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will not have any preferred set of gray-level pairs In such a case the matrix is expected to be uniformly populated Thus, a feature which measures the randomness of gray-level distribution is the entropy, defined as Entropy = -

(71)

Note that the entropy is highest when all entries in P[i, j] are equal; such a matrix corresponds to an image in which there are no preferred gray-level

Sand that is used in mortar is governed by ASTM C 144 Standard Specification for Aggregate for Masonry Mortar Permitted sand may be natural or manufactured; manufactured sand is produced

energy, contrast,

as given below:

L L p2 [i,j]

Physical Requirements for Cements in Mortar and Grout (continued) ASTM C 191 Vicat ASTM C 109 Min ASTM C 185 Air Time of Setting (in) Compressive Content of Mortar Strength (psi) at (% volume) Initial Set, Final Set, not more than 7 Days 2900 2610 2320 2030 2900 2320 2900 2320 28 Days 3620 3620 2900 2900 3620 2900 3620 2900 4060 4060 3190 Min 16 16 16 16 Max 12 12 22 22 12 22 12 22

(72) (73) (74)

- j)2 P[i, j] P[i,j]

ASTM C 595 Blended Hydraulic Cement IS 45 420 IS(MS) 45 420 IS-A 45 420 IS-A(MS) 45 420 IP 45 420 IP-A 45 420 I(PM) 45 420 I(PM)-A 45 420 ASTM C 1157 Hydraulic Cement GU 45 420 HE 45 420 MS 45 420 HS 45 420 MH 45 420 LH 45 420

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The choice of the displacement vector d is an important parameter in the definition of the gray-level co-occurrence matrix Occasionally, the co-occurrence

matrix is computed for several values of d and the one which maximizes a statistical measure computed from P[i, j] is used The gray-level co-occurrence matrix approach is particularly suitable for describing microtextures It is not suitable for textures comprising large area primitives since it does not capture shape properties Gray-level co-occurrence matrices have been used extensively in remote sensing applications for land-use classification Autocorrelation The autocorrelation function p[k, I] for an N x N image is defined as follows: 1--- ,,(N-k) (N-l) p[k, I] = (N-k)(N-l) L,i=l Lj=l f[~,J] f[~+k,j+l]

' 0 ~ k, I ~ N-l (75)

4

(Extracted, with permission, from ASTM C 91 Standard Specification for Masonry Cement, ASTM C 150 Standard Specification for Portland Cement, ASTM C 595 Standard Specification for Blended Hydraulic Cement, ASTM C 1157 Standard Performance Specification for Hydraulic Cement, and ASTM C 1329 Standard Specification for Mortar Cement, copyright ASTM International, 100 Barr Harbor Drive, West Conshohocken, PA 19428 Copies of the complete standards may be obtained from ASTM, phone: 610-832-9585, email: service@astmorg, website: wwwastmorg

For images comprising repetitive texture patterns the autocorrelation function exhibits periodic behavior with a period equal to the spacing between adjacent texture primitives When the texture is coarse, the autocorrelation function drops off slowly, whereas for fine textures it drops off rapidly The autocorrelation function is used as a measure of periodicity of texture as well as a measure of the scale of the texture primitives

When the texture primitive is large enough to be individually segmented and described, then structural methods which describe the primitives and their placement rules are useful For example, consider a simple texture formed by the repeated placement of homogeneous gray-level discs in a regular grid pattern as shown in Figure 73(a) Such a texture can be described by first segmenting the discs using a simple method such as connected component labeling, described earlier, and then determining the regular structure formed by the centroids of these connected components For more general binary images the primitives can be first extracted using morphological methods and then their placement rules determined Such morphological methods are particularly useful when the image is corrupted by noise or other nonrepeating random patterns which would be difficult to separate in a simple connected component method For example, when the image shown in Figure 73(a) is

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