ANSIG - An analytic signature for permutation-invariant two-dimensional shape representation

Many applications require a computer representation of 2D shape, usually described by a set of 2D points. The challenge of this representation is that it must not only capture the characteristics of the shape but also be invariant to relevant transformations. Invariance to geometric transformations, such as translation, rotation and scale, has received attention in the past, usually under the assumption that the points are previously labeled, i.e., that the shape is characterized by an ordered set of landmarks. However, in many practical scenarios the landmarks are obtained from an automatic process, e.g., edge/corner detection, thus without natural ordering. In this paper, we represent 2D shapes in a way that is invariant to the permutation of the landmarks. Within our framework, a shape is mapped to an analytic function on the complex plane, leading to what we call its analytic signature (ANSIG). We show that different shapes lead to different ANSIGs but that shapes that differ by a...

• Type: Conference
• Year: 2008
• Where: CVPR
• Authors: José J. Rodrigues, Pedro M. Q. Aguiar, João M. F. Xavier
• Keywords: Complex Plane, Computer Vision, CVPR 2008, Geometric Transformations, Maximal Invariant, Permutation Group, Shape-based Image Classification