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Report.pdf (1550898, 2019-12-26)
images/ (0, 2019-12-26)
images/apple.png (403235, 2019-12-26)
images/barbara.png (185727, 2019-12-26)
images/dst.jpg (170193, 2019-12-26)
images/eye.png (43265, 2019-12-26)
images/hand.png (43794, 2019-12-26)
images/mask.png (3878, 2019-12-26)
images/mask_display.png (2712, 2019-12-26)
images/maskao.png (1899, 2019-12-26)
images/orange.png (379152, 2019-12-26)
images/src.jpg (155799, 2019-12-26)
main.py (5065, 2019-12-26)

# Pyramids-and-Wavelets Use of image pyramids and wavelet transforms for various applications including seamless blending, edge-preserving denoising, and image compression. # Requirements For simplicity, you may assume that the size of each image is a power of two. You are expected to make your implementations work for colour images as well. # Image blending using pyramids Implement the Gaussian pyramid and the Laplacian pyramid as described by Burt and Adelson (1983). The output pyramid in both cases should be a list of images of smaller and smaller sizes. Further, implement a method to reconstruct the original image from the Laplacian pyramid. As discussed in class, image pyramids can be used to seamlessly blend two images. To do so, you will need three images of the same size: the two images a and b to be blended, and a region image r defining which regions the two images should contribute to. Construct the Laplacian pyramids of a and b, blend their corresponding levels using the Gaussian pyramid of r , and reconstruct the blended image. See Section 3.2 of Burt and Adelson’s paper for details. You may use the following images from the Burt and Adelson paper as test inputs to try out your implementation. However, you should also include some creative results on a pair of images of your own choice. For example, you could try swapping your face with that of another student. You can use an image editing software like GIMP to manually paint the mask image. # Haar wavelets and denoising Implement the Haar wavelet transform for images, which recursively decomposes an image into approximation and detail coefficients. The output should be in the form of a single 2D array containing the coefficients at all scales. Ensure that the transform is orthogonal, i.e. the sum of squared values is the same before and after the transform; this may require scaling the coefficients by √2 at each step. Also implement the inverse Haar transform, which reconstructs the original image from the wavelet coefficients. Multiresolution representations such as pyramids and wavelets can be used for noise removal. For natural images, most of the detail coefficients are close to zero (due to smooth regions) while a few are quite large (due to edges). Therefore, suppressing low-amplitude detail coefficients while retaining high-amplitude ones is likely to reduce noise in smooth regions without significantly affecting edges and other important image features. Two common strategies to do so are hard thresholding and soft thresholding, fhard(w)={wif |w|>t,0otherwise,fsoft(w)=wtif w>t,0if t≤w≤t,w+tif w

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