====== Poisson Image Editing ======

The two following labs deal with Poisson image editing, which can be used for image stitching, fusion, cloning, smoothing, context highlighting, color to gray conversion, and other applications.

{{:courses:b4m33dzo:labs:05_poisson_image_cloning.jpg?400|}}

The theory behind the labs can be found in the lectures:
  * [[https://dcgi.fel.cvut.cz/home/sykorad/dzo/slides/dzo-l06.pdf|L6 - Image Editing]]
 
<WRAP round download>
Start by downloading the [[https://cw.fel.cvut.cz/wiki/_media/courses/b4m33dzo/labs/dzo2022_05_poisson_student.zip|template]] of the assignment.

Use ''poisson.m'' to check your solution.
</WRAP>

===== Computing image gradients, their merge, and divergence =====
**1a:** Implement a function that for a given image computes its gradients (**''calc_grad.m''**) - **0.5 points**
  * Use convolution with simple 1D finite differences kernels in X and Y direction.
  * Make sure the gradients at image boundaries are set to zero.

**1b:** Implement a function that computes a mask preferring gradients with greater magnitude (**''get_mask.m''**) - **0.5 points**
  * In each pixel compare magnitudes of gradients in the first and in the second image. When the first image has greater magnitude store 0 in the mask otherwise store 255.

**1c:** Implement a function that merges two images according to a given mask (**''merge_image.m''**) - **0.5 points**
  * In each pixel if the mask has value 0 the output color is taken from the pixel of the first image otherwise the pixel color in the second image is used.

**1d:** Implement a function that merges two input gradient fields according to a given mask (**''merge_grad.m''**) - **0.5 points**
  * In each pixel if the mask has value 0 the output gradient vector is taken from the first image otherwise the gradient computed in the second image is used.

**1e:** Implement a function that computes divergence of a given gradient field (**''calc_div.m''**) - **0.5 points**
  * During the computation try to avoid a situation where the output divergence is shifted by one pixel.

Compare your results to the reference:

  * [[https://cw.fel.cvut.cz/wiki/_media/courses/b4m33dzo/labs/05_poisson_mona_Gx.jpg|Image gradients in X direction]]
  * [[https://cw.fel.cvut.cz/wiki/_media/courses/b4m33dzo/labs/05_poisson_mona_Gy.jpg|Image gradients in Y direction]]
  * [[https://cw.fel.cvut.cz/wiki/_media/courses/b4m33dzo/labs/05_poisson_car_mask.jpg|Gradinent selection mask]]
  * [[https://cw.fel.cvut.cz/wiki/_media/courses/b4m33dzo/labs/05_poisson_cloned_intensity.jpg|Cloned image using intensity domain]]
  * [[https://cw.fel.cvut.cz/wiki/_media/courses/b4m33dzo/labs/05_poisson_cloned_Gx.jpg|Merged gradients in X direction]]
  * [[https://cw.fel.cvut.cz/wiki/_media/courses/b4m33dzo/labs/05_poisson_cloned_Gy.jpg|Merged gradients in Y direction]]
  * [[https://cw.fel.cvut.cz/wiki/_media/courses/b4m33dzo/labs/05_poisson_cloned_divG.jpg|Divergence of merged gradients]]

===== Solving Poisson equation iteratively using Gauss-Seidel method =====
**2:** Implement a function that solves Poisson equation by discretizing it into a system of linear equations which is solved iteratively using Gauss-Seidel method (**''solve_GS.m''**) - **2.5 points**
  * Try to perform all computations implicitly without the need to build the linear system explicitly.
  * Try to provide good initialization, set sufficient number iterations, and resolve boundary conditions.
  * Try to reduce the number of equations to pixels for which the value is not known (use the given mask and/or bounding box).
  
Compare your results to the reference:
  * [[https://cw.fel.cvut.cz/wiki/_media/courses/b4m33dzo/labs/05_poisson_cloned_gradient_gs.jpg|Cloned image using gradient domain (Gauss-Seidel)]]

===== Solving Poisson equation directly using Fourier transform =====
**3:** Implement a function that solves Poisson equation by deconvolution in the frequency domain (**''solve_FT.m''**) - **4 points**
  * Compute frequency domain version of the discreet Laplace operator.
  * Use Wiener filtration to avoid division by zero during deconvolution.
  * Try to normalize the output to have similar colors and contrast as the original images.

Compare your results to the reference:
  * [[https://cw.fel.cvut.cz/wiki/_media/courses/b4m33dzo/labs/05_poisson_cloned_gradient_ft.jpg|Cloned image using gradient domain (Fourier transform)]]


===== Testing the resulting implementation =====
**4a:** Do image cloning using images and mask in the data folder (''mona_lisa.png'', ''ginevra_benci.png'', ''mona_mask.png'') - **0.5 points**
  * Merge the images ''mona_lisa.png'' and ''ginevra_benci.png'' using ''merge_image.m'' function to see the discrepancy.
  * Compute gradients of images ''mona_lisa.png'' and ''ginevra_benci.png'' using ''calc_grad.m''.
  * Merge the gradients using ''merge_grad.m'' and compute the divergence using ''calc_div.m''.
  * Solve Poisson equation using ''solve_GS.m'' and ''solve_FT.m''.
  * Compare output quality and processing speed.

**4b:** Do image fusion to simulate HDR photo using images in the data folder (''car_low.png'' and ''car_high.png'') - **0.5 points**
  * Compute gradients for images ''car_low.png'' and ''car_high.png'' using ''calc_grad.m''.
  * Compute merging mask using ''get_mask.m'', merge the gradients using ''merge_grad.m'', and compute the divergence using ''calc_div.m''. 
  * Solve Poisson equation using ''solve_FT.m''.

Compare your results to the reference:
  * [[https://cw.fel.cvut.cz/wiki/_media/courses/b4m33dzo/labs/05_poisson_cloned_intensity.jpg|Cloned image using intensity domain]]
  * [[https://cw.fel.cvut.cz/wiki/_media/courses/b4m33dzo/labs/05_poisson_cloned_gradient_gs.jpg|Cloned image using gradient domain (Gauss-Seidel)]]
  * [[https://cw.fel.cvut.cz/wiki/_media/courses/b4m33dzo/labs/05_poisson_cloned_gradient_ft.jpg|Cloned image using gradient domain (Fourier transform)]]
  * [[https://cw.fel.cvut.cz/wiki/_media/courses/b4m33dzo/labs/05_poisson_merged_gradient_ft.jpg|Merged image using gradient domain (Fourier transform)]]

<note important>
When you are done, upload the complete zip archive containing your implemented files to BRUTE:
  * ''calc_grad.m''
  * ''get_mask.m''
  * ''merge_image.m''
  * ''merge_grad.m''
  * ''calc_div.m''
  * ''solve_GS.m''
  * ''solve_FT.m''
  * ''poisson.m''
as well as your final output images generated in tasks 4a and 4b.

Keep the files in the root of the zip archive (zip directly the files, NOT a folder containing the files). The evaluation system searches for the files just in the root of zip archive. 

The points will be assigned manually by TA after the deadline.
</note>