HsH VC-3: Wavelets for Computer Graphics

This project was developed within the context of the course Visual Computing at Hannover University of Applied Sciences and Arts where the third part moderated by Prof. Dr. Dennis Allerkamp was about wavelets for computer graphics.

Images

Note: All pictures processed here have to have a shape of 2ⁿ x 2ⁿ.

Implementation for exercises Images you'll find in images.py (resp. Haar.py). Toggle booleans in main() for each subtask. Commented lines are proposals for different usages of the stated functions.

Three images are provided in list image_pathes choose index from [0,2].

1. See file Haar.py.

2. 2D Trafo (Decomp-Recon).

   decomp_and_recon_with_steps(image_pathes[1], color=False, normalized=True, standard=False, crop_min_max=False)
   

   Resulting plot contains 4 rows (columns depend on the shape):

   • First row contains the first half of the decomposition (if standard=True all rows of the image),
   • Second row contains the second half of the decomposition (if standard=True all columns of the image),
   • Reconstruction starts in row three and
   • goes on in row four. The last but one is the reconstructed image.
     The very last one is a "differences-image" containing the differences between input and reconstructed image (should be black ;)).

3. Compression on gray-scale.

   Haar.compression_2d(image_values, number_of_coeffs_left_exact=10000)
   

   • squared_error: Sum of all truncated values will be below this value. Implementing the binar search approach from lecture.
   • squared_error_stollnitz: Sum of all truncated values will be below this value. Finding threshold by starting at minimum and doubling each step until squared error is reached.
   • number_of_coeffs_left_exact: Exact this amount of coefficients will stay. Searching for the n-th greates element and truncating all below.
   • number_of_coeffs_left: Doubling threshold until sum of not truncated coefficients is reached.

   
   Lenna compressed down to 10,000 coefficients.

4. Same as 3. but for each channel of YUV. Chrominance channel Y is processed with separate values (acc. to 3.).

   Haar.compression_2d_yuv(image_values, y_number_of_coeffs_left_exact=26214, uv_number_of_coeffs_left_exact=13107)
   

   
   Here 10% of chrominance an 5% of luminance channels (of a 512x512 image).

   File util.py contains functions to convert between RGB and YUV.

5. IQA Preprocessing.

   preprocessing(image_pathes[2],number_of_coeffs_left_exact=60)
   

   
   Output of statement above.

Subdivision

Implementation for exercises 1-3 you'll find in subdivision.py.
Run main() to start GUI.

• Subdivision step can be changed by slider,
• Subdivision scheme can be chosen from radio buttons.

Implementation for exercises 4 & 5 you'll find in function_subdivision.py

• Subdivision step can be changed by slider,
• Subdivision scheme can be chosen from radio buttons,
• Functions can be chosen by radio buttons:
  • function1 is a polynom,
  • function2 is a sin and
  • scaling function is the Kronecker delta. The slider below changes the i of this function.

Curves

Note: All curves data processed here have to contain exact 2ⁿ+1 points (since we work on linear B-splines).

Implementation for exercises Curves you'll find in multi-res.py. File MRAGUI.py contains the belonging matplotlib code, file curves-data.py contains np.arrays with coordinates.

For fractional-level (selected by radio button) there are two "pumping" methods:

• doubling and
• averaging.

To change the "sweep" of the low-resolution curve, you'll have to choose discrete to see points, you can drag over the plot. Releasing them will affect the cur_points array and further resolution changes will calculate with updated points.