Nonlinear Filters

Bachelor's thesis

Topic: Nonlinear filtering for large 3D image data (Bilateral filter, Non-local means filter).

Milestones

• 2D Bilateral filter (naive implementation) ✔
• Parallel processing ✔
• Fast 2D Bilateral filter (custom optimizations) ✔
• 2D Non-local means filter ✔
• Fast 2D Non-local means filter (integral image) ✔
• CLI for 2D ✔
• rendering 3D volumetric data ✔
• 3D Bilateral filter ✔
• 3D Non-local means filter ✔
• CLI for 3D ✔
• Piecewise processing for large 3D volumetric data
• Optimizations via parallel processing using SIMD

Data samples

Image:

• House 620x620 (GrayScale) source

Volumetric data:

• CT Foot 183x255x125 (uint8) source
• C60 64x64x64 (uint8) source

Bilateral filter

Parameter	Value
Space sigma	6
Range sigma	25.5

Filter	Windows [s]	Ubuntu [s]
Bilateral (1 thread)	~ 0.56	~ 0.51
Bilateral	~ 0.16	~ 0.15
OpenCV	~ 0.30	~ 0.32
SimpleITK	~ 1.04	~ 0.70
Itk	~ 0.71	~ 0.78

Noisy vs Bilateral filter

Non-local means filter

Parameter	Value
h	15
Patch size	3x3
Window size	21x21
Samples	500

Filter	Windows [s]	Ubuntu [s]
Non-local means (1 thread)	~ 8.0	~ 6.26
Non-local means (7 threads)	~ 2.25	~ 1.83
Non-local means sampled (7 threads)	~ 1.58	~ 1.4
Fast Non-local means (1 thread)	~ 3.36	~ 3.15
Fast Non-local means (7 threads)	~ 2.1	~ 2.2
Fast Non-local means sampled (7 threads)	~ 1.5	~ 2
OpenCV	~ 0.9	~ 0.4

Note: Fast Non-local means filter complexity is independent to patch size due to integral image optimizations

Noisy vs Non-local means filter

Non-local means filter vs OpenCV Non-local means filter

Sampled Non-local means filter vs OpenCV Non-local means filter

Bilateral vs Non-local means

Rendering volumetric data

3D rendering of noisy volumetric data using ray casting

3D Bilateral filter

Parameter	Value
Domain sigma	5
Range sigma	20

Filter	Windows	Ubuntu
Fast Bilateral (1 thread)	~ 1.3 min	~ 1.6 min
Fast Bilateral (7 threads)	~ 25 sec	~ 27 sec
Simple Itk (multi-threaded)	~ 14.9 min	~ 9.2 min
Itk (multi-threaded)	~ 12 min	~ 7.75 min

Fast bilateral filter

Note: There are no differences discernible to the eye between measured filters.

3D Non-local means filter

Parameter	Value
h	20
Patch size	3x3x3
Window size	15x15x15
Samples	500

Filter	Windows	Ubuntu
Non-local means sampled (7 threads)	~ 10.6 min	~ 10.5 min
Fast Non-local means sampled (1 thread)	~ 4.0 min	~ 4.2 min
Fast Non-local means sampled (7 threads)	~ 1.4 min	~ 1.5 min
scikit (1 thread)	~ 7 min	~ 4.9 min

Note: Fast Non-local means filter (as well as scikit impl.) complexity is independent to patch size due to integral image optimizations

Non-local means sampled filter

scikit Non-local means filter

3D Bilateral vs 3D Non-local means

Testing environment

Tool	Windows 10	Ubuntu 20.04 (WSL 2)
.NET runtime	6.0.3	6.0.3
Python	3.10.2 [MSC v.1929 64 bit (AMD64)]	3.8.10 [GCC 9.4.0]
OpenCV	4.5.5	4.5.5
Itk	5.3.0	5.2.1
SimpleITK	2.2.0rc2.post35	2.1.1
scikit image	0.19.2	0.19.2

Remainder:

• Test script (test.ps1) requires 2 powershell scripts (cmp-img.ps1 and join-img.ps1 for Windows only) for full experience.

• For comparing filters with python alternatives, it's required to install dependencies:

  • Itk
  • SimpleItk
  • OpenCV
  • scikit image

  ...