To the Graduate Council: I am submitting herewith a dissertation ...

an orthonormal frame formed by a normal vector n 1 , a reference vector n 2 and theircross product. n 1 is defined as the unit normal vector of a plane P fitted through thespace curve C. The distance between C and P can be plotted as a function, whichserves as the feature of the center point and is called the Point Signature. Due to thesimple representation, matching Point Signatures is efficient.Johnson and Hebert [45] proposed the Spin Image for surface registration. To createa Spin Image, a local 2D basis is computed at an oriented point that is a 3D pointwith surface normal. The coordinates of the other points on the surface with respectto the basis are then used in a voting procedure to create the descriptive Spin Imagefor the point. With the surface point p and its normal n, two coordinates α and β of agiven point x are computed. α represents the distance from x to the tangent plane atp and β is the distance from x to n. Next, a bin is determined by discretizing (α, β)and then used to match the corresponding points.The concept of Spin Images wasdeveloped from Geometric Hashing [50], but Spin Images use the image to describe thefeature instead of performing lookup in a hash table. The term Spin Image came fromthe cylindrical symmetry of the representation. The Spin Image was also applied to 3Dobject recognition by Carmichael et al. [18].Yamany and Farag [105] proposed a modified version of Spin Image, which is calledthe Surface Point Signature (SPS), where α and β are differently defined from the SpinImage. α represents the distance between the center point and every surface point, andβ is the angle between the normal of the center point and the segment created by the18