Texture Segmentation (ii) GLMC Learning _ Texture Segmentation

One, what is GLCM.

GLCM is the abbreviation of the grey level co-occurence matrix, also known as the grey Tone Spatial Dependency matrix, the Chinese name is the gray-scale co-present matrix.

Defines the GLCM is a tabulation of how often different combinations of pixel brightness-valus (gray level) occur in a image. GLCM is used to describe the frequency of different combinations of gray values in an image.

The following test image to use below, this is a grayscale map (GLs), this diagram will also run through the entire tutorial.

Define Order Dimension

The GLCM described here is the "second order" sequence used to represent the value of the texture calculation.

The first order texture feature is a statistical result computed from the original image value, such as variance, but does not consider the relationship between neighboring pixels.

The second-order texture feature of the Second order is to consider the relationship between groups that are composed of two pixels (usually adjacent pixels) in the original image.

Third and Higer order three-and higher-dimensional textures (considering the relationship between three or more pixels) represent theoretical possibilities, but are not generally applied because of computational time complexity and interpretation complexity. Of course, there is a more efficient way to compute the latest developments in three-dimensional textures (200X): http://www.fp.ucalgary.ca/mhallbey/references.htm.

Gray Histogram is a first-order statistic describing the gray distribution of a single pixel, and the gray-scale matrix is a joint distribution of two pixels with a spatial position, which can be regarded as a joint histogram of two pixel gray pairs, and is a second order statistic.

The framework of the GLCM

The spatial relationship between two pixels

The GLCM feature represents the relationship between two pixels at a point in time, commonly referred to as the reference reference and neighbor pixel adjacent pixels. In the next illustration, the adjacent pixel is the right pixel of each reference pixel. This can be simply expressed as a (1,0) relationship, with the pixel 1 in the x direction and the Pixel 2 in the y direction.

Each pixel in the window becomes the reference pixel in turn, starting with the pixel in the upper-left corner and ending with the pixel in the lower-right corner. The right pixel of the window along the edge, without the right pixel, so they do not follow this rule.

The degree of separation between two pixels

All of the examples in this tutorial take a pixel offset (a reference pixel and its direct adjacent pixel). If the window is large enough, using a larger offset may be more perfect. There is no difference in theory of computation. The sum of all entries established by the GLCM, such as the number of pixel combinations, will be smaller than the given window size.

In the test image, the combination of gray values and their position in the matrix. GLCM subsequent representations contained only 16 data units.

Neighbor Pixel value->
Ref pixel 0 1 2 3 0 0,0 0,1 0,2 0,3 1 1,0 1,1 1,2 1,3 2 2,0 2,1 2,2 2,3 3 3,0 3,1 3,2 3,3

How to interpret the matrix frame.

The upper-left cell represents the number of (0,0) combinations, such as the number of pixels in a region of the image where the grayscale value of 0 (adjacent pixels) falls to a pixel (reference pixel) with the other grayscale value 0 on the right.

Different spatial relationships have different symbiotic matrices appearing (above, adjacent, diagonal diagonally).

For example: Right (1,0) The matrix framework of spatial relations

2 2 1 0 0 2 0 0 0 0 3 1 0 0-0 1
How to interpret the right (east) matrix framework.

(bad translation, direct English understanding) twice in the "test image" the reference pixel is 0 and it eastern neighbour is also 0. Twice the reference pixel is 0 and its eastern neighbour are 1.Three times the reference pixel are 2 and its neighbour are Al So 2.

Permutation: diagonal symmetry of the matrix

Texture computing requires a diagonal matrix, so the next step is to normalized the GLCM.

A diagonal matrix means that the symmetry of the same value appearing in the cell appears on the diagonal. For example, the values in the (3,2) cell will also appear in the diagonal (2,3). The computed Eastern matrix (east matrices) above is asymmetrical.

The East matrix computes its own reference matrix using pixels adjacent to the right. If only one direction is used and the calculation is done in this way, the number of combinations (2,3) is different from the number of (3,2). (for example, 3 May is to the right of 2 three times, but to the left of 2 only once). However, if each pixel pair is computed, symmetry can be achieved: one forward (forward) and one back (backwards) (the second to compute the exchange reference and adjacent pixels).

For example: A reference pixel of 3 and its eastern neighbour of 2 would contribute one count to the matrix (3,2) and one count to T He matrix element (2,3). Symmetry also means that when considering the East correlation (1,0), the Western Correlation ( -1,0) is also computed. This is called the "horizontal matrix".

Normalization: GLCM expression into probability

After the GLCM is symmetric, a step is still required before the texture method is computed. What this method needs is that every GLCM unit is not a simple calculation, more of a probability