imea 0.3.5

imea is an open source Python package for extracting 2D and 3D shape measurements from images.

Introduction

Quantitative measurement of 2D and 3D shapes based on images are used in many research fields, for example chemistry (Lau et al. 2013), mineral engineering (Andersson et al. 2012), medicine (Nguyen et al. 2005), biology (Smith et al. 1996) or environmental engineering (Kandlbauer et al. 2021; Weissenbach & Sarc 2021). Furthermore, a variety of different shape measurements is proposed in scientific literature (e.g. DIN ISO 9276-6; Pahl et al. 1973a, 1973b, 1973c; Pabst & Gregorova 2007; Steuer 2010).

In contrast, existing Python packages for image analysis like scikit-image (Walt et al. 2014) or opencv (Itseez, 2015) cover only a few of the 2D and 3D shape measurements proposed in scientific literature. To utilize different shape measurements researchers often have to combine results of different libaries which means dealing with different coordinate systems, data formats and conventions or implement shape measurements on their own. Both scenarios lead to unnecessary "reinventing the wheel" and can cause significant frustrations and/or potential errors in the results.

imea solves this problem: Based on binary images (2D case) or grayscale images where the grayvalue of each pixel represents its height (3D case), 53 different 2D shape measurements and 13 different 3D shape measurements are extracted and returned as an pandas dataframe (McKinney, 2010). With imea shape measurements can be extracted with a single line of code:

# 2D case
df_2d = imea.shape_measurements_2d(bw, spatial_resolution_xy)

# 3D case
df_2d, df_3d = imea.shape_measurements_3d(img_3d, threshold_mm, spatial_resolution_xy, spatial_resolution_z)

In the background imea deals with different coordinate systems and conventions to utilize the implementations of existing functions for shape measurements in scikit-image and opencv. Furthermore, custom implementations based on NumPy and SciPy are integrated in imea for shape measurements that have not been implemented in those libaries yet.

Citation

If you use imea, please cite our JOSS paper:

@article{Kroell2021,
  doi = {10.21105/joss.03091},
  url = {https://doi.org/10.21105/joss.03091},  
  year = {2021},
  publisher = {The Open Journal},
  volume = {6},
  number = {60},
  pages = {3091},
  author = {Nils Kroell},
  title = {imea: A Python package for extracting 2D and 3D shape measurements from images},
  journal = {Journal of Open Source Software}
}

Documentation

For detailed documentation and the API references of imea please visit our documentation site: imea.readthedocs.io

Installation

We recommend using imea in an Anaconda enviroment.

Install with pip (recommended)

You can install imea using the pip package manager:

pip install imea

Install from sources

An other option is to clone the imea repository and install it manually:

git clone https://git.rwth-aachen.de/ants/sensorlab/imea
cd imea
pip install .

Dependencies

imea is tested in Python 3.7+. To use imea the following packages are required:

• numpy>=1.18
• scipy>=1.10
• scikit-image>=0.16
• opencv-python>=4.5
• pandas>=1.0.5
• matplotlib>=3.2 (only for visualization in demo notebooks)
• pytest>=5.4 (only for running tests)

Requierements are also listed in requirements.txt (for using imea) and requirements-dev.txt (for development and running tests).

Tests

Unit tests are available in the tests folder. To execute the tests with pytest you can run the following command:

  python -m pytest tests

Usage

You can use imea either to extract 2D shape measurements from 2D binary images or to extract 2D as well as 3D shape measurements from grayscale images (heightmaps). Under the folder demo you can find two Jupyter notebooks that demonstrate the usage of imea, as well as several example images.

2D measurements

For 2D shape measurements insert a binary image bw and the spatial resolution in xy-direction (spatial_resolution_xy) in [mm/px] into the function extract_df_2d:

df_2d = imea.shape_measurements_2d(bw, spatial_resolution_xy)

As a result you get a pandas dataframe, in which each row represents one particle in the binary image and each column an extracted shape measurement.

