Project 3: Fun with frequencies and Gradients

Part 1.1: Warmup

To sharpen an image, I used the unsharp masking technique. Given an input image and a Gaussian kernel as a filter, we apply the convolution to sharpen the image. I used the OpenCV library for Python to create a 9x9 Gaussian kernel with sigma = 10. I then filtered the image by the kernel to create the unsharpened image, and computed :
Original + alpha * (original - unsharpened)
Where the alpha chosen was 0.5. The result is an image with heightened edges and therefore seem sharper.

Part 1.2: Hybrid Images

In this part, we take 2 images and blend them together to create one hybrid image. The end result is an image where one of the original images is more apparent from a distance and the other from up close. This is achieved by taking the high frequencies of one of the images and the low frequencies of the other. The process to create the filters is very similar to the previous part. The lowpass filter is the result of filtering with a Gaussian kernel and the highpass from subtracting the Gaussian-kernel filtered image from the original. Adding the 2 together (after they've been aligned) creates the hybrid image.

Part 1.3 Gaussian and Laplacian Stacks

Next, we create Gaussian and Laplacian stacks. When applied to images that contain structure in multiple resolutions, these stacks reveal the structure at each level. Gaussian stacks are created by filtering repeatedly with a Gaussian kernel while Laplacian stacks take the difference between the current land last level of the Gaussian stack. In the following images, the top row is the Gaussian stack and the bottom is the Laplacian.

Part 1.4: Multiresolution Blending

We use multiresolution blending in this section to create a smooth seam between 2 images and effectively blend them together. To do this, a Gaussian stack is created from a mask of ones and zeros that denotes where the seam will go. A Laplacian stack is created from the 2 images. At each layer, we combine the three and the final result is the sum at each layer.

Part 2: Gradient domain Fusion

In the previous part of the project, we blend 2 images together using Gaussian and Laplacian stacks. We now blend 2 images together using Poisson blending. The idea here is to preserve the gradients in the source image (the image that is blended into a target image) without changing the target image. However, the pixel intensities after processing the source image will change. We do this through a least squares problem that creates the pixels inside the source area of the final image such that:
- For each pixel and its neighbor where both the pixel and its neighbor are inside the source region, we guide the gradient between them to match the gradient in the source image.
- For pixels at the boundary where a neighbor is in the target image region, we look at its neighboring pixel in the target and do the same.
Note that we look at four neighbors (up, down, left, right) to get 2 gradients (x, y). Explicitly, the least squares problem we solve is: