Fast and simple to use 2D and 3D structure tensor implementation for Python.
Install package using pip install structure-tensor or clone the repository.
For CUDA support install extra (optional) dependancy CuPy. If CUDA is installed on your system, pip install cupy should be enough, but may be slow as CuPy will compile code during install. Alternatively use one of the precompiled packages.
The parameters for the structure tensor calculations are $\rho$ (rho) and $\sigma$ (sigma), which are scalar values.
The structure_tensor package support doing either 2D or 3D structure tensor analysis. Eigenvalues (val) are sorted acending.
import numpy as np
from structure_tensor import eig_special_2d, structure_tensor_2d
sigma = 1.5
rho = 5.5
# Load 2D data.
image = np.random.random((128, 128))
S = structure_tensor_2d(image, sigma, rho)
val, vec = eig_special_2d(S)For volume with shape (x, y, z) the eigenvectors (vec) are returned as zyx.
import numpy as np
from structure_tensor import eig_special_3d, structure_tensor_3d
sigma = 1.5
rho = 5.5
# Load 3D data.
volume = np.random.random((128, 128, 128))
S = structure_tensor_3d(volume, sigma, rho)
val, vec = eig_special_3d(S)CuPy functions are available in the structure_tensor.cp module. They work similar to their NumPy counterparts, except that they return cupy.ndarrays. The functions will automatically handle moving input data if necessary.
import cupy as cp
import numpy as np
from structure_tensor.cp import eig_special_3d, structure_tensor_3d
sigma = 1.5
rho = 5.5
# Load 3D data.
volume = np.random.random((128, 128, 128))
S = structure_tensor_3d(volume, sigma, rho)
val, vec = eig_special_3d(S)
# Convert from cupy to numpy. Moves data from GPU to CPU.
val = cp.asnumpy(val)
vec = cp.asnumpy(vec)The structure_tensor module also contains functions for parallel "blocked" calculation of the structure tensor and eigendecomposition. The easiest approach is to use the built-in function structure_tensor.multiprocessing.parallel_structure_tensor_analysis. This allows the computations to be distributed across many CPUs and CUDA devices. This can speed up computations many times and has the added benefit of reducing memory usage during calculation.
In the example below the volume data is split into blocks of size 200 cubed and the workload will be distributed across 16 CPUs.
S, val, vec = parallel_structure_tensor_analysis(data, sigma, rho, devices=16*['cpu'], block_size=200)Alternatively, if we have a CUDA enabled GPU available, we could use that instead.
S, val, vec = parallel_structure_tensor_analysis(data, sigma, rho, devices=['cuda'], block_size=200)If the GPU has sufficient memory we could likely speed up the calculations by using several processes to feed the GPU.
S, val, vec = parallel_structure_tensor_analysis(data, sigma, rho, devices=4*['cuda'], block_size=200)If we have four CUDA devices available, we could choose to use several specific devices, e.g., device 0 and 2.
S, val, vec = parallel_structure_tensor_analysis(data, sigma, rho, devices=4*['cuda:0'] + 4*['cuda:2'], block_size=200)We could even choose to use a mix of CPU and GPU processes, e.g., four processes for GPU 0, two for GPU 2, and 8 processes runing the calculations on the CPU.
S, val, vec = parallel_structure_tensor_analysis(data, sigma, rho, devices=4*['cuda:0'] + 2*['cuda:2'] + 8*['cpu'], block_size=200)The ideal block size depends on the sigma and rho, the devices, and the memory available for the devices. Usually values between 100 and 400 work well. If you encounter out-of-memory errors, try reducing the block size and/or the number of processes.
The notebooks published in the datasets also contains examples. The StructureTensorFiberAnalysisDemo [ notebook | HTML ] and StructureTensorFiberAnalysisAdvancedDemo [ notebook | HTML ] notebooks are a good starting point. However, these notebooks were made before the parallel_structure_tensor_analysis function was added and therefore use their own code for parallel ST computation.
Contributions are welcome, just create an issue or a PR.
If you use this any of this for academic work, please consider citing our work.
Jeppesen, N., et al. "Quantifying effects of manufacturing methods on fiber orientation in unidirectional composites using structure tensor analysis." Composites Part A: Applied Science and Manufacturing 149 (2021): 106541.
[ paper ] [ data and notebooks ]
@article{JEPPESEN2021106541,
title = {Quantifying effects of manufacturing methods on fiber orientation in unidirectional composites using structure tensor analysis},
journal = {Composites Part A: Applied Science and Manufacturing},
volume = {149},
pages = {106541},
year = {2021},
issn = {1359-835X},
doi = {https://doi.org/10.1016/j.compositesa.2021.106541},
url = {https://www.sciencedirect.com/science/article/pii/S1359835X21002633},
author = {N. Jeppesen and L.P. Mikkelsen and A.B. Dahl and A.N. Christensen and V.A. Dahl}
}Jeppesen, N., et al. "Characterization of the fiber orientations in non-crimp glass fiber reinforced composites using structure tensor." IOP Conference Series: Materials Science and Engineering. Vol. 942. No. 1. IOP Publishing, 2020.
[ paper ] [ data and notebooks ]Auenhammer, Robert M., et al. "Robust numerical analysis of fibrous composites from X-ray computed tomography image data enabling low resolutions." Composites Science and Technology (2022): 109458.
[ paper ] [ data ]Auenhammer, Robert M., et al. "X-ray computed tomography data structure tensor orientation mapping for finite element models—STXAE." Software Impacts 11 (2022): 100216.
[ paper ]
Jeppesen, N, Dahl, VA, Christensen, AN, Dahl, AB, & Mikkelsen, LP. (2020). Characterization of the Fiber Orientations in Non-Crimp Glass Fiber Reinforced Composites using Structure Tensor [Data set]. Zenodo. https://doi.org/10.5281/zenodo.3877522
Jeppesen, N, Mikkelsen, Lars P., Dahl, V.A., Nymark, A.N., & Dahl, A.B. (2021). Quantifying effects of manufacturing methods on fiber orientation in unidirectional composites using structure tensor analysis [Data set]. Zenodo. https://doi.org/10.5281/zenodo.4446499
Auenhammer, R.M., Jeppesen, N, Mikkelsen, Lars P., Dahl, V.A., Blinzler, B.J., & Asp, L.E. (2021). X-ray computed tomography aided engineering approach for non-crimp fabric reinforced composites [Data set] [Data set]. Zenodo. https://doi.org/10.5281/zenodo.5774920
See CuPy reference section.
MIT License (see LICENSE file).