## Group Yoshiyasu

Group Description ```Image editting and mesh deformation problem from Y. Yoshiyasu, Keio Univ., Japan I uploaded 5 matrices A1,b1,A2,b2 and D (for x=(A1'*A1)/(A1'*b1) and v=(A2'*D*A2)/(A2'*D*b2)). What I'm doing is template-mesh deformation to match with silhouettes. In this process, there are two kinds of linear systems that I have to solve. First one is smooth vector field construction from images, which is harmonic interpolation (minimizing laplacian: Lx=0) of intensity gradient field p. I'm solving this by normal equation and cholesky factorization. x=(A1'*A1)/(A1'*b1) where A1=[L;C] and b1=[zeros(size(length(L),1);1);C*p]. C is a square diagonal matrix containing weights. I'm doing this on a 400x300 image, so Ix=reshape(x,400,300) must be done to get the vector field. After solving y direction for Iy, the result is visualized with quiver(Ix,Iy). At each iteration the both C submatrix and the right-hand-side change but L remains unchanged. Second one is template deformation using above vector field. I'm solving this by: v=(A2'*D*A2)/(A2'*D*b2) where D is diagonal matrix containing weights. Structures of A2 and b2 are a little bit more complex than A1 and b1, but they are similar. Both systems are not quite time-consuming for themselves, but I iterate this process more than 10 times for 10 views. So I would like them to be faster and also I'd like to reuse and update the factored matrix (if it's possible). [Reply: if all of C changes at each step, this is a nearly n-rank change, so an update/downdate process would be much more expensive than refactorizing the matrix. Update/downdate is effective for low-rank changes. In the collection,]```
Displaying all 2 matrices
Id Name Group Rows Cols Nonzeros
2248 image_interp Yoshiyasu 240,000 120,000 711,683
2249 mesh_deform Yoshiyasu 234,023 9,393 853,829