Comparison of various methods.

## Abstract

The main objective of the local pattern is to describe the image with high discriminative features so that the local pattern descriptors are more suitable for face recognition. The word “local” represents the measured image with the subregion and is the key in this chapter. Regardless of the techniques proposed, the local pattern is one of the most interesting areas in face recognition. The local facial descriptor is a local pattern that generates the descriptor by considering the subregion of an image. Techniques based on various combination methods from the local facial descriptors are not unusual. This chapter is concerned primarily to help the reader to develop a basic understanding of the local pattern descriptors and how they apply to face recognition. We begin to describe the outline of the local pattern in face recognition and its relative facial descriptors. Next, we give an introduction to the popular local patterns and establish examples to demonstrate the process of each method. To the end of this chapter, we conclude those methods with a discussion of issues related to the properties of the local patterns.

### Keywords

- local pattern
- micropattern
- face recognition
- descriptor

## 1. Introduction

Due to the intelligence security monitoring is more popular in recent years, the automatically recognizing face is needed for various visual surveillance systems, for example the accessing control system for personal or company to verify the legal/illegal people, policing system for identifying the thief and the robber who presents the illegal behavior in public or private space. To construct an efficient face recognition system, the facial descriptor with discriminated characteristic is required.

The facial descriptor refers to the process of extracting the discriminative features to represent a given face image. Numerous methodologies are proposed to recognize face and those can be classified as global and local facial descriptors. The global facial descriptor describes the facial characteristics with the whole face image, such as principal component analysis (PCA) [1, 2] and linear discriminant analysis (LDA) [3, 4]. PCA converts the global facial descriptor from high dimension to low dimension by using the linear transform methodology to reduce the computational cost. Linear discriminant analysis (LDA) also called the Fishers Linear Discriminant is similar to PCA, while it is a supervised methodology. Although the global facial descriptor can extract the principal component from the facial images, reduces the computational cost, and maintains the variance of the facial image, the performance is sensitive to the change of the environment, such as the change of light.

The flexibilities of the local facial descriptors are better than the global facial descriptors because they successfully and effectively represent the spatial structure information of an input image. A well local facial descriptor generates discriminative and robust features to achieve good recognition results with computational simplicity. In this chapter, we represent a number of approaches in the local facial descriptor including the local binary pattern (LBP), local derivation pattern (LDP), local tetra pattern (LTrP), local vector pattern (LVP) and local clustering pattern (LCP).

## 2. Local pattern descriptor

A local pattern considers the variations of subregion in an image, which is also called a micropattern. In this section, we introduce the basic and several popular techniques of local pattern descriptor for facial recognition.

### 2.1. Local binary pattern

Local binary pattern (LBP) [5] is designed to describe the texture in a local neighborhood is an invariant texture measure and has been various comparative studies, such as fingerprint recognition [6], face recognition [7], and license plate recognition [8]. The main characteristics of LBP are: (1) highly discriminative capability (2) and computational efficiency.

The basic LBP encodes the pixels of an image by thresholding

where *threshold function* and this can be expressed as

where

Furthermore, to address the problem of the textures at different scales, there are some followers which extend to use neighborhoods with various scales [9, 10]. To compare with basic LBP, the local neighborhoods are evenly spaced on a circle centered at the reference pixel

where

### 2.2. Local derivative pattern

LBP is a nondirectional first-order local derivative pattern of images and fails to extract more detailed information, such as the directions between neighborhoods and referenced pixel, and the high-order gradient information. Local derivative pattern (LDP) can be considered as an extension of LBP with directional high-order local derivative pattern [11]. To encode the

where

where

The spatial relationship between two pixels includes the conditions of turning and monotonically increasing/decreasing and be coded as 1 and 0 in LDP, respectively.

Finally, the second-order LDP is defined as the concatenation of the four directional LDPs

The

Then, the

An example of high-order derivative is shown in Figure 5. Figure 5(a) is the original value of image, Figure 5(b) is the first-order derivative in

Figure 6 demonstrates an example to encode the second-order LDP in

Figure 7 demonstrates the spatial distribution of example of LDP in

### 2.3. Local tetra pattern

Local tetra pattern (LTrP) [12] adopts the concepts of LBP and LDP which extends the spatial relationship from one-dimensional to two-dimensional. LTrP uses two high-order derivative directions with four distinct values to encode the micropattern for extract more discriminative information. The

where

where

where

Figure 8 illustrates the coding scheme of Eq. (21), if the quadrant of the referenced pixel

where

where

### 2.4. Local vector pattern

Local vector pattern (LVP) [13] is inspired by local binary pattern (LBP) which is sample and intuitive. To compare with LBP and LDP, LVP further considers the neighborhood relationship with various distances from different directions and the relationship between various derivative directions.

