The angle-of-sight signature for two-dimensional shape analysis of manufactured objects

-A new two-dimensional (2D) shape-encoding scheme is introduced which is based on the idea of the angle-of-sight (AOS). Using this scheme, a shape can be efficiently transformed into a one-dimensional (ID) signature by recording the AOS vs. distance of each boundary point with respect to a shape-specific chord-of-sight (COS). The COS is selected by using an extension of the notion of shape boundary, to the idea of shape-specific points and the characteristic ellipse (CE). The AOS signature has many important properties including: it is information-preserving and thus unique, it does not require boundary smoothing; it has its own selectable smoothing property; it can provide a set of multi-scale representations by means of a simple operation; it is transformation-invariant; it is defined at all points; it preserves symmetries. As well, for matching purposes, a two-level matching process is proposed using a global measure (the eccentricity of the CE of a shape) and a dissimilarity measure based on the AOS signature. The encoding and matching techniques developed have been tested with 35 manufactured objects. The results obtained show that the AOS signature and the two-level-matching technique are quite effective and reliable for the recognition of 2D shapes of typical manufactured objects. Shape analysis Shape encoding Signature Shape matching Shape-specific properties I. I N T R O D U C T I O N Shape representation and matching is a key problem in machine-vision-system development. This problem arises, as well, in the context of a new active-vision system for three-dimensional (3D) object recognition in robotic assembly workcells, under development in the Computer Integrated Manufacturing Laboratory (at the University of Toronto). 11'2) In the latter development, the main design concept is to reduce the dimensionality of the recognition task: a 3D object is modeled in this system by using a small set of topologically distinct perspective views, called standard views. The process of shape matching is performed between the acquired two-dimensional (2D) standard view of the sensed object with unknown identity and a library of 2D standard views of a set of objects. Based on the proposed method, then, any usable 2D representation and its corresponding recognition technique must be position-, rotation-, and scale-invariant. Here, following the same concept of dimensionality reduction in a "top-down" fashion, the problem of the design of a transformation-invariant 2D shapeencoding scheme is addressed. Our goal has been the identification of a methodology by which the 2D standard views are transformed into one-dimensional (1 D) signatures suitable for signal matching. Here the required signature is defined as a 1D signal derived from the shape by using an encoding scheme for mapping the information from the 2D "shape" space to the 1D "signature" space. The general problem of 2D shape recognition (classification/discrimination) is one of the most familiar and fundamental problems in pattern recognition. Shape analysis, generally, consists of two basic processes: shape representation (description/modeling/ encoding) and shape identification (matching). Clearly, to a certain extent the type of matching technique employed is determined by the method of shape representation used. In the last three decades, various methodologies have been developed to address this problem in various contexts. These methods have been reviewed and classified in a number of papers, t3-~) In the proposed 2D shape-recognition technique for representation/encoding purposes, a new boundarybased signature is developed and used. The new 2D shape-encoding scheme is based on a new concept, the angle-of-sight (AOS), for extracting and encoding "shape" information. ~6) Parameterization of the boundary of a 2D shape provides a 1D representation (signature) of the geometrical information (which is a periodic function of one variable). This has several