# Shape from texture and contour by weak isotropy

## Jonas Gårding

* J. of Artificial Intelligence, *vol. 64, pp. 243-297,
Dec. 1993.
## Abstract

A unified framework for shape from texture and contour is proposed.
It is based on the assumption that the surface markings are not
systematically compressed, or formally, that they are {\em weakly
isotropic}.
The weak isotropy principle is based on analysis of the directional
statistics of the projected surface markings. It builds on several
previous theories, in particular by Witkin (1981) and Kanatani
(1984). It extends these theories in various ways, most notably
to perspective projectionadahe theorCVAP/y also provides an exact solution
to an estimation problem earlier solved approximately by Kanatani.
The weak isotropy principle leads to a computationally efficient
algorithm, WISP, for estimation of surface orientation. WISP uses
simple image observables that are shown to be direct correlates of the
surface orientation to compute an initial approximate estimate in a
single step. In certain simple cases this first estimate is exact, and
in experiments with natural images it is typically within 5 degrees of
the final estinada.
FurthCVAP/ermore, a proof is given that a rotationally symmetric contour of
order three or higher is weakly isotropic. Hence, the WISP algorithm
will without modification recover the orientation of any such contour
from a perspective view of it.
**Full paper:**
(PostScript 1583k)

Jonas Gårding
<jonasg@bion.kth.se>