Written description of what Gaussian and Laplacian pyramids are, with properly typeset formulas: Gaussian and Laplacian pyramids And MATLAB Course Work, Unis, UK

Task A: Written description of what Gaussian and Laplacian pyramids are, with properly typeset formulas and a worked example using a small matrix of numbers. [250 words] (10 marks)

Task B: Do some research and provide some examples of where Gaussian and Laplacian pyramids have been used in practice; e.g., using Google Scholar to identify relevant research papers. [250 words] (10 marks)

Task C: Implement a Gaussian pyramid function in MATLAB that accepts an image and the desired level of pyramid and returns an image corresponding to that level. (15 marks)

Task D: Implement a Laplacian pyramid function in MATLAB that accepts an image and the desired level of pyramid and returns an image corresponding to that level. (15 marks)

Task E: Compare the effectiveness of spatial frequency filtering using Gaussian and Laplacian pyramids to that achievable when working with an image in the spatial frequency domain, such as that created using a 2D Fast Fourier Transform (see lecture and tutorial 11). [250 words] (15 marks)

Task F: Perform an experiment to see how well an image is reconstructed by re- assembling the layers of the Laplacian pyramid. Use a metric such as RMSE to evaluate the difference between the reconstructed image and original. [250 words] (15 marks)

Task F: Perform an experiment to compare the effectiveness of different downsampling algorithms on how well spatial frequency filtering using pyramids works; specifically, compare nearest neighbour, bilinear, and bicubic approaches (see lecture and tutorial 6). Identify a suitable metric for evaluating effectiveness. For null additional credit, consider: how do you results compare to the use of a binyp tree?