This project involved playing with frequencies and using filters / gradients in order to blend images together. Some of the techniques learned are image sharpening, hybrid image creation, Laplacian stacks, multiresolution blending, and Poisson blending.

In order to sharpen an image, we can take a Gaussian filter of the original image and then subtract it from the original image. This creates a high pass filter, also known as the detail image. The detail image points out the detail, and can be added back into the original image to create a "sharp" effect.

In this part, we try to create "hybrid images", which are a concatenation of two aligned images. I implemented a high pass filter for the first image, and a low pass filter for the second image. The hybrid image for the Derek, Nutmeg example is below:

Below is an example with Fourier analysis.

Below is another successful example.

Below is a failure case between a cat and a hamster. This failed mainly because the image of the hamster barely had any high frequencies, so the low pass filter almost washed everything out. Meanwhile, the cat is just the opposite, having many high frequencies.

In this part, we obtain Gaussian and Laplacian stacks. A Gaussian stack is simply defined as GS(i) = GAUSSIAN(img, k*i), so the i-th element of the stack is simply the original image with a gaussian filter proportional to its index in the list. A Laplacian stack is defined as LS(i) = GS(i) - GS(i-1), simply the difference between the Gaussian stack element at that position and the one preceding it.

In this part, we smoothly blend two objects together using multiresolution blending with masks. Basically, this means finding the laplacian stacks of both images and the gaussian stack of the mask. Then, at each level i of the stack, use the ith mask in the stack to add the two images together. In essence, CS(i) = LS1(i)*(1-GR) + LS2(i)*GR. The elements in the concatenated stack CS are then added back together to construct the final blended image.

This part explores more advanced techniques of blending images together by using gradients. In essence, we learned how to break down images into their gradients and reconstruct them based on a system of equations and the fact that we know what the gradient in x and y directions at a certain pixel is. This is very helpful, because with this powerful technique we can break down a source image into its gradients, place it on another target image, and using the target image's information, we can reconstruct the source image in the context of the target image.

In this part, we reconstruct an image based off of its gradient data. As shown in the project description, we try to reconstruct an image v such that the difference in gradients between image v and image s are minimized.

In this part, we utilize the provided equation in order to blend a source image into the target image. The logic is similar to part 2.1 in that we set up the equation Ax = b, but when building b, instead of having an entry in b equal to only a single direction gradient, we set it equal to the sum of the gradients surrounding a certain pixel. If the pixel is not within the mask, we set the value equal to the value of the target's pixel at that position. That is how we give context to the source image, and force it to adjust its tone (it tries to minimize error by dispersing the error among all the other pixels). Below is a result of the penguin example:

Source/Target/Simple concatenation/Poisson Blending

I think this one didn't work out as well because the color of the skyscraper wasn't preserved. The bird image was more forgiving because the bird is supposed to be underwater, so we expect some sort of color distortion, but in this case it looks awkward. The sand also bleeds into the blending and creates an unnatural effect.

I tried to redo the John Cena face on Alexei Efros head with Poisson blending, and I think both are pretty close. I think the Poisson blending is a bit more natural looking, since multiresolution does a simple gradual face, so some features from one face bleed into another slowly, while Poisson has a more contextual blending on the face and doesn't run into the same issue.