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IMAGE PROGRESSING FUNDAMENTALS

Part 2: Math, Math, Math

by James Antonakos

Start ý Blob Analysis ý Edge DetectionýBehind the Mask ý A Helping Hand from Fourier ý Please Sir, May I Have Some More? ý Sources and PDF

EDGE DETECTIONýBEHIND THE MASK

If your goal is to count all the blobs that are present in an image (as in counting the number of red blood cells or IC chips on an assembly line), the first step is to identifying the edges of each object. An edge in an image is the boundary between two significantly different pixel values (black to white or white to black). So, you must search through the image looking for these changes in order to identify edges. After they are found, the pixels are modified so that the edge is enhanced and easily seen.

Photos 2aýc show horizontal edges, vertical edges, and both horizontal and vertical edges, respectively. Notice that horizontal edges do not have to be completely horizontal, simply close enough to horizontal to be detected. The same is true for vertical edges also.

a)	b)	c)
Photos 2aýcý(a) is the result of applying a horizontal mask to the image. Notice that all horizontal portions of the image have been enhanced, while non-horizontal portions are barely visible. (b) is the result of applying vertical mask to the image. All non-vertical portions of the image are eliminated or reduced. And, (c) is the result of applying the Sobel mask to the image. All horizontal and vertical edges are enhanced. (click to enlarge)

An easy way to detect edges in an image is to use a 3 ý 3 matrix, or mask, of values that use pixels in the neighborhood of the target pixel to affect how the pixel is modified. Figures 3 and 4 show the mask values used for horizontal and vertical edge detection. The corresponding 3 ý 3 array of pixel values (eight pixels surrounding the center target pixel) are multiplied by the numbers in the mask and added together, with the result replacing the center pixel value. The masks are swiped over each pixel in a row, generating a new line of pixels in the result image.

Figure 3ýThe mask values for horizontal edge detection can be seen here.

Clearly, plenty of multiplication and addition must be performed to generate the new image. In fact, nine multiplies and eight additions are required for each pixel, giving a total of almost 590,000 multiplies and 524,000 additions for a 256 ý 256 image.

Figure 4ýThe mask values for vertical edge detection can be seen here.

Applying both of the masks shown in Figures 3 and 4 to the image will reveal both horizontal and vertical edges (as indicated in Photo 2c). Together, these two operations make up the Sobel mask, just one of many different masks used to enhance or alter an image.

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