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The RSI color model represents a color in terms of hue, saturation, and intensity The intensity is the gray level of the pixels in a monochrome (black and white) image, such as the images used as examples for the machine vision algorithms presented in other chapters of this book

Figure 102: The HSI triangle represents the combinations of colors that can be represented by a linear combination of the primary colors at the corners of the triangle The HSI color triangl~ shown in Figure 102, represents the combinations of hue and saturation that can be represented by combinations of the RGB primaries The corners of the triangle correspond to the maximum amounts of each primary color (red, green, and blue) available from the imaging system Achromatic (colorless) pixels are shades of gray, corresponding to equal amounts of the primary colors, and lie at the center of the HSI triangle The HSI solid adds the dimension of image intensity (Figure 103), with black at the bottom of the solid and white at the top Shades of gray run along the axis of the solid Each cross section of the solid is an HSI triangle with the proportions of the primary colors constrained to produce a particular intensity value The HSI solid narrows to a point at the top and bottom because white and black can only be represented by unique combinations of the RGB primaries The RGB components of an image can be converted to the HSI color representation Assume that the RGB components have been normalized to 1 This allows the derivation to be done in device-independent units The intensity is the sum of the RGB values normalized to 1: 1 1= 3(R + G + B)

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Concrete Sand and gravel concrete Crushed stone and sand concrete Air-cooled slag concrete Coal cinder concrete Expanded slag concrete Pelletized-fly ash concrete Scoria concrete Expanded clay, shale, slate, and sintered fly ash concretes Pumice concrete Cellular concrete

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Figure 103: The HSI solid bounds the range of colors that can be represented by combinations of the primary colors The derivation of the formulas for hue and saturation begins by removing intensity from the RGB values:

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(Panarese, Kosmatka, & Randall, Concrete Masonry Handbook, Portland Cement Association, 1991)

The locus of all possible values for r, g, and b is the triangle in the positive octant of rgb-space with corners (1,0,0), (0,1,0), and (0,0,1) Let point P on the triangle denote the position in rgb-space of some color Let p = (r, g, b) be the vector to point P on the triangle, w be the vector to the point at the center of the triangle that represents white, and Pr be the vector to the corner of the triangle that corresponds to fully saturated red The hue is the angle from vector Pr - w to vector P - w, counterclockwise around the triangle as seen from the side of the triangle away from the origin This is the right-hand rule with the thumb aligned along the normal to the triangle pointing away

104 COLOR PROCESSING from the origin The cosine of the hue is cosH = (p - w) (Pr - w) lip - wllllPr - wll

Physical Requirements for Concrete Block Units Minimum Compressive Strength (psi)a Average of Individual Unit 1700 500 Maximum Water Absorption (pcf) of Averageof 3 Units Based on Weight Classificationb Lightweight (<105 pcf) 180 Medium Weight (105 to 125 pcf) 150 Normal (>125 pcf) 130

Split and merge operations may be used together After a presegmentation based on thresholding, a succession of splits and merges may be applied to refine the segmentation Combined split and merge algorithms are useful for segmenting complex scenes Domain knowledge may be introduced to guide the split and merge operations Suppose that an image is partitioned into a set of regions, {Rk}, for k = 1,2, , m All of the pixels in a region will be homogeneous according to some property defined by a predicate P applied to the region The predicate represents the similarity between the pixels in a region For example, the predicate could be defined using the variance in gray values within a region: P(R)

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