Project 2

Background

This project uses filters and frequencies manipulate images in various ways. For example, we can blur an image, create a hybrid image between two images, and blend two images together. Some concepts applied include finite difference operators, derivative of Gaussian filters, Gaussian stacks and Laplacian stacks. Scroll down to read more!

1.1 Finite Difference Operator

Approach

I set Dx and Dy to be 2D numpy arrays and convolved each of them with the 0th channel of the cameraman image using scipy.signal.convolve2d, setting mode=same. Afterwards, I took the gradient magnitude of the two images post-convolution using the distance formula sqrt(image1 ^ 2 + image2 ^ 2). Finally, I binarized the gradient magnitude image, setting the threshold to 75.

1.1 Images

Dx	Dy
Gradient Magnitude	Binarized

1.2 Derivative of Gaussian (DoG) Filter

Approach

I used get_gaussian_kernel_2d from discussion and set kernelSize=10 and sigma=1.5 to create my Gaussian. For the first part, I blurred the original image by convolving it with the Gaussian. Next, I convolved the blurred image with Dx and Dy, before finding its gradient magnitude and binarizing it. For the second part, I convolved my Gaussian with Dx and Dy before convolving the original image with the derivative of Gaussian. I then found the gradient magnitude and binarized, as usual.

Observations

Using this approach, we can see that the binarized edges are more defined (thicker and rounder). There is also less noise, especially near the bottom of the image. However, we also lose some details of the camera. We can also see that our two approaches yield the same output image, as expected.

1.2 Images

Cameraman	Blurred
Dx of Blurred	Dy of Blurred
Blurred Gradient Magnitude	Blurred Binarized
DoG	Binarized DoG

2.1 Image "Sharpening"

Approach

I used the formulas from lecture to derive image sharpening. Let B be the blurred image (convolving the original image with Gaussian(10, 1.5)), img be the image and alpha be the sharpening factor. Then, our sharpened image is img + alpha * (img - B). I used alpha=1 for all images below.

Observations of Sharpening, Blurring and Sharpening Again

I chose to blur and sharpen the already sharp image of the dam. It turns out that this resulting image is more blurry than the original sharpened image, due to the blur losing information in the image.

2.1 Images

Taj Mahal	Sharpened Taj Mahal
Dam	Sharpened Dam	Sharpened, Blurred, then Sharpened Dam

2.2 Hybrid Images

Approach

First, I used the skeleton code to align my images. I used Gaussian(60, 10) as the kernel for my high frequency image and Gaussian(6, 1) for my low frequency image. I blurred the images with their respective Gaussians. I averaged the blurred low frequency image and the difference between the high frequncy image and its blurred version to get a hybrid photo. I then converted it to grayscale using the rgb2gray function from discussion.

2.2 Images

Nutmeg	Derek	Cat Man
Jacob	Sean	Pookies Hybrid Image
Uniqloroo	Kingaroo	Kangaroo

Failed Hybrid

A hybrid I tried was combining the Kingaroo with a boba drink - however, that unfortunately failed. It was difficult to align it, and even more difficult to find fitting Gaussian parameters to make a good hyrbid considering the shapes of the two figures in question.

Uniqloroo

Kingaroo

Bobaroo

Fourier Analysis of Kangaroos

I chose to display the 2D Fourier transform of the Kingaroo and Uniqloroo Hybrid.

Low Frequency Image FFT	High Frequency Image FFT	Hybrid Image FFT
Filtered Low Frequency Image FFT	Filtered High Frequency Image FFT

2.3 Gaussian and Laplacian Stacks

Approach

I used the lecture slides as inspiration for creating my Gaussian and Laplacian stacks. For each level of the Gaussian stack, I blurred the previous level by Gaussian(36, 6). To make my Laplacian stack, I subtracted the value in index i-1 from the value in index i of my Gaussian stack, then added the highest level of my Gaussian stack to the end.

2.3 Images

Apple Gaussian Stack	Apple Laplacian Stack
Orange Gaussian Stack	Orange Laplacian Stack
Oraple Gaussian Stack	Oraple Laplacian Stack

2.4 Multiresolution Blending

Approach

To build my Laplacian stack for a blended image, I used the formula A[i] * mask[i] + B[i] * (1 - mask[i]) from the lecture slides as inspiration, where A and B correspond to the Laplacian stacks of the two images. To complete the blend, I summed the values in the stacks, which returned the desired image.