Finite dimensional functional spaces for image processing

Abstract:

The invariant recognition of shapes under affine distortion and
translation requires the use of invariant descriptors under these
distortions. This report is concerned with the definition of classes of
such features which are appropriate for the description of 2D shapes. As
we are concerned with the problem of classes of features as opposed to
individual features themselves, we are in position to propose very large
numbers of features that belong to these classes. These features do not
necessarily have a straight forward geometric interpretation as they are
derived algebraically.

The traditional way of viewing a distortion is to assume that the shape
to be recognised is distorted. An alternative way, however, of viewing
the same problem is to assume that the shape remains the same, but the
co-ordinate system from which we view it suffers a distortion. This way
we can see which expressions remain unaltered under the assumed
distortion and derive our invariants as functionals of these
expressions. This is the essence of the proposed "trace transformation"
according which a function of the image values is computed along many
lines that cross the image and the value of this function is plotted in
the two dimensional space of the line parameters. We can see that under
scaling, rotation, linear distortion and translation the functional form
of a line does not change. Then we can construct the features to
describe the shape as functions of measurements made on the shape along
straight lines that trace it. 

Trace transform technique accumulates ideas of some known approaches.
The closest to it are Hough transform and Gabor filtering if they
applied to pattern recognition. The difference between trace transform
applied to pattern recognition. The difference between trace transform
and the other theories is that the trace transform theory accents on
producing automatically large number of characteristics of images.

References

A Kadyrov and Maria Petrou "Linear Transformation Parameter Estimation
for Fault Detection", 14th Int'l Conference on Pattern Recognition,
August 16-20, 1998, Brisbane, Australia (ICPR98), pp. 550-552.

A Kadyrov and Maria Petrou "The Trace Transform as a Tool to Invariant
Feature Construction", 14th Int'l Conference on Pattern Recognition,
August 16-20, 1998, Brisbane, Australia (ICPR98), pp. 1037-1039.

M Petrou and A Kadyrov "The Trace transform and its application (Keynote
lecture)", Noblesse Workshop on Non-Linear Model Based Image Analysis,
Proceedings of NMBIA, 1-3 July 1998, Glasgow, Stephen Marshall, Neal
Harvey and Druti Shah (Eds), pp. 207-214.