Animation of deformable models

Although kinematic modelling methods are adequate for describing the shapes of static objects, they are insufficient when it comes to producing realistic animation. Physically based modelling remedies this problem by including forces, masses, strain energies and other physical quantities. The paper describes a system for the animation of deformable models. The system uses physically based modelling methods and approaches from elasticity theory for animating the models. Two different formulations, namely the primal formulation and the hybrid formulation, are implemented so that the user can select the one most suitable for an animation depending on the rigidity of the models. Collision of the models with impenetrable obstacles and constraining of the model points to fixed positions in space are implemented for use in the animations.     

Elastically adaptive deformable models

We present a technique for the automatic adaptation of a deformable model's elastic parameters within a Kalman filter framework for shape estimation applications. The novelty of the technique is that the model's elastic parameters are not constant, but spatio-temporally varying. The variation of the elastic parameters depends on the distance of the model from the data and the rate of change of this distance. Each pass of the algorithm uses physics-based modeling techniques to iteratively adjust both the geometric and the elastic degrees of freedom of the model in response to forces that are computed from the discrepancy between the model and the data. By augmenting the state equations of an extended Kalman filter to incorporate these additional variables, we are able to significantly improve the quality of the shape estimation. Therefore, the model's elastic parameters are always initialized to the same value and they are subsequently modified depending on the data and the noise distribution. We present results demonstrating the effectiveness of our method for both two-dimensional and three-dimensional data.     

Heating and melting deformable models

We develop physically-based graphics models of non-rigid objects capable of heat conduction, thermoelasticity, melting and fluid-like behaviour in the molten state. These deformable models feature non-rigid dynamics governed by Lagrangian equations of motion and conductive heat transfer governed by the heat equation for non-homogeneous, non-isotropic media. In its solid state, the discretized model is an assembly of hexahedral finite elements in which thermoelastic units interconnect particles situated in a lattice. The stiffness of a thermoelastic unit decreases as its temperature increases, and the unit fuses when its temperature exceeds the melting point. The molten state of the model involves a molecular dynamics simulation in which ‘fluid’ particles that have broken free from the lattice interact through long-range attraction forces and short-range repulsion forces. We present a physically-based animation of a thermoelastic model in a simulated physical world populated by hot constraint surfaces.     

Boundary finding with parametrically deformable models

Segmentation using boundary finding is enhanced both by considering the boundary as a whole and by using model-based global shape information. The authors apply flexible constraints, in the form of a probabilistic deformable model, to the problem of segmenting natural 2-D objects whose diversity and irregularity of shape make them poorly represented in terms of fixed features or form. The parametric model is based on the elliptic Fourier decomposition of the boundary. Probability distributions on the parameters of the representation bias the model to a particular overall shape while allowing for deformations. Boundary finding is formulated as an optimization problem using a maximum a posteriori objective function. Results of the method applied to real and synthetic images are presented, including an evaluation of the dependence of the method on prior information and image quality     

Interactively deformable models for surgery simulation

A methodology that addresses important issues concerned with the underlying graphical models designed for surgical simulation, as well as issues related to the real-time interactivity with, and manipulation of, these models is presented. The specific application of interest is laparoscopic surgery, which is performed using endoscopes that present a video image of the organs to the clinicians. The surgeon then performs the surgery while looking at the video monitor. The particular focus is gall bladder surgery, which involves various gastrointestinal organs. The overall objective is to simulate this environment by creating realistic, manipulable models of these organs. The models are interactively manipulable and exhibit behavior both visually acceptable and physically accurate. The approach is based on the notion of active surfaces. The rationale, mathematical formalism, and visualization techniques encompassed by the methodology are described. Recent results obtained from applying these methods to the problem of endoscopic gall bladder surgery simulation are presented     

On deformable models for visual pattern recognition

This paper reviews model-based methods for non-rigid shape recognition. These methods model, match and classify non-rigid shapes, which are generally problematic for conventational algorithms using rigid models. Issues including model representation, optimization criteria formulation, model matching, and classification are examined in detail with the objective to provide interested researchers a roadmap for exploring the field. This paper emphasizes on 2D deformable models. Their potential applications and future research directions, particularly on deformable pattern classification, are discussed.     

Visual surveillance using deformable models of vehicles

This paper presents recent developments to a vision-based traffic surveillance system which relies extensively on the use of geometrical and scene context. Firstly, a highly parametrised 3-D model is reported, able to adopt the shape of a wide variety of different classes of vehicle (e.g. cars, vans, buses etc.), and its subsequent specialisation to a generic car class which accounts for commonly encountered types of car (including saloon, batchback and estate cars). Sample data collected from video images, by means of an interactive tool, have been subjected to principal component analysis (PCA) to define a deformable model having 6 degrees of freedom.

Secondly, a new pose refinement technique using “active” models is described, able to recover both the pose of a rigid object, and the structure of a deformable model; an assessment of its performance is examined in comparison with previously reported “passive” model-based techniques in the context of traffic surveillance. The new method is more stable, and requires fewer iterations, especially when the number of free parameters increases, but shows somewhat poorer convergence.

