Project 2: Fun with Filters and Frequencies!

1.1 Finite Difference Operator

I first convolved the image with the D_x and D_y kernel to get the gradients in the vertical and hortizontal direction. In order to get the gradient magnitude image, I computed the square root of the sum of squares of the gradients in both directions. I chose a 0.1 threshold for the binarized image.

1.2 Derivative of Gaussian (DoG) Filter

I created a 2D gaussian filter by using cv2.getGaussianKernel() to create a 1D gaussian filter and then taking an outer product with its transpose. Then, I convolved the original image with the 2D gaussian filter to get a blurred image.

Then I repeat the steps I did in 1.1 on the blurred image and it appears that the binarized image appears with a lot less noise.

I then convolve the gaussian filter with the D_x and D_y filter to get these DoG filters.

To verify the DoG filters, I convolved them with the image and got the gradient magnitude and binarized images which ends up being the same as convolving the D_x and D_y filter with the blurred image.

2.1 Image "Sharpening"

I subtracted the blurry image from the original image to make a high-pass filter, and add that to the original image to sharpen it.

Another Example

In the images below, I blur an image of Soda and then sharpen the blurred image. However, it still appears more blurry than the original image since high frequency information is still lost.

2.2 Hybrid Images

I created hybrid images by running a low-pass filter on one image and running a high-pass filter on the other image

Fourier Analysis

Other Examples

Denero + Dog.

Bayen + Leopard. This hybrid does not work as well because when you low-pass filter the leopard, you can't really see the spots anymore and Bayen's face contrasts too much with the leopard's body.

2.3 Gaussian and Laplacian Stacks

I created the gaussian stack by convolving the image with a gaussian kernel repeatedly. I created the laplacian stack by subtracting the gaussian from the next level of the stack from the current level.

2.4 Multiresolution Blending

In order to blend the images I created a 5-level laplacian stack for each image. Then, I computed each level of a combined laplacian stack with the mask gaussian stack as weights. Finally, I summed up each level to get the blended image.

Gireeja Sahai Stacks