LVP is a micropattern in high-order derivative space which considers the direction value in encoding procedure, as shown in Figure 10. The derivative direction vector of the referenced pixel

where

The LVP,

where

Finally, the LVP of referenced pixel

To extend the discriminative of 2D spatial structures, LVP integrates four pairwise directions (

The coding function of LVP is a weight vector of dynamic linear decision function which is a comparative space transform (CST) and addresses the two-class problem in pattern recognition. The dynamic linear decision function,

where

where the first term of

We take the example of the local subregion of an image as shown in Figure 5(a) to illustrate the encoding process of generating first-order LVP, as shown in Figures 11 and 12. Figure 11 illustrates the first-order LVP of the referenced pixel

### 2.5. Local clustering pattern

Local clustering pattern (LCP) [14] is designed to solve the problems in face recognition: (1) to reduce feature length with low computational cost and (2) to enhance the accuracy for face recognition. To generate the local clustering pattern, four phases have to be considered: (1) to generate the local derivative variations with various directions; (2) to project the local derivative variations with various directions on the pairwise combinatorial directions in the rectangular coordinate system; (3) to transform the coordinate from the rectangular coordinate system into the polar coordinate system; and (4) encoding the facial descriptor which is local clustering pattern, as a micropattern for each pixel by applying the clustering algorithm. The details are described in the following subsections: local clustering pattern (LCP) and coding scheme.

#### 2.5.1. Local clustering pattern

Taken a subregion image

where

where

where

#### 2.5.2. Coding scheme

In this subsection, we further discuss the coding scheme in LCP which is considered as the problem of classification. The coding scheme of LCP is executed in the polar coordinate system based on the characteristics of the derivative variations in the pairwise combinatorial directions.

First, four combinations of the derivative variations in the pairwise directions are utilized in LCP, including

where

The feature vectors

where

LCP is ensemble of several decisions from the results of clustering. Each clustering result is considered as a problem of a two-class case, whose center vector

where *T* times to find the cluster two-class centers

The adjacent pixels of the reference pixel

where

#### 2.5.3. Example

The local subregion of an image as shown in Figure 5(a) is taken as an example to illustrate the encoding process of generating first-order LCP, as shown in Figure 14. First, LCP calculates the first-order derivatives along

## 3. Comparison

In this section, we discuss the characteristics of the local patterns descriptors as mentioned. The local binary pattern (LBP) generates the local facial descriptor by comparing the gray value between referenced pixel and its adjacent pixels for each pixel in the face image. The texture information, such as spots, lines and corners, in the images is extracted. Although LBP considers the spatial information to generate the local facial descriptor, it omits the directional information and is sensitivity when light is slightly changed.

The local derivation pattern (LDP) analyzes the turnings between referenced pixel and its neighborhoods from the derivative values. The derivative values with four directions are considered to generate the local facial descriptor in the high-order derivative space. However, the turnings between referenced pixel and its neighbors are discussed in the same derivative direction.

The local tetra pattern (LTrP) utilized the two-dimensional distribution with derivative values in four quadrants to describe the texture information and that can extract more discriminative information. Although LTrP considers the derivative variations with two dimensions, there exist two problems: (1) the dimension of facial descriptor and (2) the sensitivity of the features. To compare with LBP and LDP, the dimension of facial descriptor of LTrP is high. The features of LTrP in the four quadrants of the rectangular (or Cartesian) coordinate system are altered when illumination is changed.

The local vector pattern (LVP) designs the comparative space transform (CST) and that is associated with the pairwise directions of vector to encode the micropatterns. Comparing LVP with LBP, LDP, and LTrP, LVP not only successfully extracts distinctive information but also reduces the feature length. However, its computational cost is higher than LBP and LDP.

The local clustering pattern (LCP) derivatives the local variations with multidirections and that are integrated to form the pairwise combinatorial direction. To generate the discriminative local pattern, the features of local derivative variations are transformed into the polar coordinate system by generating the characteristics of magnitude (

Methods | Information used | Distribution of coding scheme | Feature Length |
---|---|---|---|

LBP | Original values | One dimensional | |

LDP | High-order derivative values | One dimensional | |

LTrP | High-order derivative values | Two dimensional | |

LVP | High-order derivative values | Two dimensional | |

LCP | High-order derivative values | Two dimensional |

In Table 1, we analyze these methods with three indicators: (1) information used, (2) distribution of coding scheme, and (3) feature length. The indicator of the information used presents the information which is used in facial descriptor generation. LBP uses the original values such, as gray value; LDP considers the single high-order derivative values; LTrP uses both horizontal and vertical high-order derivative values; LVP uses the high-order derivative values and be described as the vector representation; the high-order derivative values are utilized in clustering process of LCP.

The distribution of coding scheme is to present how many directions of used information are considered in coding at each time. LBP and LDP generate the micropattern by considering a single direction at each time, for example, LDP generates the micropatterns of one direction at a time and then integrates the results of each direction to form the facial descriptor; LTrP considers two-direction information, horizontal and vertical, when coding; LVP and LCP use the pairwise combinatorial directions.

The feature length is to demonstrate the feature length of each micropattern. LBP considers eight neighborhoods and its feature length is 8; LDP further considers four directions including

## 4. Summary

The principal object of this chapter is to present the local pattern descriptors for understanding and accessing the facial descriptor in face recognition. The concept of local pattern is sample and intuitive, and the extended techniques of the basic local pattern are widely used in various areas. A partial listing of local pattern descriptors includes local binary pattern (LBP), local derivative pattern (LDP), local tetra patterns (LTrP), local vector pattern (LVP) and local clustering pattern (LCP) are widely applied to variety of image processing problems such as object detection, object recognition, image retrieval, fingerprint recognition, character recognition, face recognition, license plate recognition. Since it is impractical to cover all the approaches of local pattern descriptor in a single chapter, the basic and popular techniques included are chosen for their value in introducing and clarifying fundamental concepts in the field.