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. 2022 Aug 13;22(16):6052.
doi: 10.3390/s22166052.

Application of the Two-Dimensional Entropy Measures in the Infrared Thermography-Based Detection of Rider: Horse Bodyweight Ratio in Horseback Riding

Małgorzata Domino  1 , Marta Borowska  2 , Łukasz Zdrojkowski  1 , Tomasz Jasiński  1 , Urszula Sikorska  3 , Michał Skibniewski  4 , Małgorzata Maśko  3
Affiliations

Application of the Two-Dimensional Entropy Measures in the Infrared Thermography-Based Detection of Rider: Horse Bodyweight Ratio in Horseback Riding

Małgorzata Domino et al. Sensors (Basel). .

Abstract

As obesity is a serious problem in the human population, overloading of the horse's thoracolumbar region often affects sport and school horses. The advances in using infrared thermography (IRT) to assess the horse's back overload will shortly integrate the IRT-based rider-horse fit into everyday equine practice. This study aimed to evaluate the applicability of entropy measures to select the most informative measures and color components, and the accuracy of rider:horse bodyweight ratio detection. Twelve horses were ridden by each of the six riders assigned to the light, moderate, and heavy groups. Thermal images were taken pre- and post-exercise. For each thermal image, two-dimensional sample (SampEn), fuzzy (FuzzEn), permutation (PermEn), dispersion (DispEn), and distribution (DistEn) entropies were measured in the withers and the thoracic spine areas. Among 40 returned measures, 30 entropy measures were exercise-dependent, whereas 8 entropy measures were bodyweight ratio-dependent. Moreover, three entropy measures demonstrated similarities to entropy-related gray level co-occurrence matrix (GLCM) texture features, confirming the higher irregularity and complexity of thermal image texture when horses worked under heavy riders. An application of DispEn to red color components enables identification of the light and heavy rider groups with higher accuracy than the previously used entropy-related GLCM texture features.

Keywords: entropy-based approaches; equine application; infrared thermography; texture analysis; two-dimensional entropy.

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Conflict of interest statement

