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Detecting Symmetry in Scalar Fields Using Augmented Extremum Graphs
"... Fig. 1. Robust scalar field symmetry identification algorithm detects symmetry even in the presence of significant noise in the electron microscopy data of the Rubisco RbcL8RbcX28 complex (EMDB 1654). (left) Volume rendering shows symmetry and noise in the data. (center) A set of seed cells is cho ..."
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Fig. 1. Robust scalar field symmetry identification algorithm detects symmetry even in the presence of significant noise in the electron microscopy data of the Rubisco RbcL8RbcX28 complex (EMDB 1654). (left) Volume rendering shows symmetry and noise in the data. (center) A set of seed cells is chosen as source vertices for traversing the augmented extremum graph of the data. During the traversal, the seed cells merge together to form four symmetric superseeds. Seed cells that belong to a common superseed are shown with the same color. (right) The initial estimate of symmetry is expanded in a region growing stage to identify the symmetric regions. A symmetryaware transfer function highlights the 4fold rotational symmetry detected in the Rubisco complex. Abstract—Visualizing symmetric patterns in the data often helps the domain scientists make important observations and gain insights about the underlying experiment. Detecting symmetry in scalar fields is a nascent area of research and existing methods that detect symmetry are either not robust in the presence of noise or computationally costly. We propose a data structure called the augmented extremum graph and use it to design a novel symmetry detection method based on robust estimation of distances. The augmented extremum graph captures both topological and geometric information of the scalar field and enables robust and computationally efficient detection of symmetry. We apply the proposed method to detect symmetries in cryoelectron microscopy datasets and the experiments demonstrate that the algorithm is capable of detecting symmetry even in the presence of significant noise. We describe novel applications that use the detected symmetry to enhance visualization of scalar field data and facilitate their exploration. Index Terms—Scalar field visualization, extremum graph, Morse decomposition, symmetry detection, data exploration. 1
Online Reconstruction of CAD Geometry
"... Abstract—In reverse engineering and computeraided design (CAD) applications point cloud data is usually manually scanned, reconstructed, and postprocessed in separated steps. When point cloud data resulting from a scanning process do not satisfy certain necessary reconstruction requirements, one m ..."
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Abstract—In reverse engineering and computeraided design (CAD) applications point cloud data is usually manually scanned, reconstructed, and postprocessed in separated steps. When point cloud data resulting from a scanning process do not satisfy certain necessary reconstruction requirements, one must perform scanning again to enable proper reconstruction. Online reconstruction of 3d geometry allows one to generate and update a CAD reconstruction online during the scanning process with an handheld laser scanner. Thus, regions where the scanned data is insufficient for the reconstruction are detected on the fly to allow an immediate correction and improvement of the scanned data. This enables the operator to focus on critical regions in the scanned data to improve the reconstruction quality. We present an online segmentation and online reconstruction of basic geometric primitives. The presented methods allow for a realtime processing of a point stream. They utilize data structures that can be updated at any time when additional data from the stream has to be processed. This data is used to complete and improve the segmentation and reconstruction during the scanning process. Keywordsonline reconstruction; handheld laser scanner; computeraided design I.
Online CAD Reconstruction with Accumulated Means of Local Geometric Properties
"... Abstract. Reconstruction of handheld laser scanner data is used in industry primarily for reverse engineering. Traditionally, scanning and reconstruction are separate steps. The operator of the laser scanner has no feedback from the reconstruction results. Online reconstruction of the CAD geometry ..."
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Abstract. Reconstruction of handheld laser scanner data is used in industry primarily for reverse engineering. Traditionally, scanning and reconstruction are separate steps. The operator of the laser scanner has no feedback from the reconstruction results. Online reconstruction of the CAD geometry allows for such an immediate feedback. We propose a method for online segmentation and reconstruction of CAD geometry from a stream of point data based on means that are updated online. These means are combined to define complex local geometric properties, e.g., to radii and center points of spherical regions. Using means of local scores, planar, cylindrical, and spherical segments are detected and extended robustly with region growing. For the online computation of the means we use socalled accumulated means. They allow for online insertion and removal of values and merging of means. Our results show that this approach can be performed online and is robust to noise. We demonstrate that our method reconstructs spherical, cylindrical, and planar segments on real scan data containing typical errors caused by handheld laser scanners. 1