Transform image or a set of point from the direction of eigenvector

Hi,

I'm using the function:

[outIm,whatScale,Direction] = FrangiFilter2D(I, options) in

https://www.mathworks.com/matlabcentral/fileexchange/24409-hessian-based-frangi-vesselness-filter

where Direction is a matrix from computing the direction of the minor eigenvector:

% Calculate (abs sorted) eigenvalues and vectors

[Lambda2,Lambda1,Ix,Iy]=eig2image(Dxx,Dxy,Dyy);

% Compute the direction of the minor eigenvector

angles = atan2(Ix,Iy)

I'd like to use Direction to transform the original image (or a set of original points) in order to correct the warping.

How could I do this without using imtransform or imwarp ?

Thank you,

Best

Answer 1

[Hari]

Hi Maia,

As per my understanding, you want to use the Direction matrix to transform the original image without using the built-in “imtransform” or “imwarp” functions in MATLAB.

You can do so by manually applying the transformation using interpolation techniques. You can follow the below steps:

1. Obtain the size of the original image.

    [height, width] = size(I); 

2. Create a grid of coordinates representing the pixel locations in the original image.

    [X, Y] = meshgrid(1:width, 1:height); 

3. Calculate the displacement vectors using the Direction matrix.

    displacementX = Direction(:,:,1); 
    displacementY = Direction(:,:,2); 

4. Apply the displacement vectors to the grid of coordinates.

    newX = X + displacementX; 
    newY = Y + displacementY; 

5. Perform interpolation to obtain the transformed image or transformed set of points.

    transformedIm = interp2(X, Y, I, newX, newY, 'linear', 0); 
    % For transforming a set of points represented by pointsX and pointsY: 
    transformedPointsX = interp2(X, Y, pointsX, newX, newY, 'linear', 0); 
    transformedPointsY = interp2(X, Y, pointsY, newX, newY, 'linear', 0); 

Refer the below documentation to learn more about “interp2” function in MATLAB.

https://www.mathworks.com/help/matlab/ref/interp2.html