Morphological Operators

Morphology deals with form and shape; in image processing, morphological operators are tools that aid the observer in defining, extracting, and manipulating the

Isophotes Photoshop
Figure 15.9 Isophote contour lines encircle a region having pixel values greater than the isophote pixel value. This highly enlarged section of the M101 image shows a knot in the spiral arm, an isophote contour line drawn around that knot, and the same isophote line superimposed on the image.

forms and shapes of objects in images. By themselves, the array of pixel values in abitmapped image has nothing to say about objects. The task of the morphological operator is to associate groups of pixels—based on their pixel values—to reveal objects as isolated groups of pixels. In the process of extracting form and shape, morphological operators discard information about brightness in return for highlighting the shapes and forms of objects.

Morphological operators isolate contour lines of constant brightness, locate edges, locate shapes, shrink lines and shapes, broaden lines and shapes, and reduce fuzzy lines and blobs to one-pixel-wide skeletons. By themselves, these operators do not produce useful results. But used in a logical sequence, each process feeding into the next toward a specific goal, they are powerful analytic tools.

15.4.1 Isophote Lines

Just as the isobars on the weather map connect regions of equal barometric reading, isophote lines connect regions of equal brightness on an image. Isophotes show how the brightness in an image is really distributed, which is quite often surprising. Where the eye sees spiral arms in a galaxy, isophotes reveal radially declining contours of brightness within the spiral arms as relatively minor departures firom the overall pattern of radial decline.

What exactly are isophote lines? You already know that a geographic elevation contour is the boundary between lower land and higher land. An isophote defines the boundary between a region with higher pixel values and another with lower values. To be an isophote pixel, a pixel must lie between one that has a higher pixel value than the isophote and another pixel that has a lower value than the

Isophotes Photoshop

Figure 15.10 While structural features—the spiral arms—lead the eye, the isophotes follow distorted circles of surface brightness. For most observers, it comes as no surprise that galactic arms are very subtle features. The inverted gray scale makes it easier to see both the underlying galaxy and the contours.

Figure 15.10 While structural features—the spiral arms—lead the eye, the isophotes follow distorted circles of surface brightness. For most observers, it comes as no surprise that galactic arms are very subtle features. The inverted gray scale makes it easier to see both the underlying galaxy and the contours.

isophote. There is just one exception: a pixel can also be an isophote by having a value equal to it.

From the definition, it is easy to craft an algorithm that draws contour lines by making pixels that do not lie on an isophote black, and by making those that do white. In the procedure below, the new pixel is first set to black, and then it is tested to determine whether it satisfies the conditions for being on an isophote.

FOR y = 1 TO ymax FOR x = 1 TO xmax new(x,y) = black

IF old(x,y) = iso THEN new(x,y) = white IF old(x,y) < iso THEN

IF old(x-1,y) > iso THEN new(x,y) = white IF old(x,y-1) > iso THEN new(x,y) = white IF old(x-1,y-1) > iso THEN new(x,y) = white END IF

IF old(x-l,y) < iso THEN new(x,y) = white IF old(x,y-1) < iso THEN new(x,y) = white

IF old(x-1, y-1) < iso THEN new(x,y) = white END IF NEXT x

NEXT y where iso is the pixel value for the isophote line, black is a pixel value that displays as black, and white is a pixel value that appears white on the screen.

The procedure begins by setting new (x, y) to black. The current pixel, old (x, y), can be equal to, less than, or greater than the isophote. If the current pixel equals the isophote value, new (x, y) is set to white. If the current pixel is less than the isophote, and if an adjacent pixel must be greater than the isophote, new(x,y) is set to white. Finally, if the current pixel is greater than the isophote and an adjacent pixel is less than the isophote, new (x, y) is set to white. The same logic could be handled equally well using CASE statements.

Since it is better to draw the isophotes between the original pixels rather than through them, to draw the best contours, resample images on which you want isophotes drawn by 200% or more. Resampling places interpolated pixels between the original ones, and provides a clean, good-looking contour line.

•Tip: AIP4Win provides the ability to draw a single contour at a fixed pixel value, as well as the ability to draw multiple isophotes that divide an image into regions having equal area.

15.4.2 Frei and Chen Operators

The contour line operator draws boundary lines at a constant pixel value, but it is often necessary to detect boundaries marked by sudden changes in brightness rather than a constant brightness. Although Kirsch, Sobel, and Prewitt operators act as edge detectors, the suite of operators described by Frei and Chen are the best small-kernel operators for detecting edges, lines, points, and ripple.

There are nine Frei and Chen kernels. They are designed to cover the range of small-neighborhood morphologies, which includes edges (high-value pixels on one side and low-value pixels on the other), ripple (intermixed high- and low-value pixels), line (aligned high-value pixels against low-value pixels), and points (isolated high-value pixels). By combining the output of these kernels, you can build a variety of edge- and boundary-detecting operators.

The first pair of Frei and Chen operators, FCOl and FC02, detects edges:

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Understanding Adobe Photoshop Features You Will Use

Understanding Adobe Photoshop Features You Will Use

Adobe Photoshop can be a complex tool only because you can do so much with it, however for in this video series, we're going to keep it as simple as possible. In fact, in this video you'll see an overview of the few tools and Adobe Photoshop features we will use. When you see this video, you'll see how you can do so much with so few features, but you'll learn how to use them in depth in the future videos.

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