Efficient Computation of Greyscale Path Openings

Path openings are morphological operators that are used to preserve long, thin, and curved structures in images. They have the ability to adapt to local image structures,which allows them to detect lines that are not perfectly straight. They are applicable in extracting cracks, roads, and similar structures. Although path openings are very efficient to implement for binary images, the greyscale case is more problematic. This study provides an analysis of the main existing greyscale algorithm, and shows that although its time complexity can be quadratic in the number of pixels, this is optimal in terms of the output (if the full opening transform is created). Also, it is shown that under many circumstances the worst-case running time is much less than quadratic. Finally, a new algorithm is provided,which has the same time complexity, but is simpler, faster in practice and more amenable to parallelizatio

Path-Based Mathematical Morphology on Tensor Fields

Traditional path-based morphology allows finding long, approximately straight, paths in images. Although originally applied only to scalarimages, we show how this can be a very good fit for tensor fields. We do thisby constructing directed graphs representing such data, and then modifyingthe traditional path opening algorithm to work on these graphs. Cycles aredealt with by finding strongly connected components in the graph. Some examples of potential applications are given, including path openings that arenot limited to a specific set of orientations.<br/