Relationship between Extinction Filters and Attribute Filters

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Attribute filters, such as the hmax, vmax, and the area-open may also be used to set the number of extrema to be preserved in an image. The procedure is simple. First, the extinction values of the crescent attribute being analyzed have to be calculated. Then, the extinction histogram is computed. The relationship between the number of extrema in the image and the parameter of the attribute filter is given by the curve attribute value versus the number of maxima minus the cumulative distribution of the extinction histogram. This curve may have discontinuities, since there may be leaves with the same extinction value, therefore when using attribute filters often it is not possible to set the exact number of extrema to be preserved. This case is illustrated in Figure 1. The height extinction histogram of the Cameraman sample image is shown in Figure 1(a). The curve height versus number of extrema is shown in Figure 1(b). The zoom in the plot highlights the discontinuities in this curve. For instance, if the image is filtered with the hmax filter with the number of maxima in the resulting image will be , but if it is filtered with the number of maxima in the resulting image will be , it is not possible to obtain exactly maxima using the hmax filter, while with the Height EF it is possible. The EF can use a second criteria to choose between the maxima that have a extinction tie.

The fact that the EF can set exactly the number of maxima to be preserved in the image may be an advantage, since in many segmentation problems we are looking for a specific number of regions in the image, and many segmentation techniques use the maxima in the image as seeds to the segmentation process.

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