Form the regularization term for the image registration problem

Discussion in 'MATLAB' started by Aaronne, Nov 18, 2011.

  1. Aaronne

    Aaronne Guest

    Hi there,

    I have got a problem using spline based image registration. I would like to add a penalty term for the cost function to regularize the system.

    I have found some codes Matlab online shown below; however, I am not really understand them. I only understand the Tikhonov regularization. May I ask two questions please?

    1. What are these Tikhonov-Phillips method and Bending operator method using 'toeplitz'?
    2. This should be a 1D case below. How to extend this for 3D problem? May be we should use 'kron' product of Matlab?

    m = 9 % Control ponits data size
    B = spdiags(ones(m,1)*[1,4,1],[-1:1],m,m); % Spline basis
    D = spdiags(ones(m,1)*[-1,1],[0,1],m-1,m); % Derivative operation
    M = toeplitz([96,-54,0,6,zeros(1,m-4)]); % Second derivative
    switch regularizer, % initialize regularization
    case ’I’, W = speye(m,m); % Identity, Tikhonov
    case ’D’, W = D’*D; % Derivative, Tikhonov-Phillips
    case ’M’, W = M; % Bending operator

    Thanks a lot.
    Aaronne, Nov 18, 2011
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