Fourier descriptors with different shape signatures: A comparative study for shape based retrieval of kinematic constraints

Fourier Descriptors (FD) has been widely used in image analysis and computer vision for shape recognition as they can be made independent of translation, rotation, as well as scaling. They have also been used for developing methods for the analysis and synthesis of four-bar linkages for path generation. This paper focuses on a comparative study of Fourier descriptors derived from various shape signatures of planar closed curves. This includes representations based on Cartesian coordinates, centroid distance, cumulative angle, and curvature. The comparison is conducted not only using commonly used criteria for shape representation and identification but also in the context of shape based retrieval of kinematic constraints for task centered mechanism design. Examples are provided to seek to extract geometric constraints such as circle, circular arc, ellipse and line-segment from a given motion.