# 3D Texture Feature Extraction and Classification Using GLCM and LBP-Based Descriptors
## 2 Background
### Block Matching and 3D Filtering Extended Local Binary Patterns (BM3 DELBP)  
Even if the LBP operator is efficient in many texture classification problems, it has a great disadvantage: the noise sensitivity. In order to handle this issue and to increase the discrimination power of the LBP, we proposed in a previous work [22], the Block Matching and 3D Filtering Extended Local Binary Patterns (BM3 DELBP) operator which was inspired by the Median Robust Extended Local Binary Patterns formalism [23]. Instead of considering raw pixel values like LBP, BM3 DELBP introduces a filtering step in the feature extraction operation and considers responses to a state-of-the-art filter, the Block Matching and 3D Filtering (BM3D) [24]. Thus, the vulnerability to noise is addressed by using this denoising technique, which is able to attenuate high levels of Gaussian noise without altering the texture structures for particular choices of the set of parameters. This is done by performing the denoising in the transform domain. In the first step, a grouping by block-matching is performed: 2D blocks that are similar to a reference block are stacked together in a 3D group. By considering a 3D transform, the signal is represented sparsely in the transform domain due to the similarity between the blocks that compose a group. In the 3D transform domain, a second step is performed: collaborative filtering. In this phase, the noise is eliminated by shrinking the transform coefficients, the textural features being still preserved. We refer to the original publication for more details regarding BM3D [24]. Despite recent developments addressing the use of deep-learning techniques in the image filtering domain, the BM3D collaborative approach remains one of the most performant [25]. The feature space of this operator is built by considering two types of features as in the Extended Local Binary Patterns [26]: pixel intensities and differences between pixel intensities. The first category includes two components: The central pixel intensity operator labelled BM3 DELBP_CI and the neighbours' intensities component denoted by BM3 DELBP_NI\({}_{\mathrm{R,P}}^{\mathrm{riu2}}\):  
\[\mathrm{BM3 DELBP\_CI}(\mathrm{x}_{\mathrm{c}})\ =\ \mathrm{s}(\mathrm{x}_{ \mathrm{c}}-\mathrm{C}_{\mathrm{I}}) \tag{3}\]where \(C_{I}\) is the mean value of the entire input image, s(x) is the sign function given in (2) and xc is the central pixel;  
\[\text{BM3 DELBP\_NlR,P}^{\text{triu2}}(x_{c})\ =\ \left\{ \begin{array}{ll}\sum\limits_{n=0}^{P-1}s(x _{R,P,n}-u_{R}),&\text{if U(BM3 DELBP\_NI)}\ \leq\ 2\\ P+1,&\text{otherwise}\end{array} \right. \tag{4}\]  
where uR is the mean value of the neighbouring pixels, being given in (5), xR,P,n is the nth neighbour pixel from a neighbourhood having P neighbours and a radius R, U is the uniformity function and the superscript riu2 indicates the use of uniform rotation invariant patterns that have U \(\ \leq\ 2\);  
\[u_{R}=\frac{1}{P}\times\sum\limits_{n=0}^{P-1}x_{R,P,n} \tag{5}\]  
The second category contains one component based on differences between pixel intensities, the radial difference operator which is denoted by BM3 DELBP_RDP(tm2):  
\[\text{BM3 DELBP\_RDP}^{\text{triu2}}(x_{c})\ =\ \left\{ \begin{array}{ll}\sum \limits_{n=0}^{P-1}s(x_{R,P,n}-x_{R-1,P,n}),&\text{if U(BM3 DELBP\_RD)}\ \leq\ 2\\ P+1,&\text{otherwise}\end{array} \right. \tag{6}\]  
where R and R \(-\) 1 are the radii of two circles on which the considered pixels are located. Figure 1 shows the diagram which describes the BM3 DELBP feature extraction process. A textured image is used as input for the feature extraction system. Then, the input image is filtered using BM3D for reducing the noise. The multi-resolution strategy is used for providing a degree of invariance to the observation scale: the features extracted from each scale of interest are concatenated. The considered scales are the ones having the radii 2, 4, 6 and 8.