# Thermogram Breast Cancer Detection: A Comparative Study of Two Machine Learning Techniques
## 4 The Proposed Method
### Image Preprocessing Stage
#### 4.1.1 Noise Reduction
\[ln(img(v,w))=ln(j(v,w))+ln(f(v,w))\]1 Adaptive histogram equalization (AHE): (**a**) normal image (**b**) benign image (**c**) malignant image. #### 4.2.1 K-Means Clustering

K-mean clustering is used in our proposed method to divide thermal images into 3 clusters based on features to extract ROI. We considered the values of image pixels are grey-level. We have selected Euclidean distance as a distance measure to minimize the total of any pixel point to cluster centroid distances. The results of applying this k-means clustering technique and segmented mass are shown in Figure 7a-c.

#### 4.2.2 Binary Morphology

To enhance thermal images, opening operations are utilized in our proposed method where they are used to remove small bright details in the image while leaving the overall pixel intensity values and large bright objects undisturbed. Mathematically, opening of image \(g\) with structuring element \(b\) is given by the following equation:

\[ln(img(v,w))=ln(j(v,w))+ln(f(v,w))\]2

#### 4.2.3 Morphological Gradient

Erosion and dilation act as a local minimum and local maximum operator respectively. Image subtraction of these two operations gives a morphological gradient. This operation is used to enhance image edges by removing the constant intensity areas. The results, as illustrated in Figure 7c, show the boundary of the lesion. The morphological gradient is given by the following equation. \[ln(img(v,w))=ln(j(v,w))+ln(f(v,w))\]3

### Feature Extraction Stage

In this paper, we used the boundary signature-based features techniques [23] to extract features from thermogram images. A boundary signature is defined as a 1-D representation of this boundary. It can be seen as a plot of the distance from the boundary centroid to this boundary. Example of applying this technique to thermograms are shown in Figure 8a-c. They show the detected boundary of normal, benign mass and malignant mass. Figure 9a-c show the signatures of the detected boundaries. \[ln(img(v,w))=ln(j(v,w))+ln(f(v,w))\]4 Detected Boundary: (**a**) Normal (**b**) Benign mass (**c**) Malignant mass. \[ln(img(v,w))=ln(j(v,w))+ln(f(v,w))\]5 K-means Clustering: (**a**) Binary Image (**b**) K-means Cluster Image (**c**) Boundary Image. \[ln(img(v,w))=ln(j(v,w))+ln(f(v,w))\]6 (**a**) Normal image (**b**) Benign image (**c**) Malignant image. #### 4.3.1 Geometrical Feature Extraction

Based on the correlation between breast tumors and its locations and shapes, it is believed that geometrical features such as area, perimeter, P/A ratio, major axis, minor axis, LS ratio, and ENC are a very important for breast cancer detection. Below, we explain each geometrical feature which was used in the proposed method. * **Area:** The total of all pixels (p) of the segmented nucleus (n). * **Perimeter:** The nuclear envelope length is computed as a polygonal length approximation of the boundary (B). * **P/A ratio:** It is measured the degree to which the perimeter of the boundary (B) is exposed area ratio of the boundary (B). * **Major Axis Length (in pixels):** It is computed as the length of the major axis of an ellipse having the same second moments as the region. * **Minor Axis Length (in pixels):** It is computed as the length of the minor axis of an ellipse having the same second moments as the region. * **LS Ratio:** It is computed as the length ratio of the major axis length to the minor axis length of the equivalent ellipse of the lesion. * **Elliptical normalized circumference(ENC):** ENC features are computed in terms of the lesion circumference ratio and its equivalent ellipse. #### 4.3.2 Textural Feature Extraction

It is medically proved that the tumor distort a breast tissue. Thus, textural features become important in tumor detection. In recent years, there are many techniques for the extraction of textural features, e.g., GLCM (Gray Level Co-occurrence Matrix (GLCM) is a well-known texture features technique [24]. In the proposed method, the textural features extraction is used in the classification: entropy, EBCM, and standard deviation.