Pymorph

Extended Morphological filter library using ARM SIMD instructions for Python on Raspberry Pi. Deep network for Gaussain denoiser and image completion examples using the library are also provided. This library and image processing applications were implemented to demostrate the fast computation in the papers ¹²³.

This library is tested on Raspbian 10, Raspberry pi 4. This library will work on other ARM systems with NEON SIMD instruction.

Install

1. Clone code and example images:

git clone https://github.com/Nkszk/Pymorph

2. Install python3-dev

sudo apt-get install python3-dev

3. Compile and install

cd Pymorph
gcc -c lodloe.c -mfpu=neon -march=armv7-a -O3 -fPIC
gcc  -c modmoe.c -mfpu=neon -march=armv7-a -O3 -fPIC
sudo python3 setup.py install

4. Run Gaussian denoising by the deep Gaussian denoser ¹² (Noise standard deviation sigma = 25, 512x512 image will be processed by about 1.8 [s]. )

python3 morph_gauss.py

5. Run image completion example ³ (Missing probability = 0.7)

python3 morph_int.py

morph_gauss_l.py and morph_gauss_m.py are using linear combinations and max/minimu of morphological Laplacians, respectively.

Extended moprhological filters

In module "pymorph", structuring elemebnts are defined by three dimentinal array as structuring_elements[index, x, y] where the set of x, y denotes the corrdinates. Images and structring elements are limited in uint8.

Maximum of erosions (MoE) The pixel-width maximum of the set of eroded images.

pymorph.moe5x5 (source, dist, structuring_elements)

(structuring_elements is defined in the size 5x5.)

pymorph.moe7x7 (source, dist, structuring_elements)

(structuring_elements is defined in the size 7x7.)

Maximum of dilations (MoD) The pixel-width maximum of the set of eroded images.

pymorph.mod5x5 (source, dist, structuring_elements)

(structuring_elements is defined in the size 5x5.)

pymorph.mod7x7 (source, dist, structuring_elements)

(structuring_elements is defined in the size 7x7.)

Linear combination of erosions (LoE) The linear combination of the set of eroded images.

pymorph.loe5x5 (source, dist, structuring_elements, weights)

(structuring_elements is defined in the size 5x5. weights are float32)

Linear combination of dilations (LoD) The linear combination of the set of dilated images.

pymorph.lod5x5 (source, dist, structuring_elements, weights)

(structuring_elements is defined in the size 5x5. weights are float32)

Morphological Laplacian defined by MoD and MoE

laplacian_simd_5x5(source, dist, structuring_elements)

laplacian_simd_7x7(source, dist, structuring_elements)

Morphological Laplacian defined by LoD and LoE

laplacian_simd_5x5(source, dist, structuring_elements, weights for Laplacian)

laplacian_simd_7x7(source, dist, structuring_elements, weights for Laplacian)

Training of parameters

All paremeters are trained by TensorFlow. The details of the training are explained in ² and ³.

Footnotes

1. H. Fujisaki, M. Nakashizuka, "Deep Morphological Filter Networks For Gaussian Denoising, " Proc. 2020 IEEE International Conference on Image Processing, pp. 918-922, Abu Dhabi, Oct. 2020. ↩ ↩²

2. H. Fujisaki, M, Nakashizuka, "Deep Gaussian denoising network based on morphological operators with low-precision arithmetic, " IEICE Trans. on Fundamentals, Vol.E105-A,No.4,pp.-,Apr. 2022. ↩ ↩² ↩³

3. G. Okada, S. Nozawa and M. Nakashizuka, "Morphological Operators with Multiple Structuring Elements and Its Training for Image Denoising and Completion," 2018 International Symposium on Intelligent Signal Processing and Communication Systems (ISPACS), pp. 406-410, Oct. 2018. ↩ ↩² ↩³