As a warmup, we try to sharpen a image.  First, we blur the image by Gaussian filter.  Then, subtracting the blurred image from the original, we are able extract details from an image.  Finally, enhancing the details by adding them back with a factor greater than 1 produces a sharpening effect.  The corresponding formula is shown below.

Described in the SIGGRAPH 2006 paper by Oliva, Torralba, and Schyns, Hybrid images can be created by blending high frequency of an image and low frequency of another.  The idea is that high frequency tends to dominate perception when it is available, but, at a distance, only the low frequency (smooth) part of the signal can be seen.  Here is a nice illustration of this method by Oliva, Torralba, and Schyns:

This example fails because the background of tiger is not very clean.

We tackle the problem above by cleaning the background of tiger image using a mask, and we now have:

This example fails because apple and orange look too similar.

Using color for low works the best.  It's because color on the high-pass image only adds some unnoticeable details to it.  Also, if we add color on the low-pass image, the color won't be too overwhelming so to affact the details of high-pass image.

In Gaussian Stacks, subsequent images are weighted down using a Gaussian average.

In Laplacian Stacks, subsequent images are the difference image of the blurred versions between each levels of Gaussian Stack and the last image is the same            

as the last image of corresponding Gaussian Stack.  

Gaussian Stacks

Laplacian Stacks

Gaussian Stacks

Laplacian Stacks

In this part, we blend two images seamlessly using a multi resolution blending as described in the 1983 paper by Burt and Adelson.

Laplacian Stacks during blending multi resolution blending

Gray Orapple

Colored Laplacian Stacks during blending multi resolution blending

Colorred Orapple

Faye Wong                                                                                             Xixi S????

Faye S????                                                                                             Xixi Wong

Sasuke                                                             mask                                                             me

😂

In the Part 1, when blending images, all we concerned about was how to make the blended image seamlessly.  Different from the implementation in part 1, for which we worked on Laplacian Stacks, in this part, we explore more about the gradient domain.  In order to make pixels around the blending boundary have the same color and to preserve features of both images, the only thing we need is just to solve an optimization problem with blending constraints (Poisson Blending):

Laplacian Stacks during blending multi resolution blending

In this part, we try to reconstruct an image only using the pixel on the top left corner of the original image and all the gradients on x-axis and y-axis.

The problem is equivalent to solve:

Result:

Original image                                        reconstructed image 

Exmaples:

  Source Image (Rasengan)                Source Mask                                        Coco (Target Image)                                                 Target Mask

Direct Copy Image                                                                                       Poisson Blended Image (Coco Rasengan)

Explanation of the Examples:

As described in Part 2.0, I first set up a system of linear equations that solves the optimization problem.  At first, I made vt represent a image of the same size as Target Image because it's easier to implement.  However, it takes about 20 minutes to run, so I later modified getMask.m such that it returns the place that the source image is copied.  Using these additional values, we are able to set up equations to solve for vs that represents an image of the same sive as Source Image, and to blend the image represented by vs into Target Image by copying pixels.  It only takes 20 seconds to run now!

Also, when I tried to directly copy the pixels of the image represented by vs to the background, there is a large black seam in-between.  I don't exactly know what caused this but I tackled this problem by adding an if statement that requires pixels to have values greater than 0.03 to be copied.

Additional Examples (success):

  Source Image                    Source Mask                                            Target Image                                                                Target Mask

Direct Copy Image                                                                                                  Poisson Blended Image

Additional Examples (failures):

While I was trying to add more penguins on the snow, as you can see, the bottom left penguin has a weird face.  It's because there is a big contrast between colors on the penguin's boundary.

The same thing happens to the Rasengan below : (

  Source Image (Rasengan)                Source Mask                                        Coco (Target Image)                                                 Target Mask

Direct Copy Image                                                                                       Poisson Blended Image (Coco Rasengan)

Source Image (Sasuke)                                                                        Target Image (me)                                                                     Source Mask

 Laplacian pyramid blending                                                                   Direct Copy                                                                     Poisson Image Blending

The Laplacian pyramid blending works better for the images above because the source image the target image don't have the same kind of color and texture.

In conclusion, if the source image the target image are drastically different,  Laplacian pyramid blending works better because we want the blended image to have not only the same color, but also the same texture and shape.  However,  if the source image the target image are compatible, like a penguin and snow, then Poisson Image Blending works better because it preserves more details of both image.