Project 2: Fun with Filters and Frequencies

Evan Huang

Part 1: Fun with Filters

1.1: Finite Different Operator

I found the gradient magnitude by convolving the image with horizontal and vertical filters to get the magnitudes of the partial derivates. The magnitude of the gradient can then be found using the l2 norm.

Original	Gradient Magnitude	Edge Image

1.2: DoG Filters

Blurring the image helped reduce some noise in the image and thickened the edges. Using a DoG can reduce the computational demand by only requiring one convolution after precomputing the DoG.

Blurred	Edge Image	Edge Image w/ DoG

Part 2: Fun with Frequencies

2.1 Image Sharpening

Sharpening was achieved by subtracting the blurred image from the original and adding it back to the original with a weight.

Original	Blurred	Sharpened

This can be simplified by using the unsharp mask filter, only requiring 1 convolution. This is done by convolving the image with (1+alpha)e-alpha(g), where e is the unit impulse and g is a gaussian kernel.

Original	Sharpened

Sharpening was then used on blurry images to "re-sharpen" images. The effect is subtle in this example, but it can especially be seen in the "road work ahead" sign.

Original	Blurred	Sharpened

2.2 Hybrid Images

I made two hybrid images by mixing low and high frequencies of different images. The first is a hybrid of Superman with Clark Kent. The second is a hybrid of my friend's cat and my dog.

Low-pass Image	High-pass Image	Hybrid Image

FFT Visualizations for cat/dog hybrid:

(Circle is the cat, Aki is the dog. )

Failed:

I also tried making a hybrid of a Samsung and iPhone, but there aren't enough distinguishing visual features to clearly differentiate the two at different distances.

Low-pass Image	High-pass Image	Hybrid Image

Multi-Resolution Blending

2.3 Gaussian and Laplacian Stacks

I made Laplacian stacks for pictures of an orange and apple, along with their blended stack. This uses a simple step function as a mask.

Apple Stack	Orange Stack	Blended Stack

2.4 Multiresolution Blending

Oraple result:

The oraple worked very well. I also made a few more multiresolution blended images using irregular masks. The masks were constructed by using a Sobel edge detection filter and then flood filling certain areas of the edge map.

Image 1	Image 2	Mask	Result
			Gojo in Smash
			Double Gudetama
			Totoro in Gudetama's Shell

Laplacian and Blended Stacks for Gojo in Smash:

Gojo Stack	Smash Stack	Blended Stack