Image calibration and spatial resolution: If your image is not calibrated (i.e. no "square" pixels) you may use skimage.transform.rescale to calibrate your image. If you want your results just in pixels then set spatial_resolution_xy=1.

Optional parameters: Optional parameters include the rotation stepsize dalpha (in degrees) for determinating statistical length and two boolean variables for experts to return the original distribution of statistical lengths (set return_statistical_lengths=True) and all chords (set return_all_chords=True).

3D measurements

For 3D shape measurements insert a 3D grayscale image (img_3d), define a threshold (threshold_mm in [mm]) and the spatial resolution of one pixel in x/y-direction (spatial_resolution_xy in [mm/Pixel]) and z-direction (spatial_resolution_z in [mm/Grayvalue]). Pixels with heights lower then threshold_mm are treated as background, the other ones are considered as objects. With the following function call you can extract 2D and 3D shape measurements from a 3D grayscale image (img_3d):

df_2d, df_3d = imea.shape_measurements_3d(img_3d, threshold_mm, spatial_resolution_xy, spatial_resolution_z)

As a result you get two pandas dataframes df_2d and df_3d, in which each row represents one particle in the binary image and each column an extracted shape measurement.

Image calibration and spatial resolution: You can define the spatial resolution of your image with the parameters spatial_resolution_xy and spatial_resolution_z. For calibration and spatial resolution the same recommandations as for the 2D case apply (see above).

Optional parameters: Optional parameters include the rotation stepsize dalpha for determinating shape measurements like the feret diameter, the minimum number of pixels per object to be considered (min_object_area) and the maximum number of objects n_objects_max you want to extract from img_3d. Set n_objects_max=-1 if you want to extract all objects, for n_objects_max > 0 the n_objects_max largest objects (determinated by area) are extracted.

License

imea is published under the MIT-License.

Contribution

If you want to contribute to imea, feel free to contact Nils Kroell via [e-mail]. Moreover, you can do so by reporting bugs and/or suggesting new shape measurements.

Reporting bugs

If you encounter any issues or inconsistent results using imea: Please report them via our issue tracker, so we can work on them. Please give details on the used version of Python and other dependencies as well as provide exemplary data together with the output of imea and your expected output, so we can reproduce your error.

Suggesting new shape measurements

If you miss any 2D or 3D shape measurement feel free to open an issue providing the following details:

• Scientific paper, where the shape measurement is introduced and defined,
• evidence why this shape measurement is of scientific relevance (cite at least three scientific papers where the shape measurement is used),
• suggestions and/or references for implementation (optional).

Current available shape measurements

2D shape measurements

Currently, 53 twodimensional shape measurements are implemented in imea, as shown in the tables below. According to DIN ISO 9276-6 these are structured in macro-, meso- and microdescriptors as well as statistical lengths, as illustrated below.

Macro measurements (imea.measure_2d.macro)

Macrodescriptors represent the overall, external shape of a particle. The following macrodescriptors are currently available in imea:

