# Highly Discriminative Physiological Parameters for Thermal Pattern Classification

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Image Database

#### 2.2. Segmentation of Breast Thermograms

#### 2.3. Heat Source Model: A Mathematical Review

#### 2.3.1. Fitting Method of Lorentz Curve

#### 2.3.2. D-I-R Model

^{3}, ${h}_{0}=8.77$ W/m

^{2}· °C, and volume of cell is ${A}_{t}=1$ μm [6]. The $d-a$ and $q-a$ curves are obtained using Equations (5) and (6) and shown in Figure 5b,c, respectively.

#### 2.4. Thermal Pattern Classification Using SVM

**e**is the unity vector, C is the upper bound, ${B}_{i,j}\equiv {y}_{i},{y}_{j}P({x}_{i}\left(a\right),{x}_{j}\left(a\right))$, $P({x}_{i}\left(a\right),{x}_{j}\left(a\right))\equiv \phi {\left({x}_{i}\left(a\right)\right)}^{T}\phi \left({x}_{j}\left(a\right)\right)$, and $\phi $ is the mapping function [25].

## 3. Results

#### Extraction of the Input Heat Source Parameters

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Scheme of the theoretical model of an internal heat source with depth d, intensity q, and radius R.

**Figure 2.**Flowchart of the proposed method. (

**a**) Thermal data were obtained from the $DMR$-$IR$. (

**b**) A well-defined RoI is delimited at an optimal radial distance a. As we can see, the RoI encircle the temperature area to be analyzed. (

**c**) Surface temperature distribution related to the hottest spot of the RoI. (

**d**) A proposed highly discriminative pattern vector is composed by the physiological parameters from the point heat source. (

**e**) Classification step using SVM.

**Figure 3.**RoI delimitation process. (

**a**) Segmentation procedure based on the detection of the inframammary line by a polynomial curve fitting. (

**b**) Visualization of a clustered thermal pattern through thermal gradients. (

**c**) Centered RoI around the hottest point with radial distance a.

**Figure 4.**(

**a**) The extraction process of the STD using thermal input data. (

**b**) Mean temperature distribution around the hottest point with radial distance a.

**Figure 5.**Comparison of the efficiency of two methods for extracting physiological parameters: fitting method of Lorentz curve (blue line) and the D-I-R model (red line). (

**a**) STD fitted using the Lorentz curve method. We use the coefficient of determination (R-squared) to quantify the fitting between the surface temperature curve and the Lorentz curve. Estimation of physiological parameters (

**b**) Depth d and (

**c**) Intensity q.

**Figure 6.**Three-dimensional space using the proposed physiological parameters ${v}_{a}^{n}\left(i\right)=\phantom{\rule{3.33333pt}{0ex}}${$\theta ,d,q$} obtained through the D-I-R model, corresponding to $n=2$ at a given position a. The support vectors define the margin’s greatest separation between the normal and abnormal classes.

**Figure 7.**The temperature at the vicinity of affected tissue is about 2 °C higher than normal tissue.

**Figure 9.**Three-dimensional scattergrams using the physiological parameters obtained by means of the fitting method of Lorentz curve at different positions $a=0.0102$ m, $a=0.0168$ m, and $a=0.018$ m. Column (

**a**) corresponds to the pattern vector ${v}_{a}^{1}\left(i\right)=${${T}_{max}$, d, q} and column (

**b**) corresponds to the pattern vector ${v}_{a}^{1}\left(i\right)=${$\theta $, d, q}. As can be seen, at the optimal position $a=0.0168$ m, the scattergrams show a correct separation between normal and abnormal thermograms. In other cases, the feature vectors are highly correlated.

**Figure 10.**Three-dimensional scattergrams using the physiological parameters obtained by means of the D-I-R model at different positions $a=0.0102$ m, $a=0.0168$ m, and $a=0.018$ m. Column (

**a**) corresponds to the pattern vector ${v}_{a}^{2}\left(i\right)=${${T}_{max}$, d, q} and column (

**b**) corresponds to the pattern vector ${v}_{a}^{2}\left(i\right)=${$\theta $, d, q}. As can be observed, at the optimal position $a=0.0168$ m, the scattergram shows a correct separation between normal and abnormal thermograms. In other cases, the feature vectors are highly correlated.

**Figure 11.**Three-dimensional scattergrams using the physiological parameters extracted from (

**a**) the fitting method of Lorentz curve and (

**b**) the D-I-R model. As can be seen, at the same optimal position $a=0.0168$ m, the scattergrams show a correct separation between normal and abnormal thermograms in both cases.

**Figure 12.**Classification results using the pattern vector ${v}_{a}^{n}\left(i\right)=${${T}_{max},d,q,R,\theta $} obtained through the fitting method of Lorentz curve and D-I-R model at different a positions using SVM as a classifier.

