There are many significant applications of Fourier Shape Descriptor characterization of boundaries of regions in images. Whenever it is desirable to compare two shapes, independent of rotation, starting point, or compensate for magnification, Fourier Shape Descriptors (FSDs) have merits. FSDs have been proposed for the automatic assessment of packaging; to check alignment of objects for automation; and characterize visual objects in video coding, and compare biomedical regions in medical images. This paper presents a technique to parameterize the boundary of the region of interest (ROI) that utilizes the casting of rays from the center of mass of the region of interest outward to points in the image that lie on the edge of the ROI. This is essentially another technique to obtain the R-S parametrization. At each step the process utilizes the sections of the boundary have radii that are a simple function of theta. The procedure then merges these simple boundary sections to create a periodic complex valued function of the boundary parameterized by a parameter s that is not required to be a function of theta. Once the complex periodic sequence is obtained, the Fourier Transform is taken resulting in the corresponding Fourier Shape Descriptors. Since the technique seeks the intersection of a known ray with the boundary (it is not boundary following), the worst-case behavior of the technique is easily calculated making it suitable for real-time applications. The technique is robust to incomplete boundaries of objects, and can be readily extended to three-dimensional datasets (spherical harmonics). The a simpler version of the technique is currently being used in the automatic selection of the axis of symmetry in Magnetic Resonance Images of the brain, and we will demonstrate the application of the technique on these types of datasets, although the technique has general application.