  Natural objects can be subject to various transformations yet still preserve
properties that we refer to as invariants. Here, we use definitions of affine
invariant arclength for surfaces in R^3 in order to extend the set of existing
non-rigid shape analysis tools. In fact, we show that by re-defining the
surface metric as its equi-affine version, the surface with its modified metric
tensor can be treated as a canonical Euclidean object on which most classical
Euclidean processing and analysis tools can be applied. The new definition of a
metric is used to extend the fast marching method technique for computing
geodesic distances on surfaces, where now, the distances are defined with
respect to an affine invariant arclength. Applications of the proposed
framework demonstrate its invariance, efficiency, and accuracy in shape
analysis.
