Utilizing Moment Invariants and Grobner Bases to Reason About Shapes

Utilizing Moment Invariants and Gröbner Bases to Reason About Shapes

Shapes such as triangles or rectangles can be defined in terms of geometric properties invariant under a group of transformations. Complex shapes can be described by logic formulae w i th simpler shapes as the atoms. A standard technique for computing invariant properties of simple shapes is the method of moment invariants, known since the early sixties. We generalize this technique to shapes d...

Using Image Moment Invariants to Distinguish Classes of Geographical Shapes

Classification of Boundary and Region Shapes Using Hu-moment Invariants

This paper attempts to introduce the concept of moment invariance into the classification algorithm based on the morphological boundary extraction and generalized skeleton transform, and tries to propose a new method about shape classification in this field. Firstly, the method extracts boundary of the object, secondly, skeleton using main skeleton extraction algorithm based on visual important...

Using Moment Invariants for Classifying Shapes on Large_scale Maps

Automated feature extraction and object recognition are large research areas in the field of image processing and computer vision. Recognition is largely based on the matching of descriptions of shapes. Numerous shapes description techniques have been developed, such as scalar features (dimension, area, number of corners etc.), Fourier descriptors and moment invariants. These techniques numeric...

Grobner-shirshov Bases for Representation Theory

In this paper, we develop the Gr6bner-Shirshov basis theory for the representations of associative algebras by introducing the notion of Gr6bner-Shirshov pairs. Our result can be applied to solve the reduction problem in representation theory and to construct monomial bases of representations of associative algebras. As an illustration, we give an explicit construction of Gr6bner-Shirshov pairs...