Use of the Radon Transform as a Method of Extracting Symbolic Representations of Shape in Two Dimensions

The perception and representation of shape plays a prominent role in computer vision research. Vision alone cannot deliver computationally realistic descriptions of shape; the image must first be processed to extract symbolic representations of the sort computers can manipulate. The present work evaluates the use of the Radon transform as a means whereby the transition from edge image data to symbolic representation may be realized. The potential of the method is developed and illustrated by consideration of the criteria fundamental to an efficient representation of shape. Geometric properties and spatial relations made explicit by the transformation are listed and used to encode representations of shape. A methodology is suggested for the extraction of the salient features of a model representation, the use of those features in object recognition and the recovery of the viewer object correspondence. The evolution of computational models for shape can be traced through successive trends in pattern recognition. In the 1960's, shape was represented by idealized templates. This method is inefficient because each object requires a unique template to represent each possible orientation and location of the object. Some years later shapes and patterns were being represented on the basis of global feature measurements, e.g., moments[l], [2] or Fourier coefficients[3]. These methods, while they are computationally efficient and reasonably insensitive to noise and quantisation, have the major disadvantage that the computed value of a global feature for the visible portion of an occluded object bears an arbitrary relationship to the value that would be computed for the whole object. Other models of shape depend on knowledge of the boundary of the object, for example, chain coding[4]. In this technique, the boundary of the object is represented by short segments. In the most basic of implementations, each segment will have associated with it, one of eight possible orientations. Thus the method has the advantage of generating shape primitives that may be used to construct a description of any curve to some finite resolution dictated by the length and possible ori-entations of the line segments. However, the weakness inherent in this and other curve approximation schemes is that, since the representation is one dimensional, the shape of the interior region is not made explicit. The method makes explicit the relationships between adjacent points along the contour but not where and in what ways the contour doubles back on itself. This doubling back has a marked effect on our …