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Image Segmentation

7.2 Segmentation by Thresholding

Thresholding is a well-known technique for image segmentation [Har92, Sah88]. Thresholding is the operation of converting a multilevel image into a binary image. In a binary image, each pixel value is represented by a single binary digit. In its simplest form, thresholding is a point-based operation that assigns the value of 0 or 1 to each pixel of an image based on a comparison with some global threshold value T.

Thresholding is an attractive early processing step because it leads to significant reduction in data storage and results in binary images that are simpler to analyze. Binary images permit the use of powerful morphological operators for shape and structure-based analysis of image content.

Threshold[img, t]	replaces every element of img less than threshold t with 0, otherwise
HysteresisThreshold[img, {t_L, t_U}]	replaces
OptimumThreshold[h]	returns an optimum threshold value given histogram h using one of three methods (default's algorithm)

Threshold functions.

This loads the package.

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This loads an example image.

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Here we show the binarization of the example image resulting from different choices for the global threshold value T (see Equation (7.2.1)).

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The hysteresis (or double) threshold uses two values. The result contains all the one-pixels coming from the high threshold and those one-pixels from the low threshold that are connected to a high threshold pixel. Eight-connected neighborhoods are used. This threshold technique is commonly used in edge detection to improve edge localization. The following graphic shows a double threshold of the example image. On the left is the double threshold binary image while on the right all the pixels that have values exceeding the low threshold and that are connected to a high threshold pixel are shown in red.

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The central question in threshold segmentation is the selection of a threshold value. This is typically done interactively, based on a visual inspection of the result. However, given some appropriate measure of the quality of the segmentation, it is possible to derive automatic threshold selection algorithms. Over the years many methods have been proposed based on a large number of possible optimization criteria [Sah88, Har92]. The function OptimumThreshold returns a threshold value based on one of three user-selectable minimization criteria. The available choices are: minimum weighted sum of group variances, where the groups are formed from the pixels that fall above and below some chosen threshold [Ots79], minimum average pixel classification error [Kit86], and minimum entropy [Kap85].

Here we use both methods to find the optimum thresholds.

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Here is a visual comparison of the two thresholds.

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In this example, we use amplitude thresholding to segment an example image according to color features. In particular, we are interested in extracting the red, green, and yellow beans from the beans image. This is accomplished by thresholding the individual color channels.

This reads a color image.

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Here are the histograms of the individual color channels.

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We now threshold each individual color channel. The threshold values were chosen based on a visual inspection of the histograms. Recall that point operators, such as threshold, will automatically thread their arguments across the individual color channels.

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We now find all the image regions that do not have red pixels and set them to black, while retaining the original pixel values in the regions occupied by red pixels. Here we use the ImageProcessing function Where and RegionProcessing to selectively change pixel values. This is basically a masking operation and may also be implemented as a matrix multiplication operation.

Where[img]	returns
Where[img, crit]	returns the positions of all elements in img meeting crit

Function Where.

Here we find all the nonred pixels.

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We repeat the process for the green and yellow beans.

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Here we display the segmented images.

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We clean the resulting color channels with a compact morphological filter to reduce small, isolated color patches.

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This shows the final result.

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