Project 2 CS 194-26: Fun with Filters and Frequencies!

By Diego Uribe

Project Description

In this project I woked on 2D convolutions of images with specific filters. These included finite difference operator filters and derivative of gaussian filters. In the second half I worked on filtering, extracting and removing certain frequencies from images. This allowed me to write image sharpening algorithms, create hybrid images, create gaussian and laplacian stacks of images, and make multiresolution blendings of images.

Part 1: Fun with Filters

Part 1.1: Finite Difference Operator

For this part I took the partial derivative with respect to x and y of the cameraman image. Then computed the gradient magnitue image and binarized it to create an edge image. The gradiend magnitude is computed by taking the norm of the gradient with respect to x and the gradient with respect to y of every pixel on the image.

The threshold I found was only considering pixels with a gradient magnitude greater than 0.06

Part 1.2: Derivative of Gaussian (DoG) Filter

For this part I created a blurred version of the original image by convolving it with a guassian filter. Then repeated the procedure in Part 1.1. The images below show that by applying the gaussian filter to the original image we removed the high frequencies in it. This allowed us to remove some of the noise in the original edge image. As we can see, the edges in the edge images are much more clear and we have reduced the noise substantially.

The results below are the same but they were generated using a single convolution by creating a derivative of gaussian filters.

Part 1.3: Image Straightening

I could not get my algorithm to work. It always returned that the 0th degree rotation was the best. Please look at my code for some partial credit. I made a lot of progress just could not get the final result to work.

Part 2: Fun With Frequencies

Part 2.1: Image "Sharpening"

In this part I implemented an image sharpening algorithm. It takes a blury image and sharpens it by subtracting the blurred version from the original image to get the high frequencies of the image. Then I added this high frequencies back to the original image which "sharpened" it. I did this using one convolution and two convolutions. The results below were generated using one convolution.

Other Images

Sharpenning a Blurred Image

For this part, I selected a sharp image of a landscape. Then I blurred it and resharpened it. From the results, we can see that I was able to recover most of the details in the original image through the resharpening process. Nevertheless, some of the high frequencies were lost when we blurred the image and I was unable to recover them fully. Maybe I could try resharpening it twice.

Part 2.2: Hybird Images

In this part I made hybrid images. The first image was passed through a low pass filter to only have low frequencies while the second image was passed through a high-pass filter to only contain high frequences. Then I added the two images. Below I also show the fourier analysis.

Other Hybrid Images (Obama Trump)

Other Hybrid Images (Bear Lion)

Part 2.3: Gaussian and Laplacian Stacks

In this part I implemented a Gaussian and Laplacian Stack. Here are the results of the laplacian and gaussian stacks on the Salvador Dali painting of Lincoln and Gala. Please note the the first image in the stack is the original image. I included it for comparing!

Gaussian and Laplacian Stacks of Trump/Obamas Hybrid Image

Part 2.4: Multiresolution Blending (a.k.a. the oraple!)

This part of the project consisted on implementing Multiresolution Blending. For this, I selected two images. Then I computed the laplacian stack for each of the two images. Then I came up with a mask to unite the images. I took the gaussian stack of this mask. Finally, I blended the laplacian stacks of the images with the guassian stack of the mask to create the multiresolution blended image.

Oraple

Mars and Earth Multiresolution Blending

Using an Irregular Mask: FireWater