CS194-26 Project 2 - Yin Deng

Part 1.1: Finite Difference Operator

When calculating gradient magnitude:

1. Find partial derivatives with respect to x.
2. Find partial derivatives with respect to y.
3. For each pixel on the image, the gradient magnitude is equal to the square root of the sum of squares of partial derivatives with respect to x and squares of partial derivatives with respect to y.

Original image:

Partial derivatives:

Binarized gradient magnitude (threshold = 0.05):

Part 1.2: Derivative of Gaussian Filter

First apply Gaussian filter, then find derivatives

We notice that the final result has considerably less noise compared to 1.1.

Blurred image:

Partial Derivatives:

Binarized gradient magnitude (threshold = 0.05):

Find derivatives of Gaussian Filter

We notice that finding derivatives of Gaussian filters first and then applying them produces roughly the same result as applying the Gaussian filters first and then finding derivatives.

Original image:

Gaussian Filter Partial Derivatives:

Partial Derivatives:

Binarized gradient magnitude (threshold = 0.05):

Part 2.1: Image "Sharpening"

Taj original vs sharpened (alpha = 5):

Face original vs sharpened (alpha = 20):

Tree original vs blurred vs sharpened (alpha = 10):

Part 2.2: Hybrid Images

Input images:

Low pass and high pass:

Hybrid image:

Input images Fourier transformation:

Low pass and high pass Fourier transformation:

Hybrid image Fourier transformation:

More examples:

LeGoat:

BasketCer:

Failed hybrid: The given inputs are not suitable for two reasons. First of all, characters' shapes are very different from each other, so it is difficult to create a hybrid image that's visually pleasing. Second, one character has one eye, and the other character has two eyes, so it is difficult to align them properly.

Part 2.3: Gaussian and Laplacian Stacks

Oraple

Part 2.4: Multiresolution Blending

Iron America

Face on sun

Face on sky