Deformation Based Curved Shape Representation

Representation and modelling of an objects' shape is critical in object recognition, synthesis, tracking and many other applications in computer vision. As a result, there is a wide range of approaches in formulating representation space and quantifying the notion of similarity between shapes. A similarity metric between shapes is a basic building block in modelling shape categories, optimizing shape valued functionals, and designing a classifier. Consequently, any subsequent shape based computation is fundamentally dependent on the computational efficiency, robustness, and invariance to shape preserving transformations of the defined similarity metric.

In this thesis, we propose a novel finite dimensional shape representation framework that leads to a computationally efficient, closed form solution, and noise tolerant similarity distance function. Several important characteristics of the proposed curved shape representation approach are discussed in relation to earlier works. Subsequently, two different solutions are proposed for optimal parameter estimation of curved shapes. Hence, providing two possible solutions for the point correspondence estimation problem between two curved shapes. Later in the thesis, we show that several statistical models can readily be adapted to the proposed shape representation framework for object category modelling. The thesis finalizes by exploring potential applications of the proposed curved shape representation in 3D facial surface and facial expression representation and modelling.