Performs texture analyses on a multiband image
Evaluates the spatial variability (texture) of an image by using one of eight texture measures. Input may be BYTE, INTEGER*2, INTEGER*4, or REAL*4.
- IN
- Input image. Its data type may be BYTE, INTEGER*2, INTEGER*4, or REAL*4.
- OUT
- Output image. Its data type is always REAL*4. (See User's Note 2.)
- TEXTOPT("INERTIA")
- Texture option. Specifies the type of texture operation to perform.
= INERTIA: Image contrast (difference moment), a measure of local variation = CORRELATION: A measure of linear gray tone dependence = HOMOGENEITY: A measure of monotonicity = ENTROPY: A measure of the average uncertainty of gray tone co-occurrence = ENERGY: Angular second moment, a measure of the average certainty of gray tone co-occurrence = VARIANCE: A measure of gray tone variance within the window (second-order moment about the mean) = SKEWNESS: Third order moment about the mean; the departure from symmetry about the mean gray level = KURTOSIS: Fourth order moment about the mean; a measure of the spread of gray tones about the mean
- KERNDIM(3,3)
- Kernel dimensions (NL, NS). NL must be from 3 to 31. NS must be greater than or equal to 3.
- LINEINC(1)
- Line increment. The number of lines that the sliding window moves each time.
- SAMPINC(1)
- Sample increment. The number of samples that the sliding window moves each time.
- ORIANG(0)
- Orientation angle. Orientation angle from which gray tone co-occurrence is to be measured within the window. Values of 0, 45, 90 or 135 are valid. The angle is measured counterclockwise with 0 degrees at the horizontal. (See User's Note 4.)
ORIANG is not applicable to the functions VARIANCE, SKEWNESS, and KURTOSIS.
- SAMPDIST(1)
- Distance between co-occurrence samples. The direction is specified by ORIANG. Not applicable to the functions VARIANCE, SKEWNESS, and KURTOSIS.
- PRINT(TERM)
- Output destination for summary statistics.
= --: No Report = TERM: Terminal = LP: Line printer = filename: User supplied file name
Inertia values for the image BARB are
calculated within a 10 x 10 sliding window. The
co-occurrence statistic is calculated between
neighboring horizontal pixels and is output to
the image BARB.TEXT.
Homogeneity values are calculated along a 45-degree orientation, at a distance of 1, within a 5 x 5 window sliding 5 x 5 at each calculation. The results form output image one-fifth the size of the input image.
The TEXTURE measures are defined as follows:
p(i,j) is the pixel value in row i, column j of the window. p(k,l) is the neighboring pixel value of the p(i,j) as defined by the specified angle and distance. n is the number of pixels for summation as defined below. It may depend on the function, angle, and distance.For simplicity, the following sums are defined:
n 1 S1 = - SUM p(i,j) n n 1 2 S2 = - SUM p(i,j) n n 1 3 S3 = - SUM p(i,j) n n 1 4 S4 = - SUM p(i,j) n n 1 S5 = - SUM p(k,l) n n 1 2 S6 = - SUM p(k,l) n n 1 S7 = - SUM p(i,j)p(k,l) n n 1 2 S8 = - SUM (p(i,j)-p(k,l)) n 2 VARIANCE = n(S2-(S1) ) ------------ n-1 SKEWNESS = S3-3(S2)(S1)+2(S1)3 ------------------- 3 2 (S2-(S1) ) 2 4 S4-4(S3)(S1)+6(S2)(S1)-3(S1) KURTOSIS = ------------------------------- 2 2 (S2-(S1) ) 2 (S1+S5) S7 - ----- 2 CORRELATION = ----------------------- 2 (S2+S6) (S1+S5) ------ - ----- 2 2 INERTIA = S8 n 1 1 HOMOGENEITY = - SUM ------------------ 2 n 1+(p(i,j)-p(k,l)) 2 m f p ENERGY = SUM --- 2 n m -f f p p ENTROPY = SUM (---) Ln (---) n nwhere the range of summation is such that each summed pixel should stay inside the window.
1. The value of n depends on the function. For VARIANCE, SKEWNESS, and KURTOSIS, n is the total number of pixels in the window.
2. For functions INERTIA and HOMOGENEITY, n is the number of pixel pairs [(i,j) and (k,l)] separated by DISTANCE and ANGLE. For example, for DISTANCE=1, ANGLE=0, there are NL(NS-1) pairs; for DISTANCE=1, ANGLE=45o, there are (NL-1)(NS-1) pairs. NL and NS are the number of lines and the number of samples in the window.
3. The summation in functions ENERGY and ENTROPY is not on the pixel pairs but on the gray tone (intensity) range.
ENERGY = SUM SUM f(a,b) a b ENTROPY = - SUM SUM f(a,b) ln f(a,b) a bwhere f(a,b) is the joint frequency distribution for gray tone intensities a,b. Frequencies f(a,b) are constructed from the pixel pairs as defined in the work of Dr. R. M. Haralick, et al. (1973), pp. 613-614.
The method of texture analysis used is called the spatial gray tone dependence (SGTD) method and is based on the work of Haralick. The following publications contain detailed descriptions of the method: Conners, R. W., "Towards a Set of Statistical Features Which Measure Visually Perceivable Qualities of Textures," Proceedings of the IEEE Computer Society Conference on Pattern Recognition and Image Processing, Chicago, IL, Aug. 6-8, 1979.
Conners, R. W., and Harlow, C. A., "A Theoretical Comparison of Texture Algorithms," IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMT-2:204-222, 1980.
Cox and Rose, "Texture Functions in Image Analysis: A Computationally Efficient Solution," NASA Technical Memorandum 85022, Goddard Space Flight Center, Greenbelt, MD, March 1983.
Haralick, R. M., "Statistical and Structural Approach to Texture," Proceedings of the IEEE, 67:786-804, 1979.
Haralick, R. M., Shanmaugam, K., and Kinstein, I., "Textural Features for Image Classification," IEEE Transactions on Systems, Man and Cybernetics, SMC-3:610-621, 1973.
KERNDIM(1) must be between 3 and 31.
KERNDIM(1) must be between 3 and 31.
KERNDIM(2) must be greater or equal to 3.
Respecify sliding window or input image size.
Specify correct parameters.
Specify correct parameters.
number of lines = INT((NLIN-KERNDIM(1))/LINEINC)+1
number of pixels = INT((NPIN-KERNDIM(2))/SAMPINC)+1
where
NLIN = number of lines in input image
NPIN = number of pixels per line in input image
o o o
135 90 45
. . .
. . .
. . .
. . .
. . . o
. . . . . . 0