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Materials and Methods

1.2.7. Texture Analysis
Texture analysis has been extensively used to classify the remotely sensed images. Landuse classification where homogeneous regions with different types of terrains need to be identified is an important application. Haralick et.al uses gray level co-occurrence features to analyze the remotely sensed images. They computed the gray level co-occurrence matrices for a distance of one with four directions (00, 450, 900 and 1350). Identifying the perceive qualities of texture in an image is an important first step towards building mathematical models for texture. The intensity variations in an image which characterize texture are generally due to some physical variations in the scene. Texture is usually characterized by the two dimensional variations in the intensities present in the image. Texture is a property of areas and the texture of a point is undefined. Texture involves the spatial distribution of gray levels. Texture in an image can be perceived at different scales or levels of resolution. A region is perceived to have texture when the number of primitive objects in the region is large. Image texture has a number of perceived qualities which plays an important role in describing texture. Many different approaches to texture analysis have been proposed. Texture does not have a structured definition. It is defined under different definitions. Some of them are given below:

• We may regard texture as what constitutes a macroscopic region. Its structure is simply attributed to the repetitive patterns in which elements or primitives are arranged according to a placement rule.
• A region in an image has a constant texture if a set of local statistics or other local properties of the picture function are constant, slowly varying, or approximately periodic.
• An image texture is described by the number and types of its (tonal) primitives and the spatial organization or layout of its (tonal) primitives.
• Texture is defined for our purposes as an attribute of a field having no components that appear enumerable.
• A fundamental characteristic of texture is that it cannot be analyzed without a frame of reference of tonal primitive being stated or implied. For any smooth grey tone surface, there exists a scale such that when the surface is examined, it has no texture. Then as resolution increases, it takes on a fine texture and then a coarse texture.

Texture analysis in images is an important area of research. The basic aim of any texture analysis is texture recognition and texture based shape analysis. Texture can be carried out at two levels, statistical and structural. A variety of statistical methods like autocorrelation, co-occurrence approach, edge frequency methods, Laws methods, etc. have been proposed for texture analysis. Among the most widely used texture measures are those derived from grey level co-occurrence matrices or difference histograms. The Grey Level Co-occurrence Matrix, GLCM (also called the Grey Tone Spatial Dependency Matrix)

The GLCM is a tabulation of how often different combinations of pixel brightness values (grey levels) occur in an image. GLCM texture considers the relation between two pixels at a time, called the reference and the neighbour pixel. The Grey Level Cooccurence Matrix (GLCM) has been described in the image processing literature by a number of names including Spatial Grey Level Dependence (SGLD) etc. As the name suggests, the GLCM is constructed from the image by estimating the pair wise statistics of pixel intensity. Each element (i,j) of the matrix represents an estimate of the probability that two pixels with a specified separation have grey levels i and j. The separation is usually specified by a displacement, d and an angle, θ which is represented by equation 1.



where, φ(d,θ) will be a square matrix of side equal to the number of grey levels in the image and is usually not symmetric. Symmetry is often introduced by effectively adding the GLCM to it's transpose and dividing every element by 2. This renders φ(d,θ) and φ(d, θ + 180⁰) identical and makes the GLCM unable to detect 180⁰ rotations.

1. Mean: The GLCM Mean is not simply the average of all the original pixel values in the image window. It is expressed in terms of the GLCM. The pixel value is weighted not by its frequency of occurrence by itself (as in a "regular" or familiar mean equation) but by its frequency of its occurrence in combination with a certain neighbour pixel value.




The left hand equation calculates the mean based on the reference pixels, µi. It is also possible to calculate the mean using the neighbour pixels, µj, as in the right hand equation. For the symmetrical GLCM, where each pixel in the window is counted once as a reference and once as a neighbour, the two values are identical.


2. Variance: Variance in texture performs the same task as does the common descriptive statistic called variance. It relies on the mean, and the dispersion around the mean, of cell values within the GLCM. However, GLCM variance uses the GLCM, therefore it deals specifically with the combinations of reference and neighbour pixel, so it is not the same as the simple variance of grey levels in the original image. Variance calculated using i or j gives the same result, since the GLCM is symmetrical.





3. Contrast: This will measure the amount of local variation in the image and is the opposite of homogeneity (when high pixel values concentrate along the diagonal).




When i and j are equal, the cell is on the diagonal and (i-j) = 0.
These values represent pixels entirely similar to their neighbour, so they are given a weight of 0.
If i and j differ by 1, there is a small similarity, and the weight is 1.
If i and j differ by 2, contrast is increasing and the weight is 4.
The weights continue to increase exponentially as (i-j) increases.


4. Homogeneity: Dissimilarity and Contrast result in larger numbers for more contrasty windows. If weights decrease away from the diagonal, the result will be larger for windows with little contrast. Homogeneity weights values by the inverse of the Contrast weight, with weights decreasing exponentially away from the diagonal.





5. Dissimilarity: Instead of weights increasing exponentially (0, 1, 4, 9, etc.) as we moves away from the diagonal, the dissimilarity weights increases linearly (0, 1, 2, 3 etc.).





6. Entropy: This measure is high when the values of the local window have similar values. It is low when the values are close to either 0 or 1 (i.e. when the pixels in the local window are uniform). Entropy is the degree of diversity. It is given by:




Where, Pi is the number of times the element has occurred to the total number of elements.


7. Angular Second Moment: It will be used to measure homogeneity of the image. This information is specified by the matrix of relative frequencies hc (i,j) with which two neighbouring pixels occur on the image, one with grey value i and the other with grey value j.





8. Correlation: This will analyze the linear dependency of grey levels of neighbouring pixels. It is typically high, when the scale of local texture is larger than the distance.

1.2.7.1. Generating the Texture Images Using Gray Level Co-occurrence Matrix (GLCM)
In this study, an attempt has been made where the Grey Level Co-occurrence Matrix (GLCM) method is used for studying the texture of the tea areas that will enable us to distinguish between the healthy as well as the affected tea patches. The GLCM technique was applied to all the images and the different parameters were studied giving different thresholdings. Once the images were generated then it is compared with the diseased maps to see whether the affects observed on the diseased maps could also be observed on the texture images. It was found that the parameter mean was giving good results as compared to other parameters. The details have been discussed in the results and discussions chapter.