In this part, I first computed the partial derivative in x and y of the cameraman image by using scipy.signal.conolve2d() to convolve the image with the finite difference operators D_x and D_y. I then used those to compute the gradient magnitude image (sqrt(dx**2 + dy**2)). Finally, I computeputed the edge image, by binarizing the gradient magnitude image with a threshold of 0.25.

Here, I first blurred the image by convolving it with a Gaussian filter before repeating the steps from part 1.1. I noticed that after blurring the image, some of the noise got smoothed out, which resulted in a much clearer gradient magnitude image as well as edge image.

Afterwards, I repeated the same process using a DoG filter, which took a single convolution instead of two.

I first applied a Gaussian, or low pass, filter with kernel=3 and sigma=1 to the original Taj Mahal image. I then subtracted the blurred image from the original to get back only the high frequencies, then added these frequencies back (alpha=3) to artificially "sharpen" the image. I played around with a few different alpha values, but using higher values (alpha=5-10) made the image look "deep fried" or artificial. I was able to sharpen the image with one convolution by using an unsharp mask filter.

I then repeated the blurring and sharpening process again with an already sharp image of a pagoda in Taipei. Using alpha=3, I think visually we can see that it does "look" sharper/crisper.

In order to create these hybrid images of Derek and his cat Nutmeg, I first used the class starter code to align (to the pupils) and crop the 2 images, then I applied a Gaussian/low pass filter with kernel=15 and sigma=30 to the one image (Nutmeg) and a high pass filter with kernel=10 and sigma=20 to the other (Derek). I then averaged the two images and added them to each other. These kernel sizes and sigma values were determined pretty arbitrarily through visual inspection. From up close, the image looks like Derek, while from far away, the image looks like Nutmeg.

I repeated the same process with a hybrid image of a cup of coffee and a cup of tea by aligning the images to the left and right edges of the cups. I first used tea as the high pass and coffee as the low pass, but it was not successful as the image of the coffee overpowers the tea greatly. I found that it worked a little better vice versa though, with coffee as the high pass and tea as the low pass.

I did the same thing with image of Sakura and Sasuke from the anime Naruto. I thought this would be pretty cool but it is a bit unsettling. I used Sakura as the high pass and Sasuke as the low pass. I also performed frequency analysis on this process by computing the log magnitude of the Fourier transform of the two input/aligned images, the high pass/lowpass versions, and the hybrid image.

In this part, I blended 2 images together by first creating a Gaussian stack and a Laplacian stack, then using those stacks to blend.

Now that I have the laplacian filtered apple and orange images, I combined them at L0, L2, and L4 respectively, then added all of these frequencies into the final image.