| This thesis proposes an innovative methodology of image understanding based on the finite element method (FEM). It provides a new perspective on image processing by treating image pixels, feature points, objects, even pedestrians detected from images and videos as interconnecting physical element models instead of discrete sample data. It also presents a direct way to understand properties of image objects by employing existing physics knowledge about the world instead of estimating inherent attributes of image objects and mining relationships among pixel data with conventional statistical and geometrical computer vision techniques. In this thesis, two fundamental computer vision issues, i.e., shape and motion, are addressed through the proposed FEM based understanding methodology.;Shape is one of the most important features for object recognition. Three FEM-based shape descriptors, the finite element region (FER), finite element contour (FEC), and finite element skeleton (FES), are designed by modelling pixels of image regions, contours and skeletons as quadrilateral or beam elements. Experimental results demonstrate the feasibility of FEM shape descriptors in object recognition. Furthermore, affine and projective transformations of planar shapes are studied from the FEM aspect, and a novel constrained active polygon (CAP) model is presented to solve projective normalization problems without prior knowledge of correspondences, which widely expands the application range of FEM shape representation.;Video contains valuable motion information far beyond that of static images. To discern the stability of human crowd behavior, a motion structural analysis approach is established based on the purposiveness description and destination driven model. It reveals the multiphase flow property of crowd movement and reflects the relationship of collectiveness and purposiveness of crowd behaviors. The crowd is represented with self-driven particle elements, which are trackable feature points detected from human bodies. From the motion of particles, an energy descriptor for violence detection is derived, which consists of social force based potential energy and orientation based weighted kinetic energy, and represent the dynamic spatial relationship among people and the intensity of body actions. Experimental results demonstrate the feasibility and effectiveness of the proposed FEM-based image understanding methodologies in the application of object recognition and human behaviors. |
