Efficient raytracing of deforming point-sampled surfaces

We present efficient data structures and caching schemes to accelerate ray-surface intersections for deforming point-sampled surfaces. By exploiting spatial and temporal coherence of the deformation during the animation, we are able to improve rendering performance by a factor of two to three compared to existing techniques. Starting from a tight bounding sphere hierarchy for the undeformed object, we use a lazy updating scheme to adapt the hierarchy to the deformed surface in each animation step. In addition, we achieve a significant speedup for ray-surface intersections by caching per-ray intersection points. We also present a technique for rendering sharp edges and corners in point-sampled models by introducing a novel surface clipping algorithm. © The Eurographics Association and Blackwell Publishing 2005

Moving Least Squares Correspondences for Iterative Point Set Registration

Registering partial shapes plays an important role in numerous applications in the fields of robotics, vision, and graphics. An essential problem of registration algorithms is the determination of correspondences between surfaces. In this paper, we provide a in-depth evaluation of an approach that computes high-quality correspondences for pair-wise closest point-based iterative registration and compare the results with state-of-the-art registration algorithms. Instead of using a discrete point set for correspondence search, the approach is based on a locally reconstructed continuous moving least squares surface to overcome sampling mismatches in the input shapes. Furthermore, MLS-based correspondences are highly robust to noise. We demonstrate that this strategy outperforms existing approaches in terms of registration accuracy by combining it with the SparseICP local registration algorithm. Our extensive evaluation over several thousand scans from different sources verify that MLS-based approach results in a significant increase in alignment accuracy, surpassing state-of-theart feature-based and probabilistic methods. At the same time, it allows an efficient implementation that introduces only a modest computational overhead

Point-based multiscale surface representation

In this article we present a new multiscale surface representation based on point samples. Given an unstructured point cloud as input, our method first computes a series of point-based surface approximations at successively higher levels of smoothness, that is, coarser scales of detail, using geometric low-pass filtering. These point clouds are then encoded relative to each other by expressing each level as a scalar displacement of its predecessor. Low-pass filtering and encoding are combined in an efficient multilevel projection operator using local weighted least squares fitting. Our representation is motivated by the need for higher-level editing semantics which allow surface modifications at different scales. The user would be able to edit the surface at different approximation levels to perform coarse-scale edits on the whole model as well as very localized modifications on the surface detail. Additionally, the multiscale representation provides a separation in geometric scale which can be understood as a spectral decomposition of the surface geometry. Based on this observation, advanced geometric filtering methods can be implemented that mimic the effects of Fourier filters to achieve effects such as smoothing, enhancement, or band-bass filtering. © 2006 ACM

Meshless Mechanics and Point-Based Visualization Methods for Surgical Simulations

Computer-based modeling and simulation practices have become an integral part of the medical education field. For surgical simulation applications, realistic constitutive modeling of soft tissue is considered to be one of the most challenging aspects of the problem, because biomechanical soft-tissue models need to reflect the correct elastic response, have to be efficient in order to run at interactive simulation rates, and be able to support operations such as cuts and sutures. Mesh-based solutions, where the connections between the individual degrees of freedom (DoF) are defined explicitly, have been the traditional choice to approach these problems. However, when the problem under investigation contains a discontinuity that disrupts the connectivity between the DoFs, the underlying mesh structure has to be reconfigured in order to handle the newly introduced discontinuity correctly. This reconfiguration for mesh-based techniques is typically called dynamic remeshing, and most of the time it causes the performance bottleneck in the simulation. In this dissertation, the efficiency of point-based meshless methods is investigated for both constitutive modeling of elastic soft tissues and visualization of simulation objects, where arbitrary discontinuities/cuts are applied to the objects in the context of surgical simulation. The point-based deformable object modeling problem is examined in three functional aspects: modeling continuous elastic deformations with, handling discontinuities in, and visualizing a point-based object. Algorithmic and implementation details of the presented techniques are discussed in the dissertation. The presented point-based techniques are implemented as separate components and integrated into the open-source software framework SOFA. The presented meshless continuum mechanics model of elastic tissue were verified by comparing it to the Hertzian non-adhesive frictionless contact theory. Virtual experiments were setup with a point-based deformable block and a rigid indenter, and force-displacement curves obtained from the virtual experiments were compared to the theoretical solutions. The meshless mechanics model of soft tissue and the integrated novel discontinuity treatment technique discussed in this dissertation allows handling cuts of arbitrary shape. The implemented enrichment technique not only modifies the internal mechanics of the soft tissue model, but also updates the point-based visual representation in an efficient way preventing the use of costly dynamic remeshing operations

Geometric representation of neuroanatomical data observed in mouse brain at cellular and gross levels

This dissertation studies two problems related to geometric representation of neuroanatomical data: (i) spatial representation and organization of individual neurons, and (ii) reconstruction of three-dimensional neuroanatomical regions from sparse two-dimensional drawings. This work has been motivated by nearby development of new technology, Knife-Edge Scanning Microscopy (KESM), that images a whole mouse brain at cellular level in less than a month. A method is introduced to represent neuronal data observed in the mammalian brain at the cellular level using geometric primitives and spatial indexing. A data representation scheme is defined that captures the geometry of individual neurons using traditional geometric primitives, points and cross-sectional areas along a trajectory. This representation captures inferred synapses as directed links between primitives and spatially indexes observed neurons based on the locations of their cell bodies. This method provides a set of rules for acquisition, representation, and indexing of KESMgenerated data. Neuroanatomical data observed at the gross level provides the underlying regional framework for neuronal circuits. Accumulated expert knowledge on neuroanatomical organization is usually given as a series of sparse two-dimensional contours. A data structure and an algorithm are described to reconstruct separating surfaces among multiple regions from these sparse cross-sectional contours. A topology graph is defined for each region that describes the topological skeleton of the region’s boundary surface and that shows between which contours the surface patches should be generated. A graph-directed triangulation algorithm is provided to reconstruct surface patches between contours. This graph-directed triangulation algorithm combined together with a piecewise parametric curve fitting technique ensures that abutting or shared surface patches are precisely coincident. This method overcomes limitations in i) traditional surfaces-from-contours algorithms that assume binary, not multiple, regionalization of space, and in ii) few existing separating surfaces algorithms that assume conversion of input into a regular volumetric grid, which is not possible with sparse inter-planar resolution

Doctor of Philosophy

dissertationShape analysis is a well-established tool for processing surfaces. It is often a first step in performing tasks such as segmentation, symmetry detection, and finding correspondences between shapes. Shape analysis is traditionally employed on well-sampled surfaces where the geometry and topology is precisely known. When the form of the surface is that of a point cloud containing nonuniform sampling, noise, and incomplete measurements, traditional shape analysis methods perform poorly. Although one may first perform reconstruction on such a point cloud prior to performing shape analysis, if the geometry and topology is far from the true surface, then this can have an adverse impact on the subsequent analysis. Furthermore, for triangulated surfaces containing noise, thin sheets, and poorly shaped triangles, existing shape analysis methods can be highly unstable. This thesis explores methods of shape analysis applied directly to such defect-laden shapes. We first study the problem of surface reconstruction, in order to obtain a better understanding of the types of point clouds for which reconstruction methods contain difficulties. To this end, we have devised a benchmark for surface reconstruction, establishing a standard for measuring error in reconstruction. We then develop a new method for consistently orienting normals of such challenging point clouds by using a collection of harmonic functions, intrinsically defined on the point cloud. Next, we develop a new shape analysis tool which is tolerant to imperfections, by constructing distances directly on the point cloud defined as the likelihood of two points belonging to a mutually common medial ball, and apply this for segmentation and reconstruction. We extend this distance measure to define a diffusion process on the point cloud, tolerant to missing data, which is used for the purposes of matching incomplete shapes undergoing a nonrigid deformation. Lastly, we have developed an intrinsic method for multiresolution remeshing of a poor-quality triangulated surface via spectral bisection

Efficient Point-Cloud Processing with Primitive Shapes

This thesis presents methods for efficient processing of point-clouds based on primitive shapes. The set of considered simple parametric shapes consists of planes, spheres, cylinders, cones and tori. The algorithms developed in this work are targeted at scenarios in which the occurring surfaces can be well represented by this set of shape primitives which is the case in many man-made environments such as e.g. industrial compounds, cities or building interiors. A primitive subsumes a set of corresponding points in the point-cloud and serves as a proxy for them. Therefore primitives are well suited to directly address the unavoidable oversampling of large point-clouds and lay the foundation for efficient point-cloud processing algorithms. The first contribution of this thesis is a novel shape primitive detection method that is efficient even on very large and noisy point-clouds. Several applications for the detected primitives are subsequently explored, resulting in a set of novel algorithms for primitive-based point-cloud processing in the areas of compression, recognition and completion. Each of these application directly exploits and benefits from one or more of the detected primitives' properties such as approximation, abstraction, segmentation and continuability

Surface modeling and rendering with line segments

Master'sMASTER OF SCIENC