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.
