The Hough transform is a standard technique for finding features such
as lines in images. Typically, edgels or other features are mapped int
o a partitioned parameter or Hough space as individual votes. The targ
et image features are detected as peaks in the Hough space. In this pa
per we consider not just the peaks but the mapping of the entire shape
boundary from image space to the Hough parameter space. We analyse th
is mapping and illustrate correspondences between features in Hough sp
ace and image space. Using this knowledge we present an algorithm to c
onstruct convex hulls of arbitrary 2D shapes with smooth and polygonal
boundaries as well as isolated point sets. We also demonstrate its ex
tension to the 3D case. We then show how this mapping changes as we mo
ve the origin in image space. The origin can be considered as a vantag
e point from which to view the object, and the occluding contour can b
e extracted easily from Hough space as those points where R = 0. We de
monstrate the potential for tracking of transitions in the mapping to
be used to construct an aspect graph of arbitrary 2D and 3D shapes.