3 D Shape Complexity using View Similarity

Shape complexity algorithms are mostly based on informatio n theory, which is based on probability theory and statistics, like Shannon’s definition of entropy or mutual information. The input of the probability density function (pdf), which is a part of the entropy function, could be the curvatur es of the 3D shape or other numbered features representing the shape. After ap plying statistical algorithms, the 3D shape’s complexity can be directly obtai ned from computing the probability density and the entropy of these features. Shannon entropy does not require any assumptions about the distribution of variables. This attribute is an advantage and at the same tim e a disadvantage. As advantage, it requires less source information. But as disad vantage, it doesn’t preserve such information. However, in this thesis, we rely exactly on this information to compute the complexity of a 3D shape. In this thesis, we present a new algorithm for computing shap e complexity that is based on the similarity of silhouettes obtained from different view points around a 3D shape. Concentrating on analyzing the similarity distance between different views leads us to a distance graph between a set of p oints (each point represents a view). From this distance graph, the complexit y of the shape is computed. Using a suitable method to analyze this graph, the loss of distribution information can also be decreased or totally avoided. Given a 3D shape, we first take binary view images from differe nt view points around it. After comparing the similarities between the sil houettes of these view images, we obtain a symmetric matrix of similarity distance s. Then we use muli ii ABSTRACT tidimensional Similarity Structure Analysis (SSA) to anal yze this similarity distance matrix. After assigning the position of starting poin ts i the corresponding SSA plot and moving these points towards their final position , we obtain a distribution graph of points (views) in which the wider the poin ts are spread out the more complex the original shape is. By describing how well the se points are distributed, we can obtain a numerical value which indicates th complexity of the 3D shape.