## Materials and Methods
### Extraction of Texture Features  
The texture is a visual pattern in the image, modelled by the computer as a vector of numerical values, which codifies the image structure. Many texture extraction techniques have been proposed in the literature and they have successfully applied to many applications [20]. Most of them are applied to rectangular or squared images. Nevertheless, in our application, the cancer tumours are irregular regions in the image. In a previous work, we have adapted some popular texture descriptors to their application on irregular patches in the image [21]. In this paper, we compare the performance of some descriptors of the two most popular families of texture descriptors: second order statistics of grey level pixels and spectral texture features. The family of statistical features encode the spatial distribution of grey levels in the image. We use the Local Binary Patterns (LBP), proposed by [PERSON] et al. in 2002 [22], and the Haralick coefficients, calculated from the grey level cooccurrence matrix [23]. The family of spectral features, like wavelets or Gabor filters, does decompositions of the signal or image in the frequency domain. Gabor filters uses the FFT (Fast Fourier Transform), which is a global technique, and they are not suitable to analyse irregular patches. Therefore, we only use the wavelet features. Let \(G=\{0,\ldots,N_{g}-1\}\) be the set of \(N_{g}\) grey levels, \(S\) a finite subset of indexes specifying the region of interest (ROI) to be analysed (in our case, the tumour), \(I(x,y)\in G\) the grey level in the pixel \((x,y)\in S\). The Grey Level Cooccurrence Matrix (\(M\)) of the image is a matrix of \(N_{g}\times N_{g}\) elements. The element \(M_{ij}\) represents the number of pairs of pixels with grey levels \(i\) and \(j\) that occur among the pixels belonging to the set \(S\) for a certain distance (i.e., scale) \(d\) and an orientation \(\theta\) from each other. For the construction of a rotation invariant cooccurrence matrix, we average the matrix to different orientations. The probability density function \(P_{d}(i,j),i,j\in G\) for each \(d\) is obtained dividing all elements of \(M_{ij}\) by the number of cooccurrences in \(M_{ij}\). This probability matrix is normally characterized by the following features: energy (\(E\)), correlation (\(Cor\)), contrast (\(Con\)), homogeneity (\(Ho\)), and entropy (\(H\)), which are defined as:  
\[E\ =\ \sum_{i}\sum_{j}P_{d}(i,j)^{2} \tag{1}\]  
\[Cor\ =\ \frac{1}{\sigma_{x}\sigma_{y}}\sum_{i}\left[\sum_{j}ijP_{d}(i,j)-\mu_{x }\mu_{y}\right] \tag{2}\]  
\[Con\ =\ \sum_{i}\sum_{j}\frac{(i-j)^{2}P_{d}(i,j)}{\left(N_{g}-1\right)^{2}} \tag{3}\]  
\[Ho\ =\ \sum_{i}\sum_{j}\frac{P_{d}(i,j)}{1+\left|i-j\right|} \tag{4}\]  
\[H\ =\ -\sum_{i}\sum_{j}P_{d}(i,j)log(P_{d}(i,j)) \tag{5}\]  
where \(\mu_{x}\ =\ \sum_{i}i\sum_{j}P_{d}(i,j)\), \(\mu_{y}\ =\ \sum_{j}j\sum_{i}P_{d}(i,j)\), \(\sigma_{x}\ =\ \sum_{i}(i-\mu_{x})^{2}\sum_{j}P(i,j)\), and \(\sigma_{y}\ =\ \sum_{j}\left(j-\mu_{y}\right)^{2}\sum_{i}P(i,j)\). All the sums over \(i\) and \(j\) are for \(i,j=0,\ldots,N_{g}-1\). We compute eight features vector HF\({}_{\text{df}}\) varying the distances used \(d\ =\ \{1,2,3,123\}\) (distance one, two or three pixels and the concatenation of these three distances) and the number of features \(f\ =\ \{4,5\}\), feature vectors are constructed using the five above features (i.e., energy, correlation, contrast, homogeneity, and entropy) or excluding the entropy. So, the number of texture features is: 4 for HF\({}_{\text{d4}}\), \(d\ =\ \{1,2,3\}\) and 5 for HF\({}_{\text{d5}}\), \(d\ =\ \{1,2,3\}\), and 12 and 15 features for HF\({}_{\text{123}}\), \(f\ =\ 4\) and \(f=5\), respectively. The original local binary pattern [22] extracts information locally from the texture of the images comparing the intensity of each pixel \(z_{c}~{}=~{}(x_{c},y_{c})\in S\) in the ROI with that of its neighbours. The neighbouring pixels \(P\) are angularly distributed over a circle with radius \(R\) centred in \(z_{c}\in S\).