# Multi-Descriptor Random Sampling for Patch-Based Face Recognition
## 2 Overview of the Proposed Method
### Multi-Scale Local Binary Patterns  
The LBP operator has gained much popularity as a local texture descriptor for various computer vision and biometric security applications including face recognition [19]. It is based on a combination of greyscale invariants and works by thresholding and labelling a pixel of an image neighbourhood (\(P\), \(R\)) (\(P\) sampling points on a circle of radius \(R\)) against the central pixel value. This results in a binary number and the histogram of the labels can the be used as a texture descriptor.  
One of the earliest LBP neighbourhoods introduced is (8, 1) and is generated by the 8 neighbouring pixels in a radius of 1, as shown in Figure 3. This scheme was later extended to other neighbourhoods having larger sizes. As can be seen in Figure 3, the threshold value is generally the value of the central pixel \(g_{c}\) which can be used for comparing the neighbourhood pixels \(g_{p}\). The result of applying the operator would give 1 if the \(g_{p}\) is larger than \(g_{c}\) and 0 otherwise. The final form of the LBP is an integer value and the features extracted by the LBP operator can be represented as histograms. Mathematically, this can be expressed as:  
\[\text{LBP}(P,R)=\sum_{p=0}^{P-1}f(g_{p}-g_{c})2^{P},f(x)=\begin{cases}1,&x\geq 0 \\ 0&x<0\end{cases} \tag{1}\]  
The local neighbourhood (\(P\), \(R\)) is a set of evenly spaced sampling points \(P\) on a circle of radius \(R\) centred at a fixed pixel. Uniform patterns [20] were inspired from the fact that some binary patterns occur more commonly in facial images than others. LBP is called uniform when the binary pattern contains at most two bitwise transitions from 0 to 1 or vice  
Figure 3: Illustration of the original LBP operator.  
Figure 2: Example of overlapping patches of an image from the AR dataset.  
versa when the bit pattern is considered circular. By using uniform patterns and computing the occurrence histogram, structural and statistical approaches are effectively combined. The distribution of micro structures-like edges, lines, and flat areas is estimated by the uniform histogram. LBP histograms have been introduced for face description in [21], where the face images are divided into a number of local regions allowing for the texture descriptors to be extracted from each region. The descriptors are then combined into one uniform histogram representing the face image as depicted in Figure 4.  
Uniform histograms were proposed as a result of the observation that some binary patterns do occur more commonly in face images than others and are therefore used to reduce the usual length of 256-bins patterns to smaller 59 patterns [20]. In addition, since the area covered by a conventional LBP algorithm is usually small, a uniform multi-scale LBP has been chosen in our work. This ensures that neighbourhoods with varying sizes can be used. Therefore, an LBP is carried out using various sample points \(P=8\), \(P=16\), and \(P=24\). The extracted feature vectors from each neighbourhood are then concatenated to form one uniform LBP histogram having 857 bins. This method covers a larger area, thus providing a much larger range of discriminative descriptors. The choice of LBP neighbourhoods is based on the best results obtained from initial experiments. The neighbourhoods LBP(3, 8), LBP(8, 16), and LBP(6, 24) offer a different range of features on different levels.