Statistics and Shape Analysis. By Marc Sobel. Shape similarity. Humans recognize shapes via both local and global features.
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Let u1,…,un be the vertices of one shape and v1,…,vm the vertices of another shape. We’d like to biuld correspondences between the vertices which properly reflect the relationship between the shapes. We use the notation (ui,vj) for a correspondence of this type. We use the terminology for a particle consisting of a set of such correspondences.
Let Xi,l be the l’th local feature measure for vertex i of the first shape and Yj,l the l’th local feature measure for vertex j of the second shape. For now assume these feature measures are observed.
We’d like to biuld a particle which reflects the local and global features of interest.
If shapes result from one another via rotation and scaling then the order of shape 1 correspondence points should match the order of shape 2 correspondence points: i.e., if (i1,j1) is one correspondence and (i2,j2) is another, then either i1<i2 and j1<j2 or i1>i2 and j1>j2. We can incorporate this into a prior.