This paper presents a segmentation technique to identify the medial axis and the boundary of cranial nerves. We utilize a 3-D deformable one-simplex discrete contour model to extract the medial axis of each cranial nerve. This contour model represents a collection of two-connected vertices linked by edges, where vertex position is determined by a Newtonian expression for vertex kinematics featuring internal and external forces, the latter of which include attractive forces toward the nerve medial axis. We exploit multiscale vesselness filtering and minimal path techniques in the medial axis extraction method, which also computes a radius estimate along the path. Once we have the medial axis and the radius function of a nerve, we identify the nerve surface using a two-simplex deformable model, which expands radially and can accommodate any nerve shape. As a result, the method proposed here combines the benefits of explicit contour and surface models, while also achieving a cornerstone for future work that will emphasize shape statistics, static collision with other critical structures, and tree-shape analysis.

The link between genetic regulation and the definition of form and size during morphogenesis remains largely an open question in both plant and animal biology. This is partially due to the complexity of the process, involving extensive molecular networks, multiple feedbacks between different scales of organization and physical forces operating at multiple levels. Here we present a conceptual and modeling framework aimed at generating an integrated understanding of morphogenesis in plants. This framework is based on the biophysical properties of plant cells, which are under high internal turgor pressure, and are prevented from bursting because of the presence of a rigid cell wall. To control cell growth, the underlying molecular networks must interfere locally with the elastic and/or plastic extensibility of this cell wall. We present a model in the form of a three dimensional (3D) virtual tissue, where growth depends on the local modulation of wall mechanical properties and turgor pressure. The model shows how forces generated by turgor-pressure can act both cell autonomously and non-cell autonomously to drive growth in different directions. We use simulations to explore lateral organ formation at the shoot apical meristem. Although different scenarios lead to similar shape changes, they are not equivalent and lead to different, testable predictions regarding the mechanical and geometrical properties of the growing lateral organs. Using flower development as an example, we further show how a limited number of gene activities can explain the complex shape changes that accompany organ outgrowth.

We present a unification of the two main approaches to simulate deformable solids, namely elasticity and constraints. Elasticity accurately handles soft to moderately stiff objects, but becomes numerically hard as stiffness increases. Constraints efficiently handle high stiffness, but when integrated in time they can suffer from instabilities in the nullspace directions, generating spurious transverse vibrations when pulling hard on thin inextensible objects or articulated rigid bodies. We show that geometric stiffness, the tensor encoding the change of force directions (as opposed to intensities) in response to a change of positions, is the missing piece between the two approaches. This previously neglected stiffness term is easy to implement and dramatically improves the stability of inextensible objects and articulated chains, without adding artificial bending forces. This allows time step increases up to several orders of magnitude using standard linear solvers.

Characters with precise internal anatomy are important in film and visual effects, as well as in medical applications. We propose the first semi-automatic method for creating anatomical structures, such as bones, muscles, viscera and fat tissues. This is done by transferring a reference anatomical model from an input template to an arbitrary target character, only defined by its boundary representation (skin). The fat distribution of the target character needs to be specified. We can either infer this information from MRI data, or allow the users to express their creative intent through a new editing tool. The rest of our method runs automatically: it first transfers the bones to the target character, while maintaining their structure as much as possible. The bone layer, along with the target skin eroded using the fat thickness information, are then used to define a volume where we map the internal anatomy of the source model using harmonic (Laplacian) deformation. This way, we are able to quickly generate anatomical models for a large range of target characters, while maintaining anatomical constraints.

A new method to simulate deformable objects with heterogeneous material properties and complex geometries is presented. Given a volumetric map of the material properties and an arbitrary number of control nodes, a distribution of the nodes is computed automatically, as well as the associated shape functions. Reference frames attached to the nodes are used to apply skeleton subspace deformation across the volume of the objects. A continuum mechanics formulation is derived from the displacements and the material properties. We introduce novel material-aware shape functions in place of the traditional radial basis functions used in meshless frameworks. In contrast with previous approaches, these allow coarse deformation functions to efficiently resolve non-uniform stiffnesses. Complex models can thus be simulated at high frame rates using a small number of control nodes.

We present a new type of deformable model which combines the realism of physically-based continuum mechanics models and the usability of frame-based skinning methods. The degrees of freedom are coordinate frames. In contrast with traditional skinning, frame positions are not scripted but move in reaction to internal body forces. The displacement field is smoothly interpolated using dual quaternion blending. The deformation gradient and its derivatives are computed at each sample point of a deformed object and used in the equations of Lagrangian mechanics to achieve physical realism. This allows easy and very intuitive definition of the degrees of freedom of the deformable object. The meshless discretization allows on-the-fly insertion of frames to create local deformations where needed. We formulate the dynamics of these models in detail and describe some precomputations that can be used for speed. We show that our method is effective for behaviors ranging from simple unimodal deformations to complex realistic deformations comparable with Finite Element simulations. To encourage its use, the software will be freely available in the simulation platform SOFA.

Abstract Creating and animating subject‐specific anatomical models is traditionally a difficult process involving medical image segmentation, geometric corrections and the manual definition of kinematic parameters. In this paper, we introduce a novel template morphing algorithm that facilitates three‐dimensional modelling and parameterization of skeletons. Target data can be either medical images or surfaces of the whole skeleton. We incorporate prior knowledge about bone shape, the feasible skeleton pose and the morphological variability in the population. This allows for noise reduction, bone separation and the transfer, from the template, of anatomical and kinematical information not present in the input data. Our approach treats both local and global deformations in successive regularization steps: smooth elastic deformations are represented by an as‐rigid‐as‐possible displacement field between the reference and current configuration of the template, whereas global and discontinuous displacements are estimated through a projection onto a statistical shape model and a new joint pose optimization scheme with joint limits.

Abstract We present a methodology for motion tracking and visualization of the hip joint by combining MR images and optical motion capture systems. MRI is typically used to capture the subject's anatomy while optical systems are used to capture and analyse the relative movement between adjacent bones of the joint. Reflective markers are attached to the subject's skin and their trajectories are tracked and processed. However, the skin surface deforms while in motion due to muscle contraction leading to significant errors in the estimation of trajectories. In order to reduce these errors, we use MR images to capture both the anatomy and the trajectories of the bone. Prior to the scanning, we attach skin markers to the subject in order to analyse the markers displacements relative to the bone. We reconstruct the anatomical models of the subject and we compute the markers trajectories from the images. Using these calculated trajectories, we select the best markers configuration based on the criteria of markers displacements. The optimized configuration is used for recording external movements with the optical motion capture system. The resulting animation is mapped onto the virtual body of the subject including internal bones and the joint motion is visualized. Copyright © 2004 John Wiley & Sons, Ltd.

3D discretized objects become more and more present in many applications for computer graphics. The need to store and transmit these data grows permanently. This paper introduces a new scheme of 3D object progressive transmission. It is based on an union of cone sections and balls selected from the medial axis and optimized for a better scalability in terms of bit rates and quality. This representation of a 3D object is a lossless approach and is very efficient for compression and progressive transmission, as shown in the results presented in this paper.