cs180-portfolio
proj2: filters and frequencies
task 1: fun with filters
1.1: finite difference operator
I first found partial derivative matrices by convolving Dx = np.array([[1, -1]]) and Dy = np.array([[1], [-1]] with cameraman.png as a gray scale image matrix. I used scipy.signal.convolve2d with mode="same to keep the dimensionality of the matrix after convolutions. Afterwards, I created a gradient magnitude matrix by using the two partial derivative matrices derived earlier. g_m = np.sqrt(dx ** 2 + dy ** 2).
dx |
dy |
gradient magnitude |
binarized, thresh=0.25 |
1.2: derivative of gaussian filter (DoG)
I applied a gaussian blur first and then found the partial derivative matrices of the blurred image to see if it helps with edge detection. The gaussian kernel was created using cv2.getGaussianKernel, and the 2d gaussian filter was creating doing the outer product of the gaussian kernel on itself. The kernel size k was 10 x 10 and the sigma was (k-1) / 6 since “the length of for the 99th percentile of gaussian pdf is 6 * sigma”.
gaussian blurred cameraman.png
dx of blurred image |
dy of blurred image |
gradient magnitude |
binarized, thresh=0.05 |
Second method I tried was to first blur the derivative matrices by convolving the gaussing filter with the finite difference matrices. Afterwards, I convolved the newly transformed gaussian filters with the original image to find the gradient magnitude.
dx of gaussian |
dy of gaussian |
dx of blurred image |
dy of blurred image |
gradient magnitude |
binarized, thresh=0.05 |
Both methods work well and the output resutls look basically the same. There might be slightly some more noise in the first one compared to the second one, but it is only noticable when gone a thorough examination of both images.
task 2: fun with frequencies
2.1: sharpening
Steps to sharpening an image:
- Extract low frequencies of image via low pass filter. I used gaussian blur.
- Extract high frequenceis of image via
image - low. - Add high frequencies multipled by alpha back to image via
image + alpha * high.
taj.jpg with alpha=1
taj.jpg |
low taj.jpg |
high taj.jpg |
sharpened taj.jpg, alpha=1 |
side note
I used
cv2operations since they automatically deal with out of range values. I tried usingnp.clipafter doing np matrix operations before butcv2operations do a much better job.
taj.jpg
alpha=0 |
alpha=1 |
alpha=2 |
alpha=5 |
alpha=20 |
mlord.png
alpha=0 |
alpha=1 |
alpha=2 |
alpha=5 |
alpha=20 |
nostudy.png
alpha=0 |
alpha=1 |
alpha=2 |
alpha=5 |
alpha=20 |
I also tried “resharpening” an image by blurring an already sharp image and then sharpening it again.
nosleep.jpg
initial sharpened image, alpha=2 |
blur of initial image |
sharpen, alpha=2 |
The resharpened image has more clear edges but has weird artifacts, presumably from creating previously nonexistant edges into edges. e.g. the face shading now has a bunch of weird cracks now.
2.2: hybrid images
To make make some hybrid images, align an the two images and then sum up one image’s low frequencies and the other’s high frequencies.
derek and nutmeg
derek |
nutmeg |
a furry |
chimera
nina from full metal alchemist |
nina's dog |
... |
gogeta
goku |
vegeta |
fusion! |
frequency analysis
goku fft |
goku high freq fft |
vegeta fft |
vegeta low freq fft |
gogeta fft |
The fft shows how the images align their frequencies an create the hybrid image of gogeta. You can tell via the white lines of frequencies from both images.
2.3: gaussian and laplacian stack
I did each stack to 10 layers.
gaussian stack of apple
layer 0 |
layer 3 |
layer 6 |
layer 10 |
gaussian stack of orange
layer 0 |
layer 3 |
layer 6 |
layer 10 |
laplacian stack of apple
layer 0 |
layer 3 |
layer 6 |
layer 10 |
laplacian stack of orange
layer 0 |
layer 3 |
layer 6 |
layer 10 |
2.4: multiresolution blending
oraple
please forigve me as i accidentally did 1 more layer than the paper itself.
|
layer 0 |
apple |
orange |
combined |
|
layer 2 |
apple |
orange |
combined |
|
layer 4 |
apple |
orange |
combined |
|
layer 7 |
apple |
orange |
combined |
apple |
orange |
mask |
combined |
oraple horizontal
|
apple |
orange |
mask |
combined |
kirby
kirby |
kirby blue |
mask |
combined |
gudetama breakfast (fail)
gudetama |
breakfast |
mask |
combined |
here’s a cursed egg instead
gudetama |
c
breakfast |
mask |
combined |
reflection
pretty fun project overall. learned how frequencies worked and basically how photoshop works with masking. made some fun references to some of my favorite animes :).