maging understanding is one of the most important tasks involving a classification system. Its primary purpose is to extract information from the images to allow the discrimination among different objects of interest. The classification process is usually based on grey level intensity, color, shape or texture. Image classification is of great interest in a variety of applications. Most of the image analysis problems are related to the neighborhood properties. Each pixel in a neighborhood or image is considered as a random variable, x r , which can assume values x r ? {0, 1?G-1}, where G is the number of grey levels of the image. The probability P (x r = x r | r), where r is the neighbor set for the element x r . The Fig. 1 illustrates different orders of neighborhood for a central pixel. Most of the research involved in image processing is mostly revolved around second order neighborhood only. This is because all the 8-neighboring pixels are well connected with central central pixels and the methods based on second order neighborhood are given extraordinary results in various issues. The present paper considering the difficulties and complexities involved in the third order neighborhood and derived a new, simple and efficient model for image analysis.

The proposed method evaluated transitions on "Trapezoids of Third Order Neighborhood of LBP (T-TN-LBP)" and based on this, derived various algorithms for the recognition of facial expressions. The proposed transition based T-TN-LBP consists of 7 steps as described below.

Step 1: Take facial image as Input Image (Img).

Step 3 : Crop the grey scale image.

Step 4: The present research evaluated TN-LBP on each 5 x 5 sub image. The TN contains only 13 pixels of 25 pixels of 5x5 neighborhood as shown in Fig. 1. The TN-LBP grey level sub image is converted into binary sub image by comparing the each pixel of TN grey level sub image with the mean value of TN grey sub image. The following Equation.1 is used for grey level to binary conversion.

Where V 0 is the mean of the TN sub matrix

Step 5: The present research for classification purpose considered the two reciprocal trapezoids i.e. Top Left (TL) and Bottom Right (BR) trapezoids of TN-LBP. The Fig. 2 shows TL and BR trapezoids of TN-LBP. The each trapezoid pattern consists of 5 pixels. The pixels P 1, P Step 6 : Each trapezoid of TN-LBP consists of five bit patterns. The present research computed the transitions from 0 to 1 and 1 to 0. Generally in 5 bit patterns, 3 types of 0 to 1 and 1 to 0 transitions occur i.e. zero, two and four transitions. The proposed method, considers two and four transitions only, which accounts for 87.5% of patterns.

Step 7 : Based on frequency occurrences of two and four transitions, the facial image is classified as one of the category (Neutral, Happiness, Sadness, Surprise, Anger, Disgust and Fear).

The proposed transition based T-TN-LBP method is experimented on a database contains 213 images of female facial expressions collected by Kamachi and Gyoba at Kyushu University, Japan In the proposed "Transitions based on T-TN-LBP method", the sample images are grouped into seven categories of expression (neutral, happiness, sadness, surprise, anger, disgust and fear). Each T-TN-LBP consists of 5 bit pattern. It results a total of 32 bit patterns. This forms two-zero transitions i.e. the decimal value 0 and 31. The decimal values 5,9,10,11,13,18,20,21,22,26 results for 0 to 1 or 1 to 0 four transitions.The rest of the binary equivalent decimal values1,2,3,4,6,7,8,12,14,15,16,17,19,23,24,25,27,28,29, 30 results two transitions. The beauty of the proposed transitions on T-TN-LBP method is it evaluated the frequency occurrences of 2 and 4 transitions. This accounts a total of 87.5% of transitions.

The proposed method not considered the zero transitions which accounts for 12.5% of patterns. Further the proposed method evaluated the frequency occurrence of 2 and 4 transitions separately. The proposed method further evaluated sum of frequency occurrences two and four transitions of both TL and BR T-TN-LBP for the different facial expressions separately and listed in tables 1, 2, 3, 4, 5, 6 and 7 respectively. In the tables, STLT denotes sum of transitions (both 2 and 4) of Top Left Trapezoid and SBRT denotes sum of transitions (both 2 and 4) of Bottom Right Trapezoid. Further, the table also gives Total number of ( 2 and 4) transitions of both Trapezoids denoted as TBT in the above tables. Comparison of The Proposed t-tn-lbp with Other Existing Methods

Table 9 shows the classification rate for various groups of facial expression by the proposed T-TN-LBP method with other existing methods like feature-based facial expression recognition within an architecture based on a two-layer perception of Zhengyou Zhang [2], Facial expression analysis by Dela Torre et.al [3] and Facial Expression Recognition Based on Distinct LBP and GLCM by Gorti SatyanarayanaMurthy et.al [4]. These methods are implemented on Kamachi and Gyoba [5] at Kyushu University-data set and compared with the proposed method. From table 9, it is clearly evident that, the proposed method exhibits a high classification rate than the existing methods. The graphical representation of this is also shown in Fig. 5.