I picked the original picture of my friend and used the sharpening technique described in class: filter extrat the high frequences of the image (threshold=sigma) and add it to the original image scaled by constant alpha.

Original

Sharpened (alpha = 0.5, sigma = 5)

Sharpened (alpha = 0.25, sigma = 5)

Photo Credit: Mica.

I blended three pairs of images. First I low-pass filter one image and high-pass filter the second image, each with its corresponding threshold sigma. Then I add them together, each weighted with its corresponding alpha.

Panda: low (sigma=5, alpha=2)
Cat: high (sigma=100, alpha=0.5)

Spiderman: low (sigma=0.5, alpha=1)
Volleyball: high (sigma=20, alpha=1)

Apple: low (sigma=1.5, alpha=1)
Earth: high (sigma=50, alpha=1)

Following is the illustration of the frequencies of the images at different stages.

Apple input Apple input FFT Earth input Earth input FFT Apple: low (sigma=1.5, alpha=1.2)
Earth: high (sigma=100, alpha=0.8)

Apple filtered Apple filtered FFT Earth filtered Earth filtered FFT Blended result FFT

It seems that using color for the high-frequency component is much better than using color for the low-frequency component. The previous examples show the results when both components are colored.

Color high-frequency component (earth) Color high-frequency component (apple)

Color low-frequency component (apple) Color low-frequency component (earth)

I implemented Gaussian stack by successively applying Gaussian filter using threshold sigma to the previous image until reach level N (e.g. N=5). Laplacian stack is created by subtracting each Gaussian image by the image at the level immediately below it.

I first computed the Gaussian and Laplacian stacks of both input images. Then I created a mask, either manually or using python, which consists of only 1 and 0. Then I create Gaussian stack for the mask. For each level of Laplacian stacks, I mask the input images using the mask on the corresponding level and blend them together. Then I blend the lowest level of Gaussian stacks of the two input images. Then I sum up all the blended images, i.e. the blended Laplacian images and the most blurred Gaussian image.

Cat and Panda

Volleyball and Spiderman

Spiderman, Apple and Earth

Below are the Laplacian stacks that I computed, as well as the masked input images that created it.

Denote the width and height of the image as w and h, respectively. I first created a matrix A of size (w*h, w*h). Each row represents the function to use to calculate the gradient at that pixel. For the 4 corner pixels, its gradient is 2 * its intensity - the intensities of the two neighbors. For the pixels on the edges, their gradient is 3 * its intensity - the intensities of the three neighbors. For the inner pixels, the gradient is 4 * its intensity - the intensities of the four neightbors. The top left pixel retains its intensity, as suggested by the spec. In this way, I formulate a least square system and reconstructed the image.

Original

Reconstructed

I picked the original picture of my friend and used the sharpening technique described in class: filter extrat the high frequences of the image (threshold=sigma) and add it to the original image scaled by constant alpha.

Marble Directly Copied

Plate Poisson Blended

More Results:

Red marble

Cake with smile

Four penguins

Contrast between multiresolution blending and poisson blending.

Multiresolution

Poisson

Contrast between using source gradient and using mixed gradient.

Source blending

Mixed blending