An efficient surface rendering method utilizing Fourier descriptors to visualize three dimensional biological image data sets

Fourier descriptors (FD) have proved to be powerful contour representation and analytical tools. After simple mathematical manipulations, complete contour descriptors which are invariant to geometrical transformations can be obtained. In this dissertation, new applications of FDs for three dimensional (3-D) image data set visualization have been devised by fully exploiting the special structure of FD. The main developments in this dissertation are the algorithmic steps in an efficient integrated 3-D reconstruction method to accomplish 3-D visualization starting from 3-D data acquisition and ending with 3-D surface rendered biomedical objects. Extension of Fourier descriptor methods to describe 3-D closed surfaces is the major contribution of this dissertation. Other contributions include the development of algorithms based on the specific characteristics of FD to solve problems encountered in digital image processing and computer vision.;Most of the 3-D data acquisition modalities used in biomedicine suffer from a lower resolution along the z-axis than on the x- and y-plane. Interpolating the 3-D data sets is an inevitable operation to produce an appealing 3-D visualization. FD can be regarded as an efficient interpolation or, more precisely, approximation tool. After 3-D data sets have been acquired, contour segmentation is applied to extract feature contours of biomedical objects from the data sets for later 3-D visualization. In this thesis, deformable models are adopted to perform edge contour following. Because a closed contour can be represented by FD, the above mentioned problem can be transformed into an iterative searching problem over the Fourier coefficient space. Fast algorithms can be developed by fully exploiting the FD's special structure. Although most of the 3-D data acquisition modalities can collect 3-D data sets with a single mounting of the object, registration of the starting points, an essential problem in 3-D visualization but seldom mentioned in the literature, is still important to achieve a reliable visual result. In this dissertation, a starting point registration algorithm based on FD has been developed and tested. As demonstrated in the dissertation, the proposed algorithm can solve the problem fast and efficiently. After all the contours in the set have been registered, surface FDs can then be applied to represent 3-D closed surfaces. Due to the orthogonality principle of complex harmonics, and the fact that FDs form an orthogonal and complete basis in the L...