Yoshiyasu/image_interp
image editting problem, Y. Yoshiyasu, Keio Univ, Japan
Name 
image_interp 
Group 
Yoshiyasu 
Matrix ID 
2248 
Num Rows

240,000 
Num Cols

120,000 
Nonzeros

711,683 
Pattern Entries

711,683 
Kind

Computer Graphics/Vision Problem 
Symmetric

No 
Date

2009 
Author

Y Yoshiyasu 
Editor

T. Davis 
Structural Rank 
120,000 
Structural Rank Full 
true 
Num Dmperm Blocks

1 
Strongly Connect Components

7,516 
Num Explicit Zeros

0 
Pattern Symmetry

0% 
Numeric Symmetry

0% 
Cholesky Candidate

no 
Positive Definite

no 
Type

real 
Download 
MATLAB
Rutherford Boeing
Matrix Market

Notes 
The problem is templatemesh 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 righthandside 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 lowrank changes.]