T (°C) | Surface temperature distribution. |

$\rho $ (Kg/m^{3}) | Biological tissue’s density. |

c (J/Kg · °C) | Thermal capacity of biological tissue. |

k (W/m/°C) | Heat conduction coefficient. |

${w}_{b}$ (Kg/m^{3} · s) | Blood perfusion rate. |

${\rho}_{b}$
(Kg/m^{3}) | Blood density. |

${c}_{b}$ (J/Kg · °C) | Blood thermal capacity. |

${T}_{a}$ (°C) | Arterial blood temperature. |

${Q}_{m}$ (W/m^{3}) | Metabolic heat rate. |

q (W) | Heat source intensity. |

d (cm) | Heat source depth. |

R (m) | Radius of spherical heat source. |

a (m) | Distance from point ${O}^{\prime}$ to an arbitrary point on the body surface. |

r (m) | Distance from point O to an arbitrary point on the body surface. |

O | Point heat source position. |

${O}^{\prime}$ | The hottest spot of the RoI. |

${T}_{max}$ (°C) | Maximum temperature. |

${h}_{0}$ (W/m^{2} · °C) | Heat exchange coefficient. |

${T}_{e}$ (°C) | Ambient temperature. |

$\theta $, $\psi $ (degrees) | Spherical coordinates. |

${\mu}_{prom}$ | Mean temperature. |

${t}_{min}$ | Minimum temperature. |

Image resolution $\mathit{M}\times \mathit{N}$ | $640\times 480$ pixels |

Pixel size | 45 μm |

Sensor size | $2.88$ cm × $2.16$ cm |

Standard temperature range | $-40$ °C to $+500$ °C |

Sensitivity | <0.04 °C |

**Table 3.**Results of CRC and Area Under Curve (AUC) using the proposed pattern vector composed of physiological parameters.

Method | Breast Thermograms | R-Squared | CRC | AUC | Optimal Position of the RoI |
---|---|---|---|---|---|

D-I-R Model | 87 | $0.9999$ | 100% | 1 | $a=0.0168$ m |

Fitting method of Lorentz curve | 87 | $0.87$ | $90.80$% | $0.9046$ | $a=0.0168$ m |

Method | Accuracy | Sensitivity | Specificity |
---|---|---|---|

D-I-R model | 100% | 100% | 100% |

Fitting method of Lorentz curve | $90.8$% | 87% | 97% |

Authors | Segmentation | Features Extracted | CRC | Thermograms Number |
---|---|---|---|---|

Sathish et al. [19] | The breast is segmented. | Histogram and Gray Level Cooccurrence Matrix (GLCM) -based texture features. | 90% | 80 |

R. Devi et al. [28] | The left and right breast are separated. | GLCM features and first-order histogram. | 95% | 60 |

V. Mishra [30] | The breast is segmented. | Gray Level Run Length Matrix (GLRLM) and GLCM. | $95.45$% | 56 |

U. R. Gogoi [31] | The breast is segmented. | First-order statistical features. | — | 60 |

S. S. Suganthi et al. [32] | The breast is segmented. | Anisotropy and orientation measures. | — | 20 |

R. Resmini et al. [34] | The breast is segmented with different approaches (with and without armpits) to compose four experiments. | GLCM, Local Ternary Pattern, Daubechies Wavelet, Higuchi, Petrosian Fractal, Dimensions, and Hurst Coefficient. | $97.18$% | 80 |

Proposed approach | The breast is segmented with a well-defined RoI using SVM. | Physiological pattern vectors ${v}_{a=0.0168m}^{1,2}\phantom{\rule{0.277778em}{0ex}}\left(i\right)$ = { ${T}_{max}$, q, d, R, $\theta $}. | 100% | 87 |

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**MDPI and ACS Style**

Alvarado-Cruz, L.B.; Toxqui-Quitl, C.; Castro-Ortega, R.; Padilla-Vivanco, A.; Arroyo-Núñez, J.H.
Highly Discriminative Physiological Parameters for Thermal Pattern Classification. *Sensors* **2021**, *21*, 7751.
https://doi.org/10.3390/s21227751

**AMA Style**

Alvarado-Cruz LB, Toxqui-Quitl C, Castro-Ortega R, Padilla-Vivanco A, Arroyo-Núñez JH.
Highly Discriminative Physiological Parameters for Thermal Pattern Classification. *Sensors*. 2021; 21(22):7751.
https://doi.org/10.3390/s21227751

**Chicago/Turabian Style**

Alvarado-Cruz, Laura Benita, Carina Toxqui-Quitl, Raúl Castro-Ortega, Alfonso Padilla-Vivanco, and José Humberto Arroyo-Núñez.
2021. "Highly Discriminative Physiological Parameters for Thermal Pattern Classification" *Sensors* 21, no. 22: 7751.
https://doi.org/10.3390/s21227751