The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

Figures

Figure 1
Figure 1
Schema of the material and methods used in the study. (A) The study protocol included horses (n = 12); riders (n = 6); and horse and rider pairs (n = 72), representing three rider groups that differed depending on the rider:horse bodyweight. (B) Data acquisition and processing included pre- and post-exercise infrared thermography (IRT) imaging of the thoracolumbar region; segmentation of two regions of interest (ROIs); thermal images converted into the grayscale images and three color components (red, green, blue); and extraction of the following five entropy measures: two-dimensional sample entropy (SampEn), two-dimensional fuzzy entropy (FuzzEn), two-dimensional permutation entropy (PermEn), two-dimensional dispersion entropy (DispEn), and two-dimensional distribution entropy (DistEn).
Figure 2
Figure 2
Entropy measures for examined grayscale images (grayscale) and color components (red, green, blue), which were found to be significantly different between the pre-exercise and post-exercise imaging for all rider groups (L, light; M, moderate; H, heavy). Data were presented separately for the withers area (ROI 1) (A) and the thoracic spine area (ROI 2) (B). SampEn—two-dimensional sample entropy, FuzzEn—two-dimensional fuzzy entropy, PermEn—two-dimensional permutation entropy, DispEn—two-dimensional dispersion entropy, DistEn—two-dimensional distribution entropy. The measures that differed between the pre-exercise and post-exercise imaging were marked by color (light gray, red, green, blue for L group; moderate gray, red, green, blue for M group; and dark gray, red, green, blue for H group) and by a cross (X).
Figure 3
Figure 3
The comparison of the selected entropy measures in the red color component between light (L), moderate (M), and heavy (H) rider groups. The withers area (ROI 1) (A–D) and the thoracic spine area (ROI 2) (E–L) are separated by a solid horizontal line. The images obtained pre-exercise (A,C,E,G,I,K) and post-exercise (B,D,F,H,J,L) are separated by dashed horizontal lines. The following entropy measures are considered: DispEn—two-dimensional dispersion entropy (A,B,I,J), DistEn—two-dimensional distribution entropy (C,D,K,L), SampEn—two-dimensional sample entropy (E,F), FuzzEn—two-dimensional fuzzy entropy (G,H). Data are presented using minimum and maximum values, lower and upper quartiles, and median. The mean value is marked by a cross. Differences between rider groups were indicated with individual p-values when p < 0.05. Different superscripts on each plot were statistically different. Measures that differ between rider groups (L, M, H) are marked with a red frame.
Figure 4
Figure 4
The comparison of the selected entropy measures in the green color component between light (L), moderate (M), and heavy (H) rider groups. The withers area (ROI 1) (A–F) and the thoracic spine area (ROI 2) (G–J) are separated by a solid horizontal line. The images obtained pre-exercise (A,C,E,G,I) and post-exercise (B,D,F,H,J) are separated by dashed horizontal lines. The following entropy measures are considered: PermEn—two-dimensional permutation entropy (A,B), DispEn—two-dimensional dispersion entropy (C,D,G,H), DistEn—two-dimensional distribution entropy (E,F,I,J). Data are presented using minimum and maximum values, lower and upper quartiles, and median. The mean value is marked by a cross. Differences between rider groups were indicated with individual p-values when p < 0.05. Different superscripts on each plot were statistically different. Measures that differ between rider groups (L, M, H) are marked with a green frame.
Figure 5
Figure 5
The comparison of the selected entropy measures in the blue color component between light (L), moderate (M), and heavy (H) rider groups. The withers area (ROI 1) (A–H) and the thoracic spine area (ROI 2) (I–L) are separated by a solid horizontal line. The images obtained pre-exercise (A,C,E,G,I,K) and post-exercise (B,D,F,H,J,L) are separated by dashed horizontal lines. The following entropy measures are considered: SampEn—two-dimensional sample entropy (A,B), FuzzEn—two-dimensional fuzzy entropy (C,D), DispEn—two-dimensional dispersion entropy (E,F,I,J), DistEn—two-dimensional distribution entropy (G,H,K,L). Data are presented using minimum and maximum values, lower and upper quartiles, and median. The mean value is marked by a cross. Differences between rider groups were indicated with individual p-values when p < 0.05. Different superscripts on each plot were statistically different. Measures that differ between rider groups (L, M, H) are marked with a blue frame.
Figure 6
Figure 6
Entropy measures (A,B) and selected gray-level run-length matrix features (C,D) for examined color components (red, green, blue), which were found to be significantly different between light (L), moderate (M), and heavy (H) rider groups on the post-exercise imaging. Data were presented separately for the withers area (ROI 1) (A,C) and the thoracic spine area (ROI 2) (B,D). SampEn—two-dimensional sample entropy, FuzzEn—two-dimensional fuzzy entropy, PermEn—two-dimensional permutation entropy, DispEn—two-dimensional dispersion entropy, DistEn—two-dimensional distribution entropy, SumEntrp—summation entropy, entropy, DifEntrp—differential entropy. The measures that differed between rider groups were marked by color (light red, green, blue for L group; moderate red, green, blue for M group; and dark red, green, blue for H group) and by a cross (X).
Figure 7
Figure 7
Comparison of studied entropy measures (DispEn—two-dimensional dispersion entropy, DistEn—two-dimensional distribution entropy) and selected gray-level run-length matrix feature (SumEntrp—summation entropy) for examined color components (red, (A,B,E); green, (F); blue, (C,D,G,H)), which were found to be significantly different between light (L), moderate (M), and heavy (H) rider groups on the post-exercise imaging. Data were presented separately for the withers area (ROI 1) (A–D) and the thoracic spine area (ROI 2) (E–H). Similarity was tested using linear regressions. A p-value of less than 0.05 was considered significant. If the difference between slopes was not significant, a single slope measurement was calculated. Plots with the entropy measures and slopes that did not differ with SumEntrp were marked by colored (red, blue) solid frames. Plots with the entropy measures and slope values that were higher than SumEntrp were marked by colored (red, blue) dashed frames.
Figure 8
Figure 8
Comparison of studied entropy measures (DispEn—two-dimensional dispersion entropy, DistEn—two-dimensional distribution entropy) and selected gray-level run-length matrix feature (entropy) for examined color components (red, (A,B,E); green, (F); blue, (C,D,G,H)), which were found to be significantly different between light (L), moderate (M), and heavy (H) rider groups on the post-exercise imaging. Data were presented separately for the withers area (ROI 1) (A–D) and the thoracic spine area (ROI 2) (E–H). Similarity was tested using linear regressions. A p-value of less than 0.05 was considered significant. If the difference between slopes was not significant, a single slope measurement was calculated. Plots with the entropy measures and slopes that did not differ with entropy were marked by colored (red, blue) solid frames. Plots with the entropy measures and slope values that were higher than entropy were marked by colored (red, blue) dashed frames.
Figure 9
Figure 9
Comparison of studied entropy measures (DispEn—two-dimensional dispersion entropy, DistEn—two-dimensional distribution entropy) and selected gray-level run-length matrix feature (DifEntrp—differential entropy) for examined color components (red, (A,B,E); green, (F); blue, (C,D,G,H)), which were found to be significantly different between light (L), moderate (M), and heavy (H) rider groups on the post-exercise imaging. Data were presented separately for the withers area (ROI 1) (A–D) and the thoracic spine area (ROI 2) (E–H). Similarity was tested using linear regressions. A p-value of less than 0.05 was considered significant. If the difference between slopes was not significant, a single slope measurement was calculated. Plots with the entropy measures and slopes that did not differ with DifEntrp were marked by colored (red, green, blue) solid frame. Plots with the entropy measures and slope values that were higher than DifEntrp were marked by colored (red, green, blue) dashed frames.
Figure 10
Figure 10
Entropy measures (A,B) and selected gray-level run-length matrix features (C,D) for examined color components (red, green, blue), which were considered to increase in a similar way throughout the light (L), moderate (M), and heavy (H) rider groups on the post-exercise imaging. Data were presented separately for the withers area (ROI 1) (A,C) and the thoracic spine area (ROI 2) (B,D). SampEn—two-dimensional sample entropy, FuzzEn—two-dimensional fuzzy entropy, PermEn—two-dimensional permutation entropy, DispEn—two-dimensional dispersion entropy, DistEn—two-dimensional distribution entropy, SumEntrp—summation entropy, entropy, DifEntrp—differential entropy. The similar measures were marked by color (light red, green, blue for L group; moderate red, green, blue for M group; and dark red, green, blue for H group) and by a cross (X).
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