# Impact of Pre- and Post-Processing Steps for Supervised Classification of Colorectal Cancer in Hyperspectral Images

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## Abstract

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## Simple Summary

## Abstract

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Patient Data

^{®}Tissue device (Diaspective Vision GmbH, Am Salzhaff-Pepelow, Germany) was used. The HS camera is set at 50 cm from the tissue. All side lights were turned off. The HS images were taken during the first 5 min after resection, and approximately 10 s were needed for each image. The output datacubes are of shape (480, 640, 100) (height, width, and the spectral axis). The spectral axis corresponds to the range 500–1000 nm with step 5 nm.

#### 2.2. Pre-Processing

#### 2.3. Supervised Binary Classification

#### 2.3.1. Architecture 1: 3D-CNN with Inception Architecture

#### 2.3.2. Architecture 2: RS-Based 3D-CNN

#### 2.3.3. Training Parameters

#### 2.3.4. Thresholding

#### 2.3.5. Choosing the Best Threshold

- A threshold where sensitivity and specificity have similar values allows for easier comparison between different models: both sensitivity and specificity are either better or worse.
- This approach allows balancing between false negatives and false positives.

#### 2.4. Post-Processing

#### 2.4.1. Definitions

#### 2.4.2. Using Median Filter (MF)

#### 2.4.3. Post-Processing Methods: The Plain Algorithm (AP) and the Algorithm with Threshold (AWT)

#### 2.4.4. Finding Optimal Parameters of Post-Processing and Estimation of the Performance Improvement

Algorithm 1. Finding optimal parameters of post-processing.
| |

Inputs: | |

sens_{baseline}, spec_{baseline} | (Section 2.3.5) |

MF_sizes_to_test | |

thresholds_to_test | |

Initialize: | |

improvements_{i,j} ← 0, where i = 1, …, length(MF_sizes_to_test) | |

j = 1, …, length(thresholds_to_test) | |

Result: optimal MF size m_{opt}, optimal threshold size t_{opt} | |

for each m in MF_sizes_to_test do | |

for each t in thresholds_to_test do | |

apply MF size m and threshold t to prediction maps | |

calculate sens_{m,t} and spec_{m,t} | |

improvement_{spec}← spec_{m,t} – spec_{baseline} | (3) |

improvement_{sens} ← sens_{m,t} – sens_{baseline} | (4) |

if improvement_{sens} > 0 and improvement_{spec} > 0 then | |

improvement_{m,t} ← improvement_{spec} + improvement_{sens} | (5) |

end if | |

end for | |

end for | |

m_{opt}, t_{opt} ← argmax(improvements) | (6) |

#### 2.5. Evaluation

#### 2.5.1. Leave-K-Out-Cross-Validation (LKOCV)

#### 2.5.2. Metrics

#### 2.6. Models

- “Architecture_” +
- “Pre-processing_” +
- “NumberOfExcludedPatients_” +
- “T(rue)/F(alse)” if every third sample was used.

- “Inc” for inception-based models;
- “RS” for RS-based models;
- “Norm” for Normalization pre-processing;
- “Stan” for Standardization pre-processing.

## 3. Results

#### 3.1. Baseline Results (before Any Post-Processing)

- Inception-based models perform better than RS-based ones. The best three models in Table 6 are inception-based.
- Inception-based networks work better with Normalization (model Inc_Norm_4_T clearly better than model Inc_Stan_1_T and other inception models even despite the fact that model Inc_Stan_1_T uses the most complete set of data) and RS-based models with Standardization (models RS_Stan_4_T and RS_Stan_4_T + SW are better than model RS_Norm_4_T).

- 3.
- Moreover, we noticed that the thresholds are very low (below 0.05) for models that use Standardization as pre-processing, unlike those that use Normalization, for which raw thresholds show regular values (Table 6).

- 4.
- Excluding one patient gives better results than excluding four patients, which is the expected behavior, because in the case of one patient there is more training data.

#### 3.2. Post-Processing Results (AWP and AP)

#### 3.3. Visual Results

## 4. Discussion

**model Inc_Norm_4_T**with corresponding sensitivity and specificity:

**92% and 94%. In a previous study**[25] performed on the exact same patient dataset (56 patients), the sensitivity and specificity were

**86% and 95%**. Therefore, we achieved a very good improvement in sensitivity with an acceptable loss in specificity and more balanced performance. The most important reason for this is

**post-processing**, which

**improves sensitivity and specificity by 4.0–6.6% in total**. Other reasons could be: (1) use of 3D convolution networks that are very well suited for the hyperspectral nature of data; (2) use of inception-based networks that concatenate useful spectral information simultaneously from different kernel sizes; (3) use of Normalization pre-processing for inception-based models (its importance will be explained further in the text).

