# Adaptive Co-occurrence Differential Texton Space for Classification

In this section, we firstly propose a CoDT feature to represent the local structure of the HEp-2 cell images. Then we exploit the image representation based on the adaptive CoDT feature space modeled by a GMM.

## Co-occurrence Differential Texton

LBP can be obtained by thresholding the gray value of the circularly symmetric surrounding pixels with that of the center pixel within a local patch (micro-texton).

**Fig. 7.1 **The LBP encoding procedure on a 3 **x **3 microtexton

We have given the details on the LBP in Sect. 2.2.1.1. Here we just give the formula for calculating the original LBP operator. Given a grayscale image I, *I (x, y)* is a gray value at location *(x, y)* in I. Mathematically, the LBP at location *(x, y)* is defined as

where *(x, y)* is the location of center pixel and *(xi, y _{i})* is the neighbors location. The LBP encoding process on a 3 x 3 microtexton is illustrated in Fig. 7.1. The histogram of LBP values over the entire image is exploited as a kind of highly discriminative textural feature.

Due to the computational simplicity and discriminative capability, LBP and its extended versions have been applied in many fields of computer vision e.g., face recognition [16], texture classification [17] and image retrieval [18]. Recently, some improved LBP features such as CoALBP [19] and RIC-LBP [20] have been applied in HEp-2 cells and shown superior performances compared with the conventional LBP. However, one major drawback of the LBP related methods is that they will lose some discriminant information since they represent the microstructure with only two quantized levels. Thus, the histogram of the corresponding LBP related values is not adequately descriptive for representing the image. We give an example in Fig. 7.2. Local patch ‘A’ and local patch ‘B’ is very different, but their LBP values are the same; ‘B’ and ‘C’ has similar local structure, but their LBP values are different.

In order to reserve more discriminant information, we propose to use a *Differential Vector* (DV) to describe the cell images. A DV is a microstructural feature based on the differential domain skipping the quantization procedure, which can be formulated as

where the notations follow (7.1). To enhance the discriminative power, we further propose a CoDT feature capturing the spatial relation between differential micro- textons. Spatial co-occurrence features can characterize more subtle and complex structure than a single feature. Thus, CoDT feature can provide more information than individual DV. The CoDT feature consisting of one pair of DVs is illustrated in Fig.7.3 and formulated as

**Fig. 7.2 ****Comparison between the LBPs for similar local structure and for different local structure**

**Fig. 7.3 **Illustration of co-occurrence differential texton. **a **An example of differential vector. **b **Two pairs of DVs with rotation angles 0° and *в* respectively. The number of neighboring pixel of DV is set as *P =* 8

where x = *(x, y)* is the position vector in image *I. x _{e} =* x +

*Ax*and

_{e}*Ax*cos

_{e}= (d*e, d*sin

*e)*is a replacement vector between a DV pair with interval

*d*.

*DVP,*(xe) is the DV at position x

_{R}_{e}with the rotation angle

*e*, which can be calculated as

In this thesis, we extract four pairs of DVs, that is *в =* 0°, 45°,135°. While the dimension of DV is *P*, the final CoDT feature will be a 5*P*-dimensional feature vector, which provides more variant and complex image patterns than the single DV. Extracting more pairs of DVs with *в =* 180°, 225°,..., 315° is unnecessary as it will bring in some redundant information and is helpless for improving classification performance.