Fun with Filters and Frequencies!

Michael Huang

Part 1

Part 1.1: Finite Difference Operator

Original	Gradient	W/ Threshold

We can compute the gradient magnitude image by convolving the image with $D_x = [1, -1]$ and $D_y = [1, -1]^T$. I convolve $D_x$ and $D_y$ first, then convolve the resulting 2d array $D_{xy}$ with the cameraman image to get its gradient magnitude image.

Part 1.2: Derivative of Gaussian (DoG) Filter

Blurred	Orignal W/ Threshold	Blur W/ Threshold

What differences do you see?

The images are less noisy for similar borders, and we can achive stronger borders for similar noise in the rest of the image.

Verify that you get the same result as before.

We get the same images.

Two Convs	Single

Part 2

Part 2.1: Image "Sharpening"

I apply the Gaussian filter, then subtract it from the orignal image, creating an image with the high frequencies. Then I added the high-pass image multiplied by alpha to the original image, clipping the values between [0, 1] to create a valid image. The resulting images are visually sharper.

Orignal	Manual/Naive Way	Single Convolution

For evaluation, pick a sharp image, blur it and then try to sharpen it again. Compare the original and the sharpened image and report your observations.

Orignal	Blurred	Sharped Blurred

The sharpened image is not as sharp as the orignal image, and information has been lost, though it visually looks sharp as compared to the blurred image.

Part 2.2: Hybrid Images

Hybrid Dog and Cat Image, Cutoff Frequency = 5

Input 1	Input 2	Merged

Hybrid Mt St Helens Before and After, Cutoff Frequency = 7, 10

Input 1	Input 2	Merged

Hybrid Bear Human, Cutoff Frequency = 6, Failure

Input 1	Input 2	Merged

This hybrid image failed, likely because the two images are too dissimilar in color.

Mt St Helens process through frequency analysis.

Image	Fourier Transform

Bells & Whistles (Trying to use color)

Merged	Merged W/ High colored only	Merged W/ Low colored only	Merged W/ Both Colored

I think it works better to use color only for the high frequency, the other two choices make it hard to see the high frequency image.

Merged	Merged W/ High colored only	Merged W/ Both Colored

Similarly, I think it works better to use color only for the high frequency, the other two choices make it hard to see the high frequency image.

Multi-resolution Blending and the Oraple journey

Part 2.3: Gaussian and Laplacian Stacks

(a)	(b)	(c)
(d)	(e)	(f)
(g)	(h)	(i)
(j)	(k)	(l)

Part 2.4: Multiresolution Blending

(a)	(b)	(c)
(d)	(e)	(f)
(g)	(h)	(i)
(j)	(k)	Final Image (l)

Tell us what is the coolest/most interesting thing you learned from this assignment!

I thought the hybrid images that change when you're looking at them at a distant or up close was very cool! I find it fascinating how the human eye can focus in on the high-frequencies when they're more visible, and use the low-frequencies otherwise.