Project 2: Fun with Filters and Frequencies!

By Tony Wan

Part 1: Fun with Filters

Part 1.1: Finite Difference Operator

To compute the gradient magnitude, I used the humble finite difference D_x=[1 -1] and D_y = [1 -1]^T to convolve with the image to get the gradient in x and y directons. Then I take the square root of their quadratic sum to get the magnitude of the gradient.

Binarized Gradient Magnitude.png

Gradient Magnitude.png

Partial Derivative.png

Part 1.2: Derivative of Gaussian (DoG) Filter

The smoothed image has less noises and clearer edges. I can convolve just once and get an equivalent result.

Derivative of Gaussian.png

Smoothed Partial Derivative.png

Smoothed Gradient Magnitude.png

Smoothed Binarized Gradient Magnitude.png

DoG Partial Derivative.png

DoG Gradient Magnitude.png

DoG Binarized Gradient Magnitude.png

Part 2: Fun with Frequencies!

Part 2.1: Image "Sharpening"

Golden Gate.png

Part 2.2: Hybrid Images

The train one kinda failed since the white train on the right is pretty visible both close and far.

train left.jpg

train right.jpg

Mitsuha Taki.jpg

Your Name.png

Your Name FFT.png

Part 2.3: Gaussian and Laplacian Stacks

Orange Gaussian Stack.png

Apple Laplacian Stack.png

Orange Laplacian Stack.png

Apple_Orange_Level 0.png

Apple_Orange_Level 2.png

Apple_Orange_Level 4.png

Part 2.4: Multiresolution Blending

Eclipse_Campanile_Level 0.png

Eclipse_Campanile_Level 2.png

Eclipse_Campanile_Level 4.png

Lake_Boat_Level 0.png

Lake_Boat_Level 2.png

Lake_Boat_Level 4.png