Fast Penetration Depth Estimation for Elastic Bodies

We present a fast penetration depth estimation algorithm between deformable polyhedral objects. We assume the continuum of non-rigid models are discretized using standard techniques, such as finite element or finite difference methods. As the objects deform, the pre-computed distance fields are deformed accordingly to estimate penetration depth, allowing enforcement of non-penetration constraints between two colliding elastic bodies. This approach can automatically handle self-penetration and inter-penetration in a uniform manner. We demonstrate its effectiveness on moderately complex simulation scenes

Design and development of a VR system for exploration of medical data using haptic rendering and high quality visualization

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Tetrahedral Image-to-Mesh Conversion Software for Anatomic Modeling of Arteriovenous Malformations

We describe a new implementation of an adaptive multi-tissue tetrahedral mesh generator targeting anatomic modeling of Arteriovenous Malformation (AVM) for surgical simulations. Our method, initially constructs an adaptive Body-Centered Cubic (BCC) mesh of high quality elements. Then, it deforms the mesh surfaces to their corresponding physical image boundaries, hence, improving the mesh fidelity and smoothness. Our deformation scheme, which builds upon the ITK toolkit, is based on the concept of energy minimization, and relies on a multi-material point-based registration. It uses non-connectivity patterns to implicitly control the number of the extracted feature points needed for the registration, and thus, adjusts the trade-off between the achieved mesh fidelity and the deformation speed. While many medical imaging applications require robust mesh generation, there are few codes available to the public. We compare our implementation with two similar open-source image-to-mesh conversion codes: (1) Cleaver from US, and (2) CGAL from EU. Our evaluation is based on five isotropic/anisotropic segmented images, and relies on metrics like geometric & topologic fidelity, mesh quality, gradation and smoothness. The implementation we describe is open- source and it will be available within: (i) the 3D Slicer package for visualization and image analysis from Harvard Medical School, and (ii) an interactive simulator for neurosurgical procedures involving vasculature using SOFA, a framework for real-time medical simulation developed by INRIA

Deformable Simplicial Complexes

In this dissertation we present a novel method for deformable interface tracking in 2D and 3D|deformable simplicial complexes (DSC). Deformable interfaces are used in several applications, such as fluid simulation, image analysis, reconstruction or structural optimization. In the DSC method, the interface (curve in 2D; surface in 3D) is represented explicitly as a piecewise linear curve or surface. However, the domain is also subject to discretization: triangulation in 2D; tetrahedralization in 3D. This way, the interface can be alternatively represented as a set of edges/triangles separating triangles/tetrahedra marked as outside from those marked as inside. Such an approach allows for robust topological adaptivity. Among other advantages of the deformable simplicial complexes there are: space adaptivity, ability to handle and preserve sharp features, possibility for topology control. We demonstrate those strengths in several applications. In particular, a novel, DSC-based fluid dynamics solver has been developed during the PhD project. A special feature of this solver is that due to the fact that DSC maintains an explicit interface representation, surface tension is more easily dealt with. One particular advantage of DSC is the fact that as an alternative to topology adaptivity, topology control is also possible. This is exploited in the construction of cut loci on tori where a front expands from a single point on a torus and stops when it self-intersects

Deformable Multisurface Segmentation of the Spine for Orthopedic Surgery Planning and Simulation

Purpose: We describe a shape-aware multisurface simplex deformable model for the segmentation of healthy as well as pathological lumbar spine in medical image data. Approach: This model provides an accurate and robust segmentation scheme for the identification of intervertebral disc pathologies to enable the minimally supervised planning and patient-specific simulation of spine surgery, in a manner that combines multisurface and shape statistics-based variants of the deformable simplex model. Statistical shape variation within the dataset has been captured by application of principal component analysis and incorporated during the segmentation process to refine results. In the case where shape statistics hinder detection of the pathological region, user assistance is allowed to disable the prior shape influence during deformation. Results: Results demonstrate validation against user-assisted expert segmentation, showing excellent boundary agreement and prevention of spatial overlap between neighboring surfaces. This section also plots the characteristics of the statistical shape model, such as compactness, generalizability and specificity, as a function of the number of modes used to represent the family of shapes. Final results demonstrate a proof-of-concept deformation application based on the open-source surgery simulation Simulation Open Framework Architecture toolkit. Conclusions: To summarize, we present a deformable multisurface model that embeds a shape statistics force, with applications to surgery planning and simulation

