An Ellipsoidal 3D Shape Representation and Wavelet Transform Feature Descriptor for 3D Shape Retrieval

For the year of past most three-dimensional objects are represented and mapped with spherical function. Since the mapping preserves important criteria such as geometrical information of a 3D object, the representation of a 3D shape in a suitable way is an important matter for 3D object retrieval. In many circumstances, spherical surface fitting to a 3D shape does not approximate very well, because of their limited degree of divergence by their radius only. Whereas, in the case of ellipsoid definition we get three axes, which gives us a free mapping along each of x, y and z axes . Due to higher degree of freedom ellipsoid give better approximation for a given 3D shape than sphere which lead to a less error and higher discriminant shape descriptor for retrieval of 3D shape. In this paper, we describe a new 3D shape representation method based on ellipsoid for the purpose of 3D shape retrieval. And we demonstrate our experimental result tested on standard 3D shape Princeton Shape Benchmark (PSB) database, inferring new wavelet shape descriptor of the represented 3D shape function on ellipsoid. Our experimental results support our expectation of our proposed hypothesis. KeywordsShape Representation; Ellipsoid Approximation; Ellipsoidal Wavelet; 3D Shape Retrieval; Wavelet Descriptor; Computer Vision