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
![346_c424adbc-e0b9-4d3a-9b52-c7a41e9b7ea1.png](https://secure.tutorsglobe.com/CMSImages/346_c424adbc-e0b9-4d3a-9b52-c7a41e9b7ea1.png)
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.
![312_27081480-9151-49fc-9a00-777159a7d69d.png](https://secure.tutorsglobe.com/CMSImages/312_27081480-9151-49fc-9a00-777159a7d69d.png)