27 June 1988 Feature-Size Dependent Selective Edge Enhancement Of X-Ray Images
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Morphological filters are nonlinear signal transformations that operate on a picture directly in the space domain. Such filters are based on the theory of mathematical morphology as formulated by Matheron [1] and Serra [2,3]. Sternberg [4,5] generalized earlier results to include graytone images. He also introduced the "rolling ball" morphological operator and pointed out that it can be used for edge enhancement. This paper reports on an variation of the rolling ball algorithm. An introduction to some of the concepts used here was given by Herman [6]. The filter being presented here features a "mask" operator (called a "structuring element" in some of the literature) which is a function of the two spatial coordinates x and y. The two basic mathematical operations are called "masked erosion" and "masked dilation". In the case of masked erosion the mask is passed over the input image in a raster pattern. At each position of the mask, the pixel values under the mask are multiplied by the mask pixel values. Then the output pixel value, located at the center position of the mask, is set equal to the minimum of the product of the mask and input values. Similarly, for masked dilation, the output pixel value is the maximum of the product of the input and the mask pixel values. The two basic processes of dilation and erosion can be used to construct the next level of operations the "positive sieve" [4] (also called "open-ing") and the "negative sieve" ("closing"). The positive sieve modifies the peaks in the image, whereas the negative sieve works on image valleys. The positive sieve is implemented by passing the output of the masked erosion step through the masked dilation function. The negative sieve reverses this procedure, using a dilation followed by an erosion. Each such sifting operator is characterized by a "hole size". If one considers a two dimensional image as a three dimensional function or surface over the two coordinates x and y, then a positive sieve will eliminate all peaks of this surface which have a cross section parallel to the x-y plane which is smaller than the hole size. Conversely, a negative sieve will clip all valleys smaller than the hole size. The hole size of a masked sifting operator in any given direction is equal to the size of the mask minus one pixel in that direction. It will be shown that the choice of hole size will select the range of pixel detail sizes which are to be enhanced. The shape of the mask will govern the shape of the enhancement. Finally positive sifting is used to enhance positive-going (peak) features, whereas negative sifting enhances the negative-going (valley) landmarks.
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Stephen Herman, "Feature-Size Dependent Selective Edge Enhancement Of X-Ray Images", Proc. SPIE 0914, Medical Imaging II, (27 June 1988); doi: 10.1117/12.968694; https://doi.org/10.1117/12.968694

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