Project 2

# Fun with Filters and Frequencies!

Author: Skylar Sarabia

# Part 1: Fun with Filters

## Part 1.1: Finite Difference Operator

Gradient magnitude image formula: $$dx = \begin{bmatrix}1 & -1\\0 & 0\end{bmatrix}, dy = \begin{bmatrix}1 & 0\\-1 & 0\end{bmatrix}$$ $$dx\_im = im * dx, dy\_im = im * dy$$  $$gradmag = { \sqrt{(dx\_im)^2 + (dy\_im)^2} }.$$
dX Image
dY Image
(thresh = 0.3)

## Part 1.2: Derivative of Gaussian (DoG) Filter

Differences between results in 1.1 vs 1.2: The derivative edges are more prominent and there is noticiably less noise do to the image now consisting of lower frequencies (blurred). Since the noise was reduced, the threshold value can be reduced since only the stronges edges remain. In this case it went from 0.3 to 0.015.

Verify: Looking at the differences between "Blur then Derivative Convolve" and "Single Convolution" they look the same.

dX Filter
dY Filter
dXdY Filter

dX Image
dY Image
(thresh = 0.115)

dX Image
dY Image
(thresh = 0.115)

# Part 2: Fun with Frequencies!

## Part 2.1: Image "Sharpening"

a = 0
a = 1
a = 2
a = 3

a = 0
a = 1
a = 2
a = 3

### Blur then sharpen

Original
Blurred
Sharpend
Fun Fact This image was created with Midjourney, a text-to-image AI model

## Part 2.2: Hybrid Images

### Hybrid #1: Given Images

Low Frequency Image In
High Frequency Image In
Hybrid

### Hybrid #2

Low Frequency Image In
High Frequency Image In
Hybrid

### Hybrid #3: Failure Case

Due to the panda bear fur pattern of the panda, the panda is still very visible when looking from close.

Low Frequency Image In
High Frequency Image In
Hybrid

### Hybrid #4 (Favorite) + Frequency Analysis

lF Image Input
lF Image Input (Low Frequency)
lF Image Input (Low Frequency FFT)
hF Image Input
hF Image Input (High Frequency)
hF Image Input (High Frequency FFT)
Hybrid FFT
Hybrid

Apple
Gaussian
Apple
Laplacian
Orange
Gaussian
Orange
Laplacian

Level 0
LHS
RHS
LHS + RHS
Level 2
LHS
RHS
LHS + RHS
Level 4
LHS
RHS
LHS + RHS
Collapsed
LHS
RHS
LHS + RHS

## Part 2.4: Multiresolution Blending

### Result #1: Official Vizsla Astronaut Nasa Portrait

Base
Blend In
Collapsed
Base vs Collapsed

### Result #2: Vizsla & Dalmation Astronaut Takeoff

Base
Blend In
Collapsed
Base vs Collapsed

### Result #3: Vizsla Astronaut on the moon

Base
Blend In
Collapsed
Base vs Collapsed
Fun Fact All Vizsla images were created with Dalle-2, a text-to-image AI model

### Favorite Result

Inputs
Base
Blend In
Level 0
Base
Blend In
Base + Blend In
Level 2
Base
Blend In
Base + Blend In
Level 3
Base
Blend In
Base + Blend In
Collapsed
Base
Blend in
Base + Blend in
Base vs Collapsed
Base vs Collapsed
Bells & Whistles Completed 2.3 & 2.4 in all color channels

## Reflection

I really enjoyed learning how to create hybrid images and multiresolution blending. I did not realize until this project how important frequencies are to our visual perception of images. I used to make face swaps using photoshop using a blending feature and I just implemented that feature myself!