Abstract
We present a method to reconstruct a disordered network of thin biopolymers, such as collagen gels, from three-dimensional (3D) image stacks recorded with a confocal microscope. The method is based on a template matching algorithm that simultaneously performs a binarization and skeletonization of the network. The size and intensity pattern of the template is automatically adapted to the input data so that the method is scale invariant and generic. Furthermore, the template matching threshold is iteratively optimized to ensure that the final skeletonized network obeys a universal property of voxelized random line networks, namely, solid-phase voxels have most likely three solid-phase neighbors in a neighborhood. This optimization criterion makes our method free of user-defined parameters and the output exceptionally robust against imaging noise.
Highlights
Many biological materials, such as the cytoskeleton or the extracellular matrix, self-organize into complex networks by the polymerization of protein molecules into fibrils (Fig. 1)
If the thickness of the fibrils is negligible compared to the pore size, the resulting structure can be mathematically described as a disordered line network
We focus on collagen gels recorded by confocal reflection microscopy, which does not require fluorescent staining, but leads to a so-called blind spot effect: the apparent brightness of fibers decreases with their angle relative to the imaging plane, leaving all fibers beyond a critical cut-off angle invisible [15]
Summary
Many biological materials, such as the cytoskeleton or the extracellular matrix, self-organize into complex networks by the polymerization of protein molecules into fibrils (Fig. 1). If the thickness of the fibrils is negligible compared to the pore size, the resulting structure can be mathematically described as a disordered line network. One aspect of the reconstruction is the binarization of the intensity values of the image stack, so that each voxel is assigned one of two possible values, corresponding either to the solid phase (1, collagen fibers) or the liquid phase (0, surrounding medium). Another aspect of the reconstruction is the skeletonization, so that the optically broadened fibers are reduced to their central (medial) axis, with a width of only one voxel
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