Simplify the comparison of the two approaches

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Here we consider the problem of shape averaging. In particular, Li , i = 1, . . . , M are each N × 2 matrices of points in IR 2 , each sampled from corresponding positions of handwritten (cursive) letters. We seek an affine invariant average V, also N × 2, VTV = I, of the M letters Li with the following property: V minimizes

Characterize the solution. This solution can suffer if some of the letters are big and dominate the average. An alternative approach is to minimize instead:

Derive the solution to this problem. How do the criteria differ? Use the SVD of the Lj to simplify the comparison of the two approaches.

Reference no: EM131044759

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