Part 1: Fun with Filters

Part 1.1. Finite Diference Operator

In this section I used the finite difference filter in order to get the partial derivatives in the x and y direction. To compute the gradient magnitude image, since gradient is an elementwise operation, I simply take the dx image and the dy image and use NumPy to compute np.sqrt(dx ** 2 + dy ** 2) to get the graident magnitude. Then I used a threshold of 0.2 to binarize the image to an edge image. These images are shown below:

original	dx	dy
gradient magnitude	edge image

Part 1.2. Derivative of Gaussian (DoG) Filter

In this section, I first blurred the image with a sigma=1.5 Gaussian and then repeated the steps above to get an edge image, this time with threshold of 0.06:

blurred	dx of blurred	dy of blurred
gradient magnitude of blurred	edge image of blurred

The result is fairly different from when I didn't blur the input image. We see that the edges are thicker and that there are less noise in the background (especially on the grass).

Now we can combine the blur and the finite difference operator to get a DoG filter, which gets us the same final result:

Dx DoG kernel

Dy DoG kernel

Edge image using DoG

Part 2: Fun with Frequencies

Part 2.1: Image "Sharpening"

For image sharpening, I first blur the image with a sigma=1.5 gaussian, then I subtract the blurred image from the normal image to get the high-passed image, and then add it back to the image to sharpen it. This is known as "unmask sharp" filter. Below I show the progression of two images through this procedure:

taj

taj blurred

taj high-passed

taj sharpened

windows (source: https://www.pinterest.com/pin/733594226771800471/)

windows

windows blurred

windows high-passed

windows sharpened

However, unsharp mask doesn't actually "sharpen" an image. For example, if I take a sharp image and blur it first and then try to sharpen it, the resulting image will not regain the sharpness of the original image. This is because unsharp mask simply increases the intensity of the high frequencies of the image, but if there isn't any high frequencies to begin with (such as a blurred image), then of course the unsharp mask won't create them out of thin air. Example image of a building (source: https://www.americanbuildings.com/project-gallery/#office):

original

original blurred

unsharp mask applied on blurred

Part 2.2: Hybrid Images

In this part, I created hybrid image by firs aligning both images, then low-pass filtering one image (using a Gaussian filter), then high-pass filtering the other (using a impulse minus Gaussian filter), and then averaging the two resulting images together. Below I show a few examples:

derek

nutmeg

derek low-pass

nutmeg high-pass

derek + nutmeg

watermelon (source: https://www.heb.com/product-detail/fresh-watermelon/583329), durian (source: https://phys.org/news/2020-02-durian.html)

watermelon

durian

watermelon low-pass

durian high-pass

watermelon + durian

For Jungkook + RM I also show the frequency domain analysis. As expected, low pass removes a lot of the low frequencies and high pass keeps all the noisy high frequences, and in the combination we see bright lines that are characteristic of both images.

(source: https://www.allure.com/story/bts-jungkook-long-hair-viral), RM (source: https://www.soompi.com/article/1425304wpp/btss-rm-donates-100-million-won-to-museum-on-his-birthday)

Jungkook	RM	Jungkook low-pass	RM high-pass	Jungkook + RM
Jungkook FFT	RM FFT	Jungkook low-pass FFT	RM high-pass FFT	Jungkook + RM FFT

For Car + Simu, I show that this one doesn't really work, because for this hybrid method to work well, both images should have objects of similar shapes. Otherwise, it just looks like two images existing at the same time.

Simu (source: https://www.today.com/popculture/shang-chi-star-simu-liu-responds-critics-about-marvel-movie-t230259), Car (source: https://www.istockphoto.com/photos/side-view)

car

simu

car low-pass

simu high-pass

car + simu

Part 2.3 + 2.4: Gaussian and Laplacian Stacks + Multiresolution Blending

For this section, I implemented multiresolution blending using Gaussian and Laplacian stacks. How this works is by splitting the two input images into different frequency bands, then blending the bands together using masks blurred at different levels, and then adding the blurred bands together.

Bells and Whistles: I implemented everything with RGB colors. However, I will show the final result of Orapple using grayscale just for comparison (the colored version looks better).

Orapple

I first apply this on the Orapple, i.e. blending together an apple on the left and orange on the right. For all the blends, I used 5 levels and initial sigma of 4.0, doubling sigma at each level. For all the visualizations, I will show the laplacian pyramid at level 0, 2, and 4, and the combined image. I will also show the initial images, the mask, and the final image.

apple

orange

mask

orapple

grayscale

Cucumber Shark

The next one is combining Benedict Cumberbatch (a.k.a cucumber), and a shark. Sources: https://www.thesun.co.uk/news/6432784/benedict-cumberbatch-saves-deliveroo-assault/, https://www.nytimes.com/2020/08/14/science/great-white-shark.html

cucumber

shark

mask

cucumber shark

Illuminati

The next one is combining a pyramid and an eye into illuminati. This one also uses an irregular mask. Sources: https://www.livescience.com/3919-human-eye-works.html, https://www.mentalfloss.com/article/512833/scientists-discover-mysterious-void-great-pyramid-giza