Naming in imea	Description	Implementation	Reference
perimeter	Perimeter.	skimage.measure.regionprops	(DIN ISO 9276-6)
convex_perimeter	Perimeter of the convex hull.	custom based on skimage.measure.regionprops	(DIN ISO 9276-6)
area_projection	Projection area.	skimage.measure.regionprops	(DIN ISO 9276-6)
area_filled	Filled projection area.	skimage.measure.regionprops	(DIN ISO 9276-6)
area_convex	Area of the convex hull.	skimage.measure.regionprops	(DIN ISO 9276-6)
major_axis_length	Major axis length of the legendre ellipse of inertia (ellipse that has the same normalized second central moments as the particle shape).	skimage.measure.regionprops	(DIN ISO 9276-6)
minor_axis_length	Minor axis length of the legendre ellipse of inertia.	skimage.measure.regionprops	(DIN ISO 9276-6)
diameter_max_inclosing_circle	Diameter of the maximum incircle of the projection area.	based on cv2.distanceTransform	(Pahl et al. 1973a)
diameter_min_enclosing_circle	Diameter of the minimum circumference of the projection area.	cv2.minEnclosingCircle	(Pahl et al. 1973a)
diameter_circumscribing_circle	Diameter of the circumcircle with same center as the particle contour and maximum area, which touches the particle contour from the inside.	custom based on spatial.distance.cdist	(Li et al. 2020)
diameter_inscribing_circle	Diameter of the circumcircle with same center as the particle contour and minimum area, which touches the particle contour from the outside.	custom based on spatial.distance.cdist	(Li et al. 2020)
diameter_equal_area	Diameter of a circle of equal projection area.	custom based on DIN ISO 9276-6	(DIN ISO 9276-6)
diameter_equal_perimeter	Diameter of a circle of equal perimeter.	custom based on DIN ISO 9276-6	(DIN ISO 9276-6)
x_max	Maximum longest chord.	custom	(Steuer 2010)
y_max	Longest chord orthogonal to y_max	custom	(Steuer 2010)
width_min_bb	Width of minimal 2D bounding box.	cv2.minAreaRect	(Steuer 2010)
length_min_bb	Length of minimal 2D bounding box (width_min_bb <= length_min_bb).	cv2.minAreaRect	(Steuer 2010)
geodeticlength	Geodetic length.	custom based on DIN ISO 9276-6	(DIN ISO 9276-6; Pons et al. 1999)
thickness	Thickness.	custom based on DIN ISO 9276-6	(DIN ISO 9276-6; Pons et al. 1999)

Meso measurements (imea.measure_2d.meso)

Mesodescriptors describe details in the particle shape and/or surface structure whose magnitude are not much smaller than the particle proportions. The following mesodescriptors are currently available in imea:

Naming in imea	Description	Implementation	Reference
n_erosions	Number of pixel erosions to completely erase the silhouette of a particle in the binary image.	custom based on skimage.morphology.binary_erosion	(DIN ISO 9276-6)
n_erosions_complement	Number of pixel erosions to completely erase the complement between convex hull and object.	custom based on skimage.morphology.binary_erosion	(DIN ISO 9276-6)

Micro measurements (imea.measure_2d.micro)

Microdescriptors describe the roughness of particle contours. The following microdescriptors are currently available in imea:

Naming in imea	Description	Implementation	Reference
fractal_dimension_boxcounting_method	Fractal dimension determined by the box counting method	custom based on (So et al. 2017)	(So et al. 2017)
fractal_dimension_perimeter_method	Fractal dimension determined by the perimeter method according to DIN ISO 9276-6 (evenly structured gait).	custom based on DIN ISO 9276-6	(DIN ISO 9276-6)

Statistical lengths (imea.measure_2d.statistical_length)

Statistical lengths are macrodescriptors that are evaluated at different rotation angles of the shape. Based on the resulting distribution of statistical length different metrics like the minimum or maximum value can be obtained. The following statistical length are currently available in imea:

Naming in imea	Description	Implementation	Reference
feret_max	Maximum Feret diameter.	custom	(Pahl et al. 1973a)
feret_min	Minimum Feret diameter.	custom	(Pahl et al. 1973a)
feret_median	Median of all Feret diameters.	custom	(Pahl et al. 1973a)
feret_mean	Arithmetic mean of all Feret diameters.	custom	(Pahl et al. 1973a)
feret_mode	Mode of all Feret diameters.	custom	(Pahl et al. 1973a)
feret_std	Standard deviation of all Feret diameters.	custom	(Pahl et al. 1973a)
martin_max	Maximum Martin diameter.	custom	(Pahl et al. 1973a)
martin_min	Minimum Martin diameter.	custom	(Pahl et al. 1973a)
martin_median	Median of all Martin diameters.	custom	(Pahl et al. 1973a)
martin_mean	Arithmetic mean of all Martin diameters.	custom	(Pahl et al. 1973a)
martin_mode	Mode of all Martin diameters.	custom	(Pahl et al. 1973a)
martin_std	Standard deviation of all Martin diameters.	custom	(Pahl et al. 1973a)
nassenstein_max	Maximum Nassenstein diameter.	custom	(Pahl et al. 1973a)
nassenstein_min	Minimum Nassenstein diameter.	custom	(Pahl et al. 1973a)
nassenstein_median	Median of all Nassenstein diameters.	custom	(Pahl et al. 1973a)
nassenstein_mean	Arithmetic mean of all Nassenstein diameters.	custom	(Pahl et al. 1973a)
nassenstein_mode	Mode of all Nassenstein diameters.	custom	(Pahl et al. 1973a)
nassenstein_std	Standard deviation of all Nassenstein diameters.	custom	(Pahl et al. 1973a)
maxchords_max	Maximum of max chords (max chord = max of all chords for one particle rotation).	custom	(Pahl et al. 1973a)
maxchords_min	Minimum of max chords.	custom	(Pahl et al. 1973a)
maxchords_median	Median of max chords.	custom	(Pahl et al. 1973a)
maxchords_mean	Mean of max chords.	custom	(Pahl et al. 1973a)
maxchords_mode	Mode of max chords.	custom	(Pahl et al. 1973a)
maxchords_std	Standard deviation of max chords.	custom	(Pahl et al. 1973a)
allchords_max	Maximum of all chords for all rotations.	custom	(Pahl et al. 1973a)
allchords_min	Minimum of all chords for all rotations.	custom	(Pahl et al. 1973a)
allchords_median	Median of all chords for all rotations.	custom	(Pahl et al. 1973a)
allchords_mean	Mean of all chords for all rotations.	custom	(Pahl et al. 1973a)
allchords_mode	Mode of all chords for all rotations.	custom	(Pahl et al. 1973a)
allchords_std	Standard deviation of all chords for all rotations.	custom	(Pahl et al. 1973a)

3D shape measurements

For 3D recordings, there are 13 threedimensional shape measurements implemented in imea, as shown in the table below.

Naming in imea	Description	Implementation	Reference
volume	Volume.	np.sum	(Pahl et al. 1973a)
volume_convexhull	Volume of convex hull.	scipy.spatial.ConvexHull	-
surface_area	Surface area (determined by convex hull).	scipy.spatial.ConvexHull	(Pahl et al. 1973a)
diameter_volume_equivalent	Diameter of a volume-equivalent sphere.	custom based on (Stieß 2009)	(Stieß 2009)
diameter_surfacearea_equivalent	Diameter of a sphere with the same surface area.	custom based on (Stieß 2009)	(Stieß 2009)
width_3d_bb	Width of minimal 3D bounding box (equal to minimal 2D bounding box, as minimum 3D bounding box is assumed to lay on conveyer surface).	cv2.minAreaRect	(Steuer 2010)
length_3d_bb	Length of minimal 3D bounding box (width_3d_bb <= length_3d_bb, ).	cv2.minAreaRect	(Steuer 2010)
height_3d_bb	Height of minimal 3D bounding box in z-direction.	np.max	(Steuer 2010)
feret_3d_max	Maximum 3D feret diameter.	custom based on scipy.spatial.ConvexHull	(Pahl et al. 1973a)
feret_3d_min	Minimum 3D feret diameter.	custom based on scipy.spatial.ConvexHull	(Pahl et al. 1973a)
x_max_3d	Maximum particle dimension (equal to feret_3d_max)	custom	(Steuer 2010)
y_max_3d	Mean particle dimension (y_max_3d >= x_max_3d, y_max_3d orthogonal to x_max_3d)	custom	(Steuer 2010)
z_max_3d	M particle dimension (z_max_3d <= y_max_3d, z_max_3d orthogonal to y_max_3d and x_max_3d)	custom	(Steuer 2010)

Conventions

Coordinate system

imea uses right hand cardesian coordinate system, which is also used in scikit-image (o: origin of coordinate system):

# (row, col, channel)
# 
#      o ----------> y
#     /|
#    / |
#   /  |
# z    |
#      v
#      x

Literature

T. Andersson, M. J. Thurley and J. E. Carlson (2012). "A machine vision system for estimation of size distributions by weight of limestone particles". In: Minerals Engineering, 25(1), pp. 38–46. https://doi.org/10.1016/j.mineng.2011.10.001

Deutsches Institut für Normung e. V. (2012). DIN ISO 9276-6 - Darstellung der Ergebnisse von Par-tikelgrößenanalysen: Teil 6: Deskriptive und quantitative Darstellung der Form und Morphologie von Partikeln.

