%-------------------------------------------------------------------------------
% UF Sparse Matrix Collection, Tim Davis
% http://www.cise.ufl.edu/research/sparse/matrices/Yoshiyasu/image_interp
% name: Yoshiyasu/image_interp
% [image editting problem, Y. Yoshiyasu, Keio Univ, Japan]
% id: 2248
% date: 2009
% author: Y Yoshiyasu
% ed: T. Davis
% fields: name title A id date author ed kind b notes
% kind: computer graphics/vision problem
%-------------------------------------------------------------------------------
% notes:
% The problem is template-mesh deformation to match with silhouettes.  In this 
% process, there are two kinds of linear systems to solve.  This system        
% (Yoshiyasu/image_interp) is a smooth vector field construction from images,  
% which is harmonic interpolation (minimizing laplacian: Lx=0) of intensity    
% gradient field p.  This can be solved 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.  This is for 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.  [Note by T. Davis:      
% since C is of high rank, update/downdate will not be effective, since it is  
% meant for low-rank changes.]                                                 
%-------------------------------------------------------------------------------