Shape Animation with Combined Captured and Simulated Dynamics

We present a novel volumetric animation generation framework to create new types of animations from raw 3D surface or point cloud sequence of captured real performances. The framework considers as input time incoherent 3D observations of a moving shape, and is thus particularly suitable for the output of performance capture platforms. In our system, a suitable virtual representation of the actor is built from real captures that allows seamless combination and simulation with virtual external forces and objects, in which the original captured actor can be reshaped, disassembled or reassembled from user-specified virtual physics. Instead of using the dominant surface-based geometric representation of the capture, which is less suitable for volumetric effects, our pipeline exploits Centroidal Voronoi tessellation decompositions as unified volumetric representation of the real captured actor, which we show can be used seamlessly as a building block for all processing stages, from capture and tracking to virtual physic simulation. The representation makes no human specific assumption and can be used to capture and re-simulate the actor with props or other moving scenery elements. We demonstrate the potential of this pipeline for virtual reanimation of a real captured event with various unprecedented volumetric visual effects, such as volumetric distortion, erosion, morphing, gravity pull, or collisions

Real-time hybrid cutting with dynamic fluid visualization for virtual surgery

It is widely accepted that a reform in medical teaching must be made to meet today's high volume training requirements. Virtual simulation offers a potential method of providing such trainings and some current medical training simulations integrate haptic and visual feedback to enhance procedure learning. The purpose of this project is to explore the capability of Virtual Reality (VR) technology to develop a training simulator for surgical cutting and bleeding in a general surgery

Animating physical phenomena with embedded surface meshes

Accurate computational representations of highly deformable surfaces are indispensable in the fields of computer animation, medical simulation, computer vision, digital modeling, and computational physics. The focus of this dissertation is on the animation of physics-based phenomena with highly detailed deformable surfaces represented by triangle meshes. We first present results from an algorithm that generates continuum mechanics animations with intricate surface features. This method combines a finite element method with a tetrahedral mesh generator and a high resolution surface mesh, and it is orders of magnitude more efficient than previous approaches. Next, we present an efficient solution for the challenging problem of computing topological changes in detailed dynamic surface meshes. We then introduce a new physics-inspired surface tracking algorithm that is capable of preserving arbitrarily thin features and reproducing realistic fine-scale topological changes like Rayleigh-Plateau instabilities. This physics-inspired surface tracking technique also opens the door for a unique coupling between surficial finite element methods and volumetric finite difference methods, in order to simulate liquid surface tension phenomena more efficiently than any previous method. Due to its dramatic increase in computational resolution and efficiency, this method yielded the first computer simulations of a fully developed crown splash with droplet pinch off.Ph.D.Committee Chair: Turk, Greg; Committee Member: Essa, Irfan; Committee Member: Liu, Karen; Committee Member: Mucha, Peter J.; Committee Member: Rossignac, Jare

Distance fields on unstructured grids: Stable interpolation, assumed gradients, collision detection and gap function

AbstractThis article presents a novel approach to collision detection based on distance fields. A novel interpolation ensures stability of the distances in the vicinity of complex geometries. An assumed gradient formulation is introduced leading to a C1-continuous distance function. The gap function is re-expressed allowing penalty and Lagrange multiplier formulations. The article introduces a node-to-element integration for first order elements, but also discusses signed distances, partial updates, intermediate surfaces, mortar methods and higher order elements. The algorithm is fast, simple and robust for complex geometries and self contact. The computed tractions conserve linear and angular momentum even in infeasible contact. Numerical examples illustrate the new algorithm in three dimensions

Woodification of polygonal meshes

An evolving polygonal mesh based on stem\u27s tree growth coupled with a physical simulation of bark\u27s cracking is presented. This process is denominated woodification. Whereas previous approaches use a fixed resolution voxel grid, woodification is built on the deformable simplicial complex representation, which robustly simulates growth with adaptive subdivision. The approach allows any meshed object to be grown and textured. Features, such as interaction with obstacles, attributes interpolation, and sketching tools, are added to provide control during the woodifible process