Moments And Its Applications In Geometric Shape Description

Geometric shape description is one of the main research topics in computer graphics,computer vision and pattern recognition. It's hard to define shape which has been widely understood. In human being's vision, recognition and understanding, shape is a significant parameter. Hence, it's gaining increasing attension to express this definition and obtain the corresponding parameters in mathmatics. Moments are defined in terms of Riemann integrals of shape density function and kernel function. And geometric moments are composed of coefficients of Fourier transform of shape. Therefore, the shape of object is uniquely determined by geometric moments. Other extended form of moments is generalized transformation or function. In this paper, we extend moment expressions of both shape density function and kernel function, and propose new moments which are called structure moments, curve structure moments, Bezier moments, B-spline moments, 3D polar-radius invariant moments and so on. These methods are applied in shape recognition. The main contributions of this thesis are summarized as follows:(1) Structure moment invariants are introduced,which are based on the geometric moment invariants from transforming the density in geometric moments into a new density. The difference in the shapes is increased by using the structure moment invariants. Therefore, this method can be used in object shape analysis.(2) The curve structure moment and curve structure moment invariants are proposed, which are suitable to be used not only in the pattern recognition of closed shapes, but also in that of any curved shapes. Experiments give an encouraging high computing rates.(3) A novel moment, called 3D polar-radius-invariant-moment, is proposed for the 3D object recognition and classification. We define the polar-radius-invariant-moment and its normalized moment, and the central polar-radius-invariant-moment and its normalized central moment. The translation, scale and rotation invariance of the normalized moment and normalized central moment are proved theoretically. To support our new theory, an algorithm for object shape recognition is designed based on the new moments and experiments are conducted. Examples are presented to illustrate the performance of these moments. In the comparing experiment of recognition of objects, 3D polar-radius-invariant-moments give an encouraging high recognition rates.