**sensitivity of 99.5% and specificity of 94%**. The corresponding best values from Martinez-Vega et al. were

**86% and 87%.**As we can see, there is a big improvement, but this improvement also could rely on the fact that models in the Martinez-Vega et al. were trained only on 12 patients, which again emphasizes that a larger dataset contributes to better scores.

**The presented post-processing algorithms (AP and AWT) produce the same quantitative results**, but AP is slighly faster to visualize (no need for additional thresholding) and much faster during the calculating of optimal parameters. That is why

**we recommend using AP.**Additionaly, judging by the visual results in Figure 12, Figure 13, Figure 14 and Figure 15, images following AP convey more information because probability can be inferred, which can be useful in real clinical use cases.

**Inception-based networks work better then RS-based networks.**The likely reason is branching. Inception-based networks concatenate filters simultaneously after several kernel sizes, so different spatial wavelengths can be obtained and used in the next layers. Another reason is that one of the branches in inception-based architectures uses kernel size 5. In RS-based architectures, the maximal kernel size is 3. As discovered in [37], larger sample sizes perform better. Probably it can be also applicable to kernel sizes. In future research we will explore higher kernel sizes, more branches, and stack several inception blocks. The other reason why inception-based models perform better than RS-based models is that inception-based models have ~11 times more training parameters. Additionally, inception-based networks do not perform better in all HSI applications, which seems to be dataset-dependent. For example, ResNet-18 had a higher accuracy than inception-v3 in the case of HSI-based harmful algal bloom detection [31].

**low discrimination threshold,**as we can see on models that use Standardization (Table 6). Traditionally, an activation function of the last layer in binary classification neural networks is a sigmoid function. It converts a raw value from the network to a probability. If the value from the network is large and negative, then the probability will be close to 0. If thresholds are so low, it means that most probabilities are very close to 0, which in turn implies large negative output values from the network. In Figure 2 it can be seen that most spectral values after Standardization are in the range (−3, 1), so most values seen by the networks are negative. We suppose that this particular situation creates an imbalance that causes more negative values and a lot of near-zero probabilities at the end. Figure 11 depicts probability distributions of some wavelengths. As can be seen, they are not normally distributed, especially at the beginning and end of the spectra. This can be a reason for the imbalance, because a precondition for using Standardization is that all wavelengths have to be normally distributed. This opens the next future research directions: (1) an exclusion of outliers before wavelength scaling and (2) application of the Min-Max scaler after Standardization. This would return a standardized spectrum, but in the range 0–1, which could level out the imbalance.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Key Wavelengths Detection Algorithm

## Appendix B. Proof Why AP and AWT Give the Same Results

#### Appendix B.1. MF and Thresholding Are Commutative: Simple Example

**Figure A2.**An example of the fact that MF and thresholding are commutative and therefore AWT and AP dives the same quantitative results.

#### Appendix B.2. Proof That MF and Thresholding Are Commutative

**Theorem**

**A1.**

**Proof of Theorem**

**A1.**

- a > threshold and b > threshold. Then a′ = A, b′ = A.A = A => a′ >= b′. Satisfies the theorem.
- a > threshold and b < threshold. Then a′ = A, b′ = BA > B => a′ >= b′. Satisfies the theorem.
- a < threshold and b > threshold. Not possible, because in this case a < threshold < b => a < b, which contradicts the given conditions.
- a < threshold and b < threshold. Then a′ = B, b′ = B.B = B => a′ >= b′. Satisfies the theorem.
- a = b. Then a′ = b′. Satisfies the theorem.

#### Appendix B.3. Detailed Description of AWT and AP

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**Figure 1.**Examples of masks with ground truth labels, where purple is non-malignant tissue, yellow is cancerous, and red is margin of cancerous tissue.

**Figure 2.**Examples of spectra before (

**left**) and after pre-processing techniques (

**middle**,

**right**). Please note that y-axes have different scales. Non-malignant spectra are purple and cancerous are yellow.

**Figure 4.**Sensitivity and specificity obtained for one of the implemented models. The red point is the intersection point of both curves and represents the optimal threshold value used to define the binary probability map.

**Figure 6.**(

**a**) Original image; (

**b**) Original image with added salt-and-pepper noise; (

**c**) Image B after the application of the median filter with window size 5.

**Figure 7.**Prediction map examples in the left column and ground truth annotated by physicians on the right side, with the correspondence between colors and output probabilities shown on the color bar. Yellow represents cancerous tissue, purple non-malignant tissue, and red the margin of the cancer.

**Figure 8.**Pipeline with both post-processing algorithms. On the images, yellow is cancerous, purple is non-malignant. Color bars are added to the steps in which the maps contain uncertain pixels (shades of green).