Typical applications for this work include robot surveillance and navigation tasks.     

Metamorphs: deformable shape and appearance models

This paper presents a new deformable modeling strategy aimed at integrating shape and appearance in a unified space. If we think traditional deformable models as active contours or evolving curve fronts, the new deformable shape and appearance models we propose are deforming disks or volumes. Each model has not only boundary shape but also interior appearance. The model shape is implicitly embedded in a higher dimensional space of distance transforms, thus represented by a distance map image. In this way, both shape and appearance of the model are defined in the pixel space. A common deformation scheme, the Free Form Deformations (FFD), parameterizes warping deformations of the volumetric space in which the model is embedded in, hence deforming both model boundary and interior simultaneously.     

Statistical cue integration in DAG deformable models

Deformable models are a useful modeling paradigm in computer vision. A deformable model is a curve, a surface, or a volume, whose shape, position, and orientation are controlled through a set of parameters. They can represent manufactured objects, human faces and skeletons, and even bodies of fluid. With low-level computer vision and image processing techniques, such as optical flow, we extract relevant information from images. Then, we use this information to change the parameters of the model iteratively until we find a good approximation of the object in the images. When we have multiple computer vision algorithms providing distinct sources of information (cues), we have to deal with the difficult problem of combining these, sometimes conflicting contributions in a sensible way. In this paper, we introduce the use of a directed acyclic graph (DAG) to describe the position and Jacobian of each point of deformable models. This representation is dynamic, flexible, and allows computational optimizations that would be difficult to do otherwise. We then describe a new method for statistical cue integration method for tracking deformable models that scales well with the dimension of the parameter space. We use affine forms and affine arithmetic to represent and propagate the cues and their regions of confidence. We show that we can apply the Lindeberg theorem to approximate each cue with a Gaussian distribution, and can use a maximum-likelihood estimator to integrate them. Finally, we demonstrate the technique at work in a 3D deformable face tracking system on monocular image sequences with thousands of frames.     

Image-based collision detection for deformable cloth models

Modeling the natural interaction of cloth and garments with objects in a 3D environment is currently one of the most computationally demanding tasks. These highly deformable materials are subject to a very large number of contact points in the proximity of other moving objects. Furthermore, cloth objects often fold, roll, and drape within themselves, generating a large number of self-collision areas. The interactive requirements of 3D games and physically driven virtual environments make the cloth collisions and self-collision computations more challenging. By exploiting mathematically well-defined smoothness conditions over smaller patches of deformable surfaces and resorting to image-based collision detection tests, we developed an efficient collision detection method that achieves interactive rates while tracking self-interactions in highly deformable surfaces consisting of a large number of elements. The method makes use of a novel technique for dynamically generating a hierarchy of cloth bounding boxes in order to perform object-level culling and image-based intersection tests using conventional graphics hardware support. An efficient backward voxel-based AABB hierarchy method is proposed to handle deformable surfaces which are highly compressed.     

Animation of deformable models using implicit surfaces

The paper presents a general approach for designing and animating complex deformable models with implicit surfaces. Implicit surfaces are introduced as an extra layer coating any kind of structure that moves and deforms over time. Offering a compact definition of a smooth surface around an object, they provide an efficient collision detection mechanism. The implicit layer deforms in order to generate exact contact surfaces between colliding bodies. A simple physically based model approximating elastic behavior is then used for computing collision response. The implicit formulation also eases the control of the object's volume with a new method based on local controllers. We present two different applications that illustrate the benefits of these techniques. First, the animation of simple characters made of articulated skeletons coated with implicit flesh exploits the compactness and enhanced control of the model. The second builds on the specific properties of implicit surfaces for modeling soft inelastic substances capable of separation and fusion that maintain a constant volume when animated     

Active blobs: region-based, deformable appearance models

A region-based approach to nonrigid motion tracking is described. Shape is defined in terms of a deformable triangular mesh that captures object shape plus a color texture map that captures object appearance. Photometric variations are also modeled. Nonrigid shape registration and motion tracking are achieved by posing the problem as an energy-based, robust minimization procedure. The approach provides robustness to occlusions, wrinkles, shadows, and specular highlights. The formulation is tailored to take advantage of texture mapping hardware available in many workstations, PCs, and game consoles. This enables nonrigid tracking at speeds approaching video rate.     

Parallelized deformable part models with effective hypothesis pruning

Computational Visual Media - As a typical machine-learning based detection technique, deformable part models (DPM) achieve great success in detecting complex object categories. The heavy...     

