Homological methods for extraction and analysis of linear features in multidimensional images

We show that the problem of extracting linear features from a noisy image and counting the number of branching points may be successfully solved by homological methods applied directly to the image without the need of skeletonization and the analysis of the resulting graph. The method is based on the superimposition of a mask set over the original image and works even when the homology of the feature is trivial and in arbitrary dimension. We tested the method on computer-generated data, 2D images of blood vessels, 2D satellite images and 3D images of collagen fibers.