Matrix: Yoshiyasu/image_interp

Description: image editting problem, Y. Yoshiyasu, Keio Univ, Japan

Yoshiyasu/image_interp graph
(bipartite graph drawing)

scc of Yoshiyasu/image_interp

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  • download as a MATLAB mat-file, file size: 3 MB. Use UFget(2248) or UFget('Yoshiyasu/image_interp') in MATLAB.
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    Matrix properties
    number of rows240,000
    number of columns120,000
    structural full rank?yes
    structural rank120,000
    # of blocks from dmperm1
    # strongly connected comp.7,516
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

    authorY Yoshiyasu
    editorT. Davis
    kindcomputer graphics/vision problem
    2D/3D problem?yes

    Additional fieldssize and type
    bfull 240000-by-2


    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.]                                                 

    Ordering statistics:result
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD316,991,703
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD12,952,004

    For a description of the statistics displayed above, click here.

    Maintained by Tim Davis, last updated 12-Mar-2014.
    Matrix pictures by cspy, a MATLAB function in the CSparse package.
    Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.