Physically based models with rigid and deformable components

A class of physically based models suitable for animating flexible objects in simulated physical environments was proposed earlier by the authors (1987). The original formulation works as well in practice for models whose shapes are moderately to highly deformable, but it tends to become numerically ill conditioned as the rigidity of the models is increased. An alternative formulation of deformable models is presented in which deformations are decomposed into a reference component, which may represent an arbitrary shape, and a displacement component, allowing deformation away from this reference shape. The application of the deformable models to a physically based computer animation project is illustrated     

Frequency domain formulation of active parametric deformable models

Active deformable models are simple tools, very popular in computer vision and computer graphics, for solving ill-posed problems or mimic real physical systems. The classical formulation is given in the spatial domain, the motor of the procedure is a second-order linear system, and rigidity and elasticity are the basic parameters for its characterization. This paper proposes a novel formulation based on a frequency-domain analysis: the internal energy functional and the Lagrange minimization are performed entirely in the frequency domain, which leads to a simple formulation and design. The frequency-based implementation offers important computational savings in comparison to the original one, a feature that is improved by the efficient hardware and software computation of the FFT algorithm. This new formulation focuses on the stiffness spectrum, allowing the possibility of constructing deformable models apart from the elasticity and rigidity-based original formulation. Simulation examples validate the theoretical results.     

Flexible simulation of deformable models using discontinuous Galerkin FEM

We propose a simulation technique for elastically deformable objects based on the discontinuous Galerkin finite element method (DG FEM). In contrast to traditional FEM, it overcomes the restrictions of conforming basis functions by allowing for discontinuous elements with weakly enforced continuity constraints. This added flexibility enables the simulation of arbitrarily shaped, convex and non-convex polyhedral elements, while still using simple polynomial basis functions. For the accurate strain integration over these elements we propose an analytic technique based on the divergence theorem. Being able to handle arbitrary elements eventually allows us to derive simple and efficient techniques for volumetric mesh generation, adaptive mesh refinement, and robust cutting. Furthermore, we show DG FEM not to suffer from locking artifacts even for nearly incompressible materials, a problem that in standard FEM requires special handling.     

Interactive collision detection for deformable models using streaming AABBs

We present an interactive and accurate collision detection algorithm for deformable, polygonal objects based on the streaming computational model. Our algorithm can detect all possible pairwise primitive-level intersections between two severely deforming models at highly interactive rates. In our streaming computational model, we consider a set of axis aligned bounding boxes (AABBs) that bound each of the given deformable objects as an input stream and perform massively-parallel pairwise, overlapping tests onto the incoming streams. As a result, we are able to prevent performance stalls in the streaming pipeline that can be caused by expensive indexing mechanism required by bounding volume hierarchy-based streaming algorithms. At runtime, as the underlying models deform over time, we employ a novel, streaming algorithm to update the geometric changes in the AABB streams. Moreover, in order to get only the computed result (i.e., collision results between AABBs) without reading back the entire output streams, we propose a streaming en/decoding strategy that can be performed in a hierarchical fashion. After determining overlapped AABBs, we perform a primitive-level (e.g., triangle) intersection checking on a serial computational model such as CPUs. We implemented the entire pipeline of our algorithm using off-the-shelf graphics processors (GPUs), such as nVIDIA GeForce 7800 GTX, for streaming computations, and Intel Dual Core 3.4G processors for serial computations. We benchmarked our algorithm with different models of varying complexities, ranging from 15K up to 50K triangles, under various deformation motions, and the timings were obtained as 30 approximately 100 FPS depending on the complexity of models and their relative configurations. Finally, we made comparisons with a well-known GPU-based collision detection algorithm, CULLIDE [4] and observed about three times performance improvement over the earlier approach. We also made comparisons with a SW-based AABB culling algorithm [2] and observed about two times improvement.     

d-Dimensional parametric models for dynamic animation of deformable objects

This paper introduces an accurate, efficient, and unified engine dedicated to dynamic animation of d-dimensional deformable objects. The objects are modelled as d-dimensional manifolds defined as functional combinations of a mesh of 3D control points, weighted by parametric blending functions. This model ensures that, at each time step, the object shape conforms to its manifold definitions. The object motion is deduced from the control points dynamic animation. In fact, control points should be viewed as the degrees of freedom of the continuous object. The chosen dynamic equations (Lagrangian formalism) reflect this generic modelling scheme and yield an exact and computationally efficient linear system.     

Surface reconstruction using deformable models with interior andboundary constraints

The authors introduce a technique for 3D surface reconstruction using elastic deformable-models. The model used is an imaginary elastic grid, which is made of membranous, thin-plate-type material. The elastic grid can bent, twisted, compressed, and stretched into any desired 3D shape, which is specified by the shape constraints derived automatically from images of a real 3D object. Shape reconstruction is guided by a set of imaginary springs that enforce the consistency in the position, orientation, and/or curvature measurements of the elastic grid and the desired shape. The dynamics of a surface reconstruction process is regulated by Hamilton's principle or the principle of the least action. Furthermore, a 1D deformable template that borders the elastic grid may be used. This companion boundary template is attracted/repelled by image forces to conform with the silhouette of the imaged object. Implementation results using simple analytic shapes and images of real objects are presented