Inference of Syntax for Point Sets

This paper discusses a method for extracting structure in point sets in ℝ n . It may be applied repeatedly to such problems as decomposing images into constituent parts, as in the recognition of handwritten characters, where we treat a character as a point set in ℝ 2 , or for more general issues of image understanding, as when we recognise an image as made up out of cuboids, themselves made up out of faces, in turn made out of lines, in turn made out of pixels. It has been used for recognising hand printed Kanji characters, for finding hand drawn boxes in images, for finding faces in video-images, and for classifying images of flaws in metal. Details of the applications are discussed elsewhere; this paper discusses the theoretical issues.