Hierarchical curvature estimation in computer vision

This thesis concerns the estimation and description of curvature for computer vision applications. Different types of multi-dimensional data are considered: images (2D); volumes (3D); time sequences of images (3D); and time sequences of volumes (4D). The methods are based on local Fourier domain models and use local operations such as filtering. A hierarchical approach is used. Firstly, the local orientation is estimated and represented with a vector field equivalent description. Secondly, the local curvature is estimated from the orientation description. The curvature algorithms are closely related to the orientation estimation algorithms and the methods as a whole give a unified approach to the estimation and description of orientation and curvature. In addition, the methodology avoids thresholding and premature decision making. Results on both synthetic and real world data are presented to illustrate the algorithms performance with respect to accuracy and noise insensitivity. Examples illustrating the use of the curvature estimates for tasks such as image enhancement are also included