Texture Transformations

IntroductionHumans are quite adapt at dealing with textures - in our thought process we intuitively take

into the nature of variability and patterns, edges etc when analyzing an image. Most imageprocessing algorithms only work with spectral or tonal information. However, several methods tomeasure texture have been developed to measure texture automatically.

If a set of contiguous pixels have identical or similar DN values they are said to comprise adiscrete tonal feature. Conversely if these pixels have a wide range of DN values, then a property of thisarea is texture (Jensen, 1997). There are numerous methods that have been developed to measuretexture. The majority of these operate in the spatial domain. The approaches include first- andsecond-order statistics and fractal analysis. Attempts to undertake texture analysis in the frequencydomain (e.g. using Fourier analysis) have met with limited success.

Simple Texture MeasurementsOne of the simplest measurements of texture would simply to determine the difference

between the maximum and minimum gray values occurring in a moving window. A slightmodification to this simple max - min operator has been proposed. It is a five element movingwindow shaped like this:

A

B C D

E

For this moving window a texture measurement is also calculated simply as the differencebetween the brightest and darkest pixels in the window.

First Order StatisticsOne approach to attempting to quantify the texture of small areas uses standard first-order

statistical measures of local areas using. 3x3, 5x5 , 7x7 or other sizes of moving windows. Three ofthese metrics are Average, Standard Deviation, and Entropy (from Jensen, 1997) and they aredefined as follows:

In the above equations, fi is the frequency of gray level i occuring in a moving window andquantk is the possible range of gray values in a the band (k) of interest and W is the total number ofpixels in the moving window

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Second-Order StatisticsHarlick (1979,1986) has proposed a higher order of texture metrics. The fundamental

concept behind these metrics is the idea of a spatially dependent gray level co-occurrence matrix(GLCM). In this approach a set of matrices are created that show the probability that a pair ofbrightness values (i,j) will occur at a certain separation from each other (∆x,∆y). The assumption isthat the textural dependence will be at angles of 0°, 45°, 90° or 135° (with 0° being to the right and90° above) from the original pixel that means four GLCM matrices would have to be created.

For example (taken from Jensen, 1997), here is a small portion of image…

0 1 1 2 3

0 0 2 3 3

0 1 2 2 3

1 2 3 2 2

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The GLCM for an angle of 0°and a separation of one pixel in x and y is as follows:

0 1 2 3

0 1 2 1 0

1 0 1 3 0

2 0 0 3 5

3 0 0 2 2

Once a set of 4 GLCM have been created a number of useful metrics can be derived. Threeof the most widely used (and actually implemented in image processing packages) are angular secondmoment (ASM), contrast (CON) and correlation (COR):

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These metrics are calculated for each pixel for each using each of the four GCLMs and thena final texture value is usually calculated as an average of all four. It is obvious that thesemeasurements can be computationally expensive especially as the quantization level becomes large.For many applications it may be beneficial to quantize the image into a smaller number of gray levelsprior to creating the GLCMs.

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