Chamfer

Intuition

The intuition behind the Chamfer is that it represents the distance to the closed feature Where a feature represents a notable change in the luminousity

Two vectors of chamfer distances are considered Similar, when determining the scalar dot product, is similar to the dot product with itself.

Calculation

The Chamfer calculation, is defined as the

Chamfer(p) = min( abs(lastFeature.position-p.position) , abs(nextFeature.position-p.position)  )

In implementation, the first and last pixel are always considered to be features

Similarity

Chamfer Similarity can calculated in O(n) time with the fomula below,

Similarity = (c1 . c2)/ max( c1.c1,c2.c2)

Where the . represents the scalar dot product of the vectors being compares