**Figure 10.**Blue lines specify the most important wavelengths (key wavelengths) for inception-based models (

**left column**) and RS-based models (

**right**). Spectrum of non-malignant tissues is plotted with purple color, cancerous with yellow. Please note that y axes have different scales.

**Figure 14.**How different MF sizes and thresholds affect the output. Purple is non-malignant tissue, yellow is cancerous, red is cancerous margin, and shades of green are uncertain.

Standardization (Z-Score) | Scaling to Unit Length (Normalization) |
---|---|

${x}^{\prime}=\frac{x-\overline{x}}{\sigma}$ | ${x}^{\prime}=\frac{x}{\left|\right|x\left|\right|}$ |

$\sigma $—standard deviation$\stackrel{-}{x}=average(x)$ | ||x||—Euclidian length of x |

x—original spectrum x ^{′}—scaled spectrum |

Training Parameter Name | Value |
---|---|

Epochs | 40 |

Batch size | 100 |

Loss | Binary cross entropy |

Optimizer | Adam with β_{1} = 0.9 and β_{2} = 0.99 |

Learning rate | 0.0001 |

Dropout | 0.1 |

Activation | ReLU, except the last layer, where Sigmoid |

Number of wavelengths | 92 (we exclude the first 8 values because they are very noisy) |

Number of parameters in models | 393,633 (inception) and 27,156 (RS) |

Shape of samples | [5, 5] |

Abbreviation | Description | Meaning |
---|---|---|

TP | True Positives | Cancerous detected as cancerous |

TN | True Negatives | Non-malignant tissue detected as non-malignant tissue |

FP | False Positives | Non-malignant tissue detected as cancerous |

FN | False Negatives | Cancerous detected as non-malignant tissue |

Metric | Formula/Description |
---|---|

Sensitivity (also known as recall) | $sensitivity=recall=\frac{TP}{TP+FN}$ |

Specificity | $specificity=\frac{TN}{TN+FP}$ |

F1-score (also known as Sørensen–Dice coefficient) | ${F}_{1}=\frac{2\xb7precision\xb7recall}{precision+recall}=\frac{2\xb7TP}{2\xb7TP+FP+FN}$, where $precision=\frac{TP}{TP+FP}$ |

AUC | Area Under the Receiver Operating Characteristic Curve (ROC AUC) |

MCC (Matthew correlation coefficient) | $MCC=\frac{TP\xb7TN-FP\xb7FN}{\sqrt{(TP+FP)(TP+FN)(TN+FP)(TN+FN)}}$ |

Name | Pre-Processing | Architecture | How Many Patients Are Excluded for Cross-Validation | Every Third Sample | |||
---|---|---|---|---|---|---|---|

Normalization | Standardization | Inception | RS | 1 Patient | 4 Patients | ||

Inc_Norm_4_T | x | x | x | x | |||

Inc_Stan_1_F | x | x | x | ||||

Inc_Stan_4_T | x | x | x | x | |||

RS_Stan_4_T | x | x | x | x | |||

RS_Stan_4_T + SW ^{1} | x | x | x | x | |||

RS_Norm_4_T | x | x | x | x | |||

Inc_Stan_1_T | x | x | x | x |

^{1}Sample Weights (see Section 2.3.3). whether every third sample was used noted with “x” in corresponding columns.

Name | Threshold | Accuracy | Sensitivity | Specificity | F1-n ^{1} | F1-c ^{1} | AUC | MCC |
---|---|---|---|---|---|---|---|---|

Inc_Norm_4_T | 0.211 | 90.2 ± 15 | 89.1 ± 19 | 89.5 ± 17 | 92.8 ± 14 | 65.9 ± 29 | 96.8 ± 10 | 64.3 ± 30 |

Inc_Stan_1_F | 0.0189 | 89.2 ± 14 | 88.5 ± 21 | 88.2 ± 15 | 92.5 ± 11 | 60.8 ± 29 | 95.7 ± 13 | 59.7 ± 28 |

Inc_Stan_4_T | 0.0456 | 87.6 ± 16 | 88 ± 21 | 87.1 ± 18 | 91.5 ± 14 | 59 ± 29 | 95.6 ± 13 | 57.8 ± 30 |

RS_Stan_4_T | 0.0367 | 89 ± 12 | 87.1 ± 20 | 88.3 ± 14 | 92.7 ± 9 | 61.4 ± 28 | 95.5 ± 9 | 60.3 ± 27 |

RS_Stan_4_T + SW | 0.45 | 87.1 ± 18 | 87 ± 21 | 86.1 ± 20 | 90.5 ± 15 | 59.1 ± 29 | 95.2 ± 10 | 57.4 ± 29 |

RS_Norm_4_T | 0.1556 | 88.1 ± 16 | 86.8 ± 22 | 87.5 ± 18 | 91.6 ± 13 | 62.6 ± 29 | 94.9 ± 10 | 61.4 ± 28 |

Inc_Stan_1_T | 0.0456 | 88.6 ± 16 | 86.1 ± 23 | 88 ± 17 | 92 ± 13 | 60.3 ± 30 | 95.5 ± 14 | 59.1 ± 29 |

^{1}n—non-malignant, c—cancerous.

