Chapter 4 SEGMENTATION

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16 CHAPTER 4. <strong>SEGMENTATION</strong>Figure 4.7: Histograms of muscle fibres image: (a) original pixel values, displayed on a squarerootscale; (b) image after smoothing by Gaussian filter (σ 2 =6 2 ); (c) bivariate histogram of3original pixel values and those after smoothing, with all counts exceeding 25 displayed as blackand the parallel diagonal lines indicating the points extracted for (d); (d) histogram of pixelvalues after smoothing those values within 5 of those before smoothing, the arrows indicate thethresholds used in Fig 4.8.
4.1. THRESHOLDING 17Figure 4.8: Thresholded muscle fibres image. Pixels in the range 0 to 50 and 166 to 255 aredisplayed as white, those between 51 and 90 are black, between 91 and 130 they are dark greyand between 131 and 165 they are shown as light grey.histogram from non-edge pixels only, its peaks should be clearer.Another way of using contextual information is by applying a majority filter to a segmentedimage, termed post-classification smoothing. For example, if pixel (i, j) has been labelledas category g ij by a segmentation algorithm, then a majority filter relabels (i, j) asthe most common category in a (2m +1)× (2m + 1) window centred on pixel (i, j), i.e. the set{g i+k,j+l for k, l = −m,...,m}.Contextual information can also be used in automatic segmentation algorithms. Mardia andHainsworth (1988) investigated incorporating post-classification smoothing into a thresholdingalgorithm. (Their paper also provides a succinct review of algorithms for thresholding imageswhose pixel values are mixtures of Gaussian distributions.) To explain the method, we willconsider the simplest case. First we will discuss it in words, and then more formally.From an initial guess at a threshold, an image is segmented. Then the classified image issmoothed using a majority filter, so that neighbouring pixels are more often classified thesame. Mean pixel values are evaluated in each category and the threshold is re-estimated usingthe intermeans criterion (§4.1.1). The image is segmented and smoothed again, and so on untilthe threshold does not change between successive iterations. Formally:1. Make an initial guess at a threshold t.
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Chapter 4 SEGMENTATION

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