Implement a MATLAB function for a least squares correlation

Reference no: EM132274118

Assignment - Least Squares Correlation

Due to diverse perspective distortions, a surface-based relation of homologeous image points is quite difficult. A geometric transformation can help to reduce these distortions.

This project focusses on geometric alignment using an affine deformation model:

1. Use a well textured, small (approx. 150 x 150 pix.), greyscale image. Transform this image by applying an arbitrarily chosen affine transformation H. For the application of H to an image, a function is provided (moodle): geotrans.m

Your task is to compute the six parameters d₁,...,d₆ that enable a transformation of the distorted image back to its initial state. The idea is to use grey value differences of the two images for this computation. In order to avoid problems in image border regions, you may use the central image area (e.g. 100 x 100 pix).

2. Implement a MATLAB function for a least squares correlation. In each iteration, a linearized inhomogeneous equation system has to be solved. Use the Moore-Penrose-Pseudoinverse (pinv) and centered image coordinates here. For the computation of image gradients in x- and in y-direction, the function gradient.m can be used.

3. Quantitatively compare the estimated deformation parameters with the initially applied parameters and qualitatively describe the visual effect of the geometric adjustment.

4. Provide a detailed documentation of your work. Any external sources that you use should be included in the reference section of your documentation. Specify if you have used an image that you captured or one from an external source. Include images showing the initial image distortion and your final results. Explain your choice of number of iterations.

Reference no: EM132274118

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