Date of Award
Doctor of Philosophy (PhD)
Shape contains information. The identification and extraction of this information is not straightforward and is the main problem of Shape Analysis. The current trend of manipulating visual information, makes this problem more important. The abundant work published about shape analysis can be classified into two main approaches: statistical shape analysis and structural shape analysis. The structural approach was proposed around thirty years ago by K. S. Fu. The large amount of works published since then, prove the difficulty of defining a universal set of primitives. The structural description of shape is based on the assumption that shape recognition is a hierarchical process. Nevertheless, no effective general mechanism that captures hierarchical description has been found, and the existing representations may be applied to restricted applications. We propose a new structural representation of shape using convexity. Instead of using a predefined set of primitives, we use two basic components to decompose any shape: convexity and concavity. The decomposition obtained results in a natural hierarchy, of these basic components. We represent the decomposition by a new shape descriptor: the Convexity-Concavity Tree (CCT), which is a binary tree. The CCT representation is used for matching the shapes of two objects. The matching of two CCTs is represented by a binary tree, that we call the Matching Tree (MT). The Matching Tree represents the location and magnitude of the mismatch between corresponding convexities-concavities of the two shapes. Two shapes match if their corresponding CCTs match. Some of the advantages of our representation method are: (1) it is information preserving, (2) it has the desired properties of a good description method: invariance, uniqueness and stability, (3) it is economical, (4) it is robust in the presence of noise. Our matching method, based on convexity representation is superior to other methods in terms of simplicity, ability to explain and measure mismatches and also it may be used with other well known methods.
Martinez, Gustavo, "A Hierarchical Shape Representation by Convexities and Concavities and Its Application to Shape Matching." (2001). LSU Historical Dissertations and Theses. 244.