An efficient surface rendering technique utilizing Fourier descriptors to visualize three dimensional biomedical image data sets

Three dimensional (3-D) reconstruction of structures and their visualization are becoming essential components to understanding pertinent relationships in branches of biological sciences, engineering, and medicine. The most popular algorithm for 3-D surface rendering for anatomical data utilizes cross-sectional planar contours. In this paper we will introduce a new technique to achieve 3-D surface representation and subsequent visualization using Fourier descriptors. Owing to the orthogonal principle of complex exponential harmonics, we can transform an original 2-D (two Dimensional) problem into 1-D (One Dimensional) problems, thus reducing the computational load dramatically. Examples from NMR (Nuclear Magnetic Resonance) and CSLM (Confocal Scanning Laser Microscopy) will be given to demonstrate surface Fourier descriptors. This paper discusses not only how Fourier descriptors can represent 3-D surfaces efficiently, but also how they can be used to solve preprocessing data problems to create an appealing 3-D visualization. For example, Fourier descriptors can be applied to solve the alignment of starting points in an data set, a problem seldom mentioned in the literature