Modelling Rod-like Flexible Biological Tissues for Medical Training

This paper outlines a framework for the modelling of slender rod-like biological tissue structures in both global and local scales. Volumetric discretization of a rod-like structure is expensive in computation and therefore is not ideal for applications where real-time performance is essential. In our approach, the Cosserat rod model is introduced to capture the global shape changes, which models the structure as a one-dimensional entity, while the local deformation is handled separately. In this way a good balance in accuracy and efficiency is achieved. These advantages make our method appropriate for the modelling of soft tissues for medical training applications

Physics-Based Modeling of Nonrigid Objects for Vision and Graphics (Dissertation)

This thesis develops a physics-based framework for 3D shape and nonrigid motion modeling for computer vision and computer graphics. In computer vision it addresses the problems of complex 3D shape representation, shape reconstruction, quantitative model extraction from biomedical data for analysis and visualization, shape estimation, and motion tracking. In computer graphics it demonstrates the generative power of our framework to synthesize constrained shapes, nonrigid object motions and object interactions for the purposes of computer animation. Our framework is based on the use of a new class of dynamically deformable primitives which allow the combination of global and local deformations. It incorporates physical constraints to compose articulated models from deformable primitives and provides force-based techniques for fitting such models to sparse, noise-corrupted 2D and 3D visual data. The framework leads to shape and nonrigid motion estimators that exploit dynamically deformable models to track moving 3D objects from time-varying observations. We develop models with global deformation parameters which represent the salient shape features of natural parts, and local deformation parameters which capture shape details. In the context of computer graphics, these models represent the physics-based marriage of the parameterized and free-form modeling paradigms. An important benefit of their global/local descriptive power in the context of computer vision is that it can potentially satisfy the often conflicting requirements of shape reconstruction and shape recognition. The Lagrange equations of motion that govern our models, augmented by constraints, make them responsive to externally applied forces derived from input data or applied by the user. This system of differential equations is discretized using finite element methods and simulated through time using standard numerical techniques. We employ these equations to formulate a shape and nonrigid motion estimator. The estimator is a continuous extended Kalman filter that recursively transforms the discrepancy between the sensory data and the estimated model state into generalized forces. These adjust the translational, rotational, and deformational degrees of freedom such that the model evolves in a consistent fashion with the noisy data. We demonstrate the interactive time performance of our techniques in a series of experiments in computer vision, graphics, and visualization

A spring force formulation for elastically deformable models

Cataloged from PDF version of article.Continuous deformable models are generally represented using a grid of control points. The elastic properties are then modeled using the interactions between these points. The formulations based on elasticity theory express these interactions using stiffness matrices. These matrices store the elastic properties of the models and they should be evolved in time according to changing elastic properties of the models. However, forming the stiffness matrices at any step of an animation is very difficult and sometimes the differential equations that should be solved to produce animation become ill-conditioned. Instead of modeling the elasticities using stiffness matrices, the interactions between model points could be expressed in terms of external spring forces. In this paper, a spring force formulation for animating elastically deformable models is presented. In this formulation, elastic properties of the materials are represented as external spring forces as opposed to forming complicated stiffness matrices. (C) 1997 Elsevier Science Ltd

Active Printed Materials for Complex Self-Evolving Deformations

We propose a new design of complex self-evolving structures that vary over time due to environmental interaction. In conventional 3D printing systems, materials are meant to be stable rather than active and fabricated models are designed and printed as static objects. Here, we introduce a novel approach for simulating and fabricating self-evolving structures that transform into a predetermined shape, changing property and function after fabrication. The new locally coordinated bending primitives combine into a single system, allowing for a global deformation which can stretch, fold and bend given environmental stimulus

Detection and modelling of contacts in explicit finite-element simulation of soft tissue biomechanics

Realistic modelling of soft-tissue biomechanics and mechanical interactions between tissues is an important part of surgical simulation, and may become a valuable asset in surgical image-guidance. Unfortunately, it is also computationally very demanding. Explicit matrix-free FEM solvers have been shown to be a good choice for fast tissue simulation, however little work has been done on contact algorithms for such FEM solvers. This work introduces such an algorithm that is capable of handling the scenarios typically encountered in image-guidance. The responses are computed with an evolution of the Lagrange-multiplier method first used by Taylor and Flanagan in PRONTO 3D with spatio-temporal smoothing heuristics for improved stability with coarser meshes and larger time steps. For contact search, a bounding-volume hierarchy (BVH) capable of identifying self collisions, and which is optimised for the small time steps by reducing the number of bounding-volume refittings between iterations through identification of geometry areas with mostly rigid motion and negligible deformation, is introduced. Further optimisation is achieved by integrating the self-collision criterion in the BVH creation and updating algorithms. The effectiveness of the algorithm is demonstrated on a number of artificial test cases and meshes derived from medical image data

Embedded Implicit Stand-ins for Animated Meshes: a Case of Hybrid Modelling

In this paper we address shape modelling problems, encountered in computer animation and computer games development that are difficult to solve just using polygonal meshes. Our approach is based on a hybrid modelling concept that combines polygonal meshes with implicit surfaces. A hybrid model consists of an animated polygonal mesh and an approximation of this mesh by a convolution surface stand-in that is embedded within it or is attached to it. The motions of both objects are synchronised using a rigging skeleton. This approach is used to model the interaction between an animated mesh object and a viscoelastic substance, normally modelled in implicit form. The adhesive behaviour of the viscous object is modelled using geometric blending operations on the corresponding implicit surfaces. Another application of this approach is the creation of metamorphosing implicit surface parts that are attached to an animated mesh. A prototype implementation of the proposed approach and several examples of modelling and animation with near real-time preview times are presented