**Table 7.**Optimal post-processing parameters, metrics after post-processing (both AWP and AP) and statistical differences in comparison with the baseline approach without post-processing. * means p ≤ 0.05, ** means p ≤ 0.01, *** means p ≤ 0.001. The smaller the p, the more intense the green color that was used.

Name | MF Size | Threshold | Accuracy | Sensitivity | Specificity | F1-n ^{1} | F1-c ^{2} | AUC | MCC |
---|---|---|---|---|---|---|---|---|---|

Inc_Norm_4_T | 51 | 0.3166 | 94.2 ± 14 *** | 91.6 ± 22 * | 93.6 ± 16 *** | 95.3 ± 14 * | 78.4 ± 29 *** | 98.4 ± 9 *** | 76.6 ± 32 *** |

Inc_Stan_1_F | 41 | 0.009 | 91 ± 16 ** | 92.6 ± 21 *** | 89.8 ± 18 ** | 93.2 ± 14 | 70.5 ± 31 *** | 97.2 ± 15 *** | 69.1 ± 32 *** |

Inc_Stan_4_T | 51 | 0.0192 | 89.2 ± 20 * | 92.7 ± 21 *** | 88.4 ± 22 | 91.5 ± 20 | 68.8 ± 32 *** | 97.2 ± 15 ** | 66.5 ± 38 *** |

RS_Stan_4_T | 75 | 0.0251 | 92.8 ± 12 *** | 87.8 ± 29 | 92.1 ± 14 *** | 95 ± 9 *** | 68.7 ± 34 * | 96.7 ± 14 | 68.1 ± 33 * |

RS_Stan_4_T + SW | 41 | 0.2842 | 88.1 ± 21 | 90.5 ± 23 | 86.7 ± 24 | 90.1 ± 21 | 67.3 ± 33 ** | 96.9 ± 10 *** | 65.4 ± 35 ** |

RS_Norm_4_T | 41 | 0.1515 | 90.9 ± 17 *** | 90.5 ± 25 * | 90.1 ± 19 *** | 93.1 ± 14 *** | 71.9 ± 30 *** | 97.6 ± 7 ** | 71.5 ± 30 *** |

Inc_Stan_1_T | 51 | 0.0168 | 89.9 ± 19 * | 91.4 ± 23 *** | 88.7 ± 21 | 91.9 ± 18 | 69.1 ± 31 *** | 97.1 ± 15 *** | 67.6 ± 34 *** |

^{1}F1-score for non-malignant class.

^{2}F1-score for cancerous class.

Name | Improvement Sensitivity (Algorithm 1. Equation (4)) | Improvement Specificity (Algorithm 1. Equation (3)) | Improvement (Algorithm 1. Equation (5)) |
---|---|---|---|

Inc_Norm_4_T | 2.34 | 4.292 | 6.638 |

Inc_Stan_1_F | 4.20 | 1.486 | 5.689 |

Inc_Stan_4_T | 5.12 | 0.796 | 5.925 |

RS_Stan_4_T | 0.02 | 4.378 | 4.399 |

RS_Stan_4_T + SW | 3.87 | 0.155 | 4.032 |

RS_Norm_4_T | 3.33 | 2.905 | 6.241 |

Inc_Stan_1_T | 4.42 | 1.641 | 6.065 |

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## Share and Cite

**MDPI and ACS Style**

Tkachenko, M.; Chalopin, C.; Jansen-Winkeln, B.; Neumuth, T.; Gockel, I.; Maktabi, M.
Impact of Pre- and Post-Processing Steps for Supervised Classification of Colorectal Cancer in Hyperspectral Images. *Cancers* **2023**, *15*, 2157.
https://doi.org/10.3390/cancers15072157

**AMA Style**

Tkachenko M, Chalopin C, Jansen-Winkeln B, Neumuth T, Gockel I, Maktabi M.
Impact of Pre- and Post-Processing Steps for Supervised Classification of Colorectal Cancer in Hyperspectral Images. *Cancers*. 2023; 15(7):2157.
https://doi.org/10.3390/cancers15072157

**Chicago/Turabian Style**

Tkachenko, Mariia, Claire Chalopin, Boris Jansen-Winkeln, Thomas Neumuth, Ines Gockel, and Marianne Maktabi.
2023. "Impact of Pre- and Post-Processing Steps for Supervised Classification of Colorectal Cancer in Hyperspectral Images" *Cancers* 15, no. 7: 2157.
https://doi.org/10.3390/cancers15072157