The chord length transform and the segmentation of crossing fibres

Segmentation of crossing fibres is a complex problem of image processing. In the present paper, various solutions are presented basing on tools of morphological image processing. Two new image transforms are introduced--the lineal distance transform and the chord length transform. Both transforms are applied to two-dimensional images and their results are three-dimensional images. Thus, the segmentation problem originally formulated for crossing fibres observed in a two-dimensional image can be reformulated as a segmentation problem in a three-dimensional image. This can be solved by a segmentation in the three-dimensional image. Algorithms for the lineal distance transform and the chord length transform are given and their use in image analysis is demonstrated. Furthermore, the chord length distribution function of the foreground of a binary image can efficiently be estimated via the chord length transform.