Axsi-based Shape Representation And Clustering

As more and more images have been generated in digital form around the world. There is a growing interest in finding objects using digital image in large collections. In order to find an object accurately, the object has to be described or represented by certain features. Shape is an important visual feature of an object in an image. It is important to represent an object by its shape. Searching for images or object recognition using shape features has attracted much attention. There are many shape representation and description techniques in the literature. There are mainly two approaches to shape representation. The first is based on the use of shape boundary points and another is based on the use of the interior points of the shape. Here, we are interested in studying the techniques based on axis which belongs to the later.In this thesis, we study the shape representation problem and propose new methods for shape representation and clustering based on shape skeleton. Firstly, we introduce a new method for shape representation with spectral graph theory. We consider the discrete points set of a shape as a graph. After the singular vale decomposition of the Q-Laplacian of the graph, the eigenvalue is used to describe the shape. By using MDS, we analyze the result of the clustering after project the eigenvalue into two-dimensional space.Secondly, the scale-free network is introduced into the shape analysis. The discrete points set of a shape skeleton is modeled as a scale-free network. Some measurements of the network are assembled into a vector to describe the shape. The high dimension vector is projected to three-dimensional space use MDS. The result of clustering is analysed in this space.