Local Grayscale Granulometries Based on Opening Trees

Granulometries are morphological image analysis tools that are particularly useful for estimating object sizes in binary and grayscale images, or for characterizing textures based on their pattern spectra (i.e., granulometric curves). Though granulometric information is typically extracted globally for an image or a collection of images, local granulometries can also be useful for such applications as segmentation of texture images. However, computing local granulometries from a grayscale image by means of traditional sequences of openings and closings is either prohibitively slow, or produces results that are too coarse to be really useful. In the present paper, using the concept of opening trees proposed in [14], new local grayscale granulometry algorithms are introduced, that are both accurate and e cient. These algorithms can be used for any granulometry based on openings or closings with line segments or combinations of line segments. Among others, these local granulometries can be used to compute size transforms directly from grayscale images, a grayscale extension of the concept of an opening function. Other applications include adaptive openings and closings, as well as granulometric texture segmentation.