inner-distance for shape matching

inner-distance

the length of the shortest path within the shape boundary, to build shape descriptors.

  • insensitive to articulation
  • sensitive to part structures, a desirable property for complex shape comparison

Euclidean distance

does not consider whether the line segment crosses shape boundaries.

  • the inner-distance replaces the Euclidean distance to extend the shape context

object recognition – combine shape and texture

leaves from different species often share similar shapes but have different vein structures

Using the gradient information along the shortest path

Shape Context

1) Given the points on two shapes A and B, first the point correspondences are found through a weighted bipartite matching.

2) Then, TPS is used iteratively to estimate the transformation between them.

3) After that, the similarity D between A and B is measured as a weighted combination of three parts:
D = aDac + Dsc + bDbe

    • Dac measures the appearance difference
    • Dbe measures the bending energy
    • Dsc shape context distance, measures the average distance between a point on A and its most similar counterpart on B
    • a, b are weights (a = 1.6, b = 0.3

Inner-Distance Shape Context (IDSC)

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