Fast and robust curve skeletonization for real-world elongated objects

We consider the problem of extracting curve skeletons of three-dimensional, elongated objects given a noisy surface, which has applications in agricultural contexts such as extracting the branching structure of plants. We describe an efficient and robust method based on breadth-first search that can determine curve skeletons in these contexts. Our approach is capable of automatically detecting junction points as well as spurious segments and loops. All of that is accomplished with only one user-adjustable parameter. The run time of our method ranges from hundreds of milliseconds to less than four seconds on large, challenging datasets, which makes it appropriate for situations where real-time decision making is needed. Experiments on synthetic models as well as on data from real world objects, some of which were collected in challenging field conditions, show that our approach compares favorably to classical thinning algorithms as well as to recent contributions to the field.Comment: 47 pages; IEEE WACV 2018, main paper and supplementary materia

An Unified Multiscale Framework for Planar, Surface, and Curve Skeletonization

Computing skeletons of 2D shapes, and medial surface and curve skeletons of 3D shapes, is a challenging task. In particular, there is no unified framework that detects all types of skeletons using a single model, and also produces a multiscale representation which allows to progressively simplify, or regularize, all skeleton types. In this paper, we present such a framework. We model skeleton detection and regularization by a conservative mass transport process from a shape's boundary to its surface skeleton, next to its curve skeleton, and finally to the shape center. The resulting density field can be thresholded to obtain a multiscale representation of progressively simplified surface, or curve, skeletons. We detail a numerical implementation of our framework which is demonstrably stable and has high computational efficiency. We demonstrate our framework on several complex 2D and 3D shapes

Occlusion Reasoning for Skeleton Extraction of Self-Occluded Tree Canopies

In this work, we present a method to extract the skeleton of a self-occluded tree canopy by estimating the unobserved structures of the tree. A tree skeleton compactly describes the topological structure and contains useful information such as branch geometry, positions and hierarchy. This can be critical to planning contact interactions for agricultural manipulation, yet is difficult to gain due to occlusion by leaves, fruits and other branches. Our method uses an instance segmentation network to detect visible trunk, branches, and twigs. Then, based on the observed tree structures, we build a custom 3D likelihood map in the form of an occupancy grid to hypothesize on the presence of occluded skeletons through a series of minimum cost path searches. We show that our method outperforms baseline methods in highly occluded scenes, demonstrated through a set of experiments on a synthetic tree dataset. Qualitative results are also presented on a real tree dataset collected from the field.Comment: 7 pages, 10 figures, submitted to ICRA 202

Semiautomated Skeletonization of the Pulmonary Arterial Tree in Micro-CT Images

We present a simple and robust approach that utilizes planar images at different angular rotations combined with unfiltered back-projection to locate the central axes of the pulmonary arterial tree. Three-dimensional points are selected interactively by the user. The computer calculates a sub- volume unfiltered back-projection orthogonal to the vector connecting the two points and centered on the first point. Because more x-rays are absorbed at the thickest portion of the vessel, in the unfiltered back-projection, the darkest pixel is assumed to be the center of the vessel. The computer replaces this point with the newly computer-calculated point. A second back-projection is calculated around the original point orthogonal to a vector connecting the newly-calculated first point and user-determined second point. The darkest pixel within the reconstruction is determined. The computer then replaces the second point with the XYZ coordinates of the darkest pixel within this second reconstruction. Following a vector based on a moving average of previously determined 3- dimensional points along the vessel\u27s axis, the computer continues this skeletonization process until stopped by the user. The computer estimates the vessel diameter along the set of previously determined points using a method similar to the full width-half max algorithm. On all subsequent vessels, the process works the same way except that at each point, distances between the current point and all previously determined points along different vessels are determined. If the difference is less than the previously estimated diameter, the vessels are assumed to branch. This user/computer interaction continues until the vascular tree has been skeletonized

A Geometric Approach for Deciphering Protein Structure from Cryo-EM Volumes

Electron Cryo-Microscopy or cryo-EM is an area that has received much attention in the recent past. Compared to the traditional methods of X-Ray Crystallography and NMR Spectroscopy, cryo-EM can be used to image much larger complexes, in many different conformations, and under a wide range of biochemical conditions. This is because it does not require the complex to be crystallisable. However, cryo-EM reconstructions are limited to intermediate resolutions, with the state-of-the-art being 3.6A, where secondary structure elements can be visually identified but not individual amino acid residues. This lack of atomic level resolution creates new computational challenges for protein structure identification. In this dissertation, we present a suite of geometric algorithms to address several aspects of protein modeling using cryo-EM density maps. Specifically, we develop novel methods to capture the shape of density volumes as geometric skeletons. We then use these skeletons to find secondary structure elements: SSEs) of a given protein, to identify the correspondence between these SSEs and those predicted from the primary sequence, and to register high-resolution protein structures onto the density volume. In addition, we designed and developed Gorgon, an interactive molecular modeling system, that integrates the above methods with other interactive routines to generate reliable and accurate protein backbone models

clDice -- a Novel Topology-Preserving Loss Function for Tubular Structure Segmentation

Accurate segmentation of tubular, network-like structures, such as vessels, neurons, or roads, is relevant to many fields of research. For such structures, the topology is their most important characteristic; particularly preserving connectedness: in the case of vascular networks, missing a connected vessel entirely alters the blood-flow dynamics. We introduce a novel similarity measure termed centerlineDice (short clDice), which is calculated on the intersection of the segmentation masks and their (morphological) skeleta. We theoretically prove that clDice guarantees topology preservation up to homotopy equivalence for binary 2D and 3D segmentation. Extending this, we propose a computationally efficient, differentiable loss function (soft-clDice) for training arbitrary neural segmentation networks. We benchmark the soft-clDice loss on five public datasets, including vessels, roads and neurons (2D and 3D). Training on soft-clDice leads to segmentation with more accurate connectivity information, higher graph similarity, and better volumetric scores.Comment: * The authors Suprosanna Shit and Johannes C. Paetzold contributed equally to the wor