthi - A. Yezzi

Tracking deforming objects by filtering and prediction in the space of curves.

created by mennucci on 14 Nov 2012
modified by paolini on 19 Nov 2012


Published Paper

Inserted: 14 nov 2012
Last Updated: 19 nov 2012

Journal: Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on . Shanghai, China, December, 2009,
Pages: 2395-2401
Year: 2009
Doi: 10.1109/CDC.2009.5400786


We propose a dynamical model-based approach for tracking the shape and deformation of highly deforming objects from time-varying imagery. Previous works have assumed that the object deformation is smooth, which is realistic for the tracking problem, but most have restricted the deformation to belong to a finite-dimensional group, such as affine motions, or to finitely-parameterized models. This, however, limits the accuracy of the tracking scheme. We exploit the smoothness assumption implicit in previous work, but we lift the restriction to finite-dimensional motions/deformations. To do so, we derive analytical tools to define a dynamical model on the (infinite-dimensional) space of curves. To demonstrate the application of these ideas to object tracking, we construct a simple dynamical model on shapes, which is a first-order approximation to any dynamical system. We then derive an associated nonlinear filter that estimates and predicts the shape and deformation of a object from image measurements.