This assignment is our first fourier into the realm of fourier transforms (heh).
Part 1: Fun with Filters
Finite Difference Operator
Taking the partial derivative of the cameraman image in the x & y directions to find its edges.
Simply taking the derivative of the cameraman in the x and y direction results in an image with a lot of noise. This is because pixels in the image differ from the others in close proximity. By filtering with a threshold, I was able to clean up the images and show only the edges of the image. I removed the pixels from the grass by taking the Gaussian G(6,2) of the image and highlight the man, camera, and edges in the background.
Original image
X Derivative
Y Derivative
X and Y Derivatives combined
Commutativity of Convolution
Comparing the convolution of the gaussian with the original image and the derivative of the gaussian demonstrates the commutativity of convolution.
Gaussian Convolution
Derivatives of Gaussian
Part 2: Fun with Frequencies
2.1 Image Sharpening
Using the same Gaussian technique as before but subtracting the resulting image from the original produces a sharpening effect. This technique is demonstrated by blurring then sharpening images. The resharpening performs better on images that are sharper and higher resolution to begin with.
Original
Sharpened
Blurred
Resharpened
Original
Blurred
Resharpened
2.2 Hybrid Images
I create hybrid images by combining the low frequency of one image with the high frequency of another.
Catman
Emir Returns
Fourier Analysis
Here is the fourier analysis of the frequencies of this image.
Reign of Raccoons
Dwayne “The Rock(et)” Johnson
Multi-resolution Blending and the Orapple journey
2.3 Gaussian & Laplacian stacks
Beginning with the original image, I created Laplacian and Gaussian stacks with the intent of blending two photos.
Apple
Orange
Orapple
2.4 Multi-resolution Blending and the Orapple journey
With an image mask and Laplacian & Gaussian stacks, I create an image spline between two images and display the result. I found that the biggest factor in the smoothness of the spline came from varying the gradient in the image mask.
Fun with Filters and Frequencies!
CS194-26 Fall 2021
Spencer Hamilton
Introduction
This assignment is our first fourier into the realm of fourier transforms (heh).
Part 1: Fun with Filters
Finite Difference Operator
Taking the partial derivative of the cameraman image in the x & y directions to find its edges.
Simply taking the derivative of the cameraman in the x and y direction results in an image with a lot of noise. This is because pixels in the image differ from the others in close proximity. By filtering with a threshold, I was able to clean up the images and show only the edges of the image. I removed the pixels from the grass by taking the Gaussian G(6,2) of the image and highlight the man, camera, and edges in the background.
Original image
X Derivative
Y Derivative
X and Y Derivatives combined
Commutativity of Convolution
Comparing the convolution of the gaussian with the original image and the derivative of the gaussian demonstrates the commutativity of convolution.
Gaussian Convolution
Derivatives of Gaussian
Part 2: Fun with Frequencies
2.1 Image Sharpening
Using the same Gaussian technique as before but subtracting the resulting image from the original produces a sharpening effect. This technique is demonstrated by blurring then sharpening images. The resharpening performs better on images that are sharper and higher resolution to begin with.
Original
Sharpened
Blurred
Resharpened
Original
Blurred
Resharpened
2.2 Hybrid Images
I create hybrid images by combining the low frequency of one image with the high frequency of another.
Catman
Emir Returns
Fourier Analysis
Here is the fourier analysis of the frequencies of this image.
Reign of Raccoons
Dwayne “The Rock(et)” Johnson
Multi-resolution Blending and the Orapple journey
2.3 Gaussian & Laplacian stacks
Beginning with the original image, I created Laplacian and Gaussian stacks with the intent of blending two photos.
2.4 Multi-resolution Blending and the Orapple journey
With an image mask and Laplacian & Gaussian stacks, I create an image spline between two images and display the result. I found that the biggest factor in the smoothness of the spline came from varying the gradient in the image mask.
Mask
Orapple
Mr. Gates
Mask
Berry Tree
Sunflower Balcony
Mask