Itseez (2015). Open source computer vision library. https://github.com/opencv/opencv.

L. Kandlbauer, K. Khodier, D. Ninevski, R. Sarc (2021). "Sensor-based Particle Size Determination of Shredded MixedCommercial Waste based on two-dimensional Images". In: Waste Management, 120, pp. 794-794. https://doi.org/10.1016/j.wasman.2020.11.003

Y. M. Lau, N. G. Deen and J. A. M. Kuipers (2013). "Development of an image measurement technique for size distribution in dense bubbly flows". In: Chemical Engineering Science, 94, pp. 20–29. https://doi.org/10.1016/j.ces.2013.02.043

X. Li, Z. Wen, H. Zhu, Z. Guo and Y. Liu (2020). "An improved algorithm for evaluation of the minimum circumscribed circle and maximum inscribed circle based on the local minimax radius". In: The Review of scientific instruments 91(3), pp. 035103. DOI: https://doi.org/10.1063/5.0002233

W. McKinney (2010). "Data Structures for Statistical Computing in Python". In: Stéfan 54 van der Walt & Jarrod Millman (Eds.): Proceedings of the 9th Python in Science Conference. (pp. 56–61). https://doi.org/10.25080/Majora-92bf1922-00a

T. M. Nguyen and R. M. Rangayyan (2005). "Shape Analysis of Breast Masses in Mammograms via the Fractal Dimension". In: 2005 IEEE Engineering in Medicine and Biology 27th Annual Conference, Shanghai, pp. 3210-3213. https://doi.org/10.1109/IEMBS.2005.1617159

W. Pabst und E. Gregorova (2007). Characterization of particles and particle systems.

M. Pahl, G. Schädel und H. Rumpf (1973a). "Zusammenstellung von Teilchenformbeschreibungs-methoden: 1. Teil". In: Aufbereitungstechnik, 14(5), pp. 257–264.

M. Pahl, G. Schädel und H. Rumpf (1973b). "Zusammenstellung von Teilchenformbeschreibungs-methoden: 2. Teil". In: Aufbereitungstechnik, 14(10), pp. 672–683.

M. Pahl, G. Schädel und H. Rumpf (1973c). "Zusammenstellung von Teilchenformbeschreibungs-methoden: 3. Teil". In: Aufbereitungstechnik, 14(11) , pp. 759–764.

T. G. Smith, G. D. Lange and W. B. Marks (1996). "Fractal methods and results in cellular morphology — dimensions, lacunarity and multifractals". In: Journal of Neuroscience Methods, 69(2), pp. 123–136. https://doi.org/10.1016/s0165-0270(96)00080-5

M. Steuer (2010). "Serial classification". In: AT Mineral Processing 51(1).

M. Stieß (2009). Mechanische Verfahrenstechnik - Partikeltechnologie 1. 3rd edition. Springer-Verlag: Berlin, Heidelberg. http://doi.org/10.1007/978/3-540-32552-9

G.-B. So, H.-R. So, G.-G. Jin (2017): "Enhancement of the Box-Counting Algorithm for fractal dimension estimation". In: Pattern Recognition Letters, 98, pp. 53-58. https://doi.org/10.1016/j.patrec.2017.08.022

S. Walt, J. Schönberger, J. Nunez-Iglesias, F. Boulogne, J. Warner, N. Yager, E. Gouillart, T. Yu and the scikit-image contributors (2014). "scikit-image: Image processing in Python". In: PeerJ 2:e453 https://doi.org/10.7717/peerj.453

T. Weissenbach, R. Sarc (2021). "Investigation of particle-specific characteristics of non-hazardous, fine shredded mixed waste". In: Waste Management, 119, pp. 162-171. https://doi.org/10.1016/j.wasman.2020.09.033