Streaming 3D deforming surfaces with dynamic resolution control

Real‐time streaming of shape deformations in a shared distributed virtual environment is a challenging task due to the difficulty of transmitting large amounts of 3D animation data to multiple receiving parties at a high frame rate. In this paper, we present a framework for streaming 3D shape deformations, which allows shapes with multi‐resolutions to share the same deformations simultaneously in real time. The geometry and motion of deforming mesh or point‐sampled surfaces are compactly encoded, transmitted, and reconstructed using the spectra of the manifold harmonics. A receiver‐based multi‐resolution surface reconstruction approach is introduced, which allows deforming shapes to switch smoothly between continuous multi‐resolutions. On the basis of this dynamic reconstruction scheme, a frame rate control algorithm is further proposed to achieve rendering at interactive rates. We also demonstrate an efficient interpolation‐based strategy to reduce computing of deformation. The experiments conducted on both mesh and point‐sampled surfaces show that our approach achieves efficient performance even if deformations of complex 3D surfaces are streamed. Copyright © 2013 John Wiley & Sons, Ltd.     

Multi-Level Shape Representation Using Global Deformations and Locally Adaptive Finite Elements

We present a model-based method for the multi-level shape, pose estimation and abstraction of an object's surface from range data. The surface shape is estimated based on the parameters of a superquadric that is subjected to global deformations (tapering and bending) and a varying number of levels of local deformations. Local deformations are implemented using locally adaptive finite elements whose shape functions are piecewise cubic functions with C ¹ continuity. The surface pose is estimated based on the model's translational and rotational degrees of freedom. The algorithm first does a coarse fit, solving for a first approximation to the translation, rotation and global deformation parameters and then does several passes of mesh refinement, by locally subdividing triangles based on the distance between the given datapoints and the model. The adaptive finite element algorithm ensures that during subdivision the desirable finite element mesh generation properties of conformity, non-degeneracy and smoothness are maintained. Each pass of the algorithm uses physics-based modeling techniques to iteratively adjust the global and local parameters of the model in response to forces that are computed from approximation errors between the model and the data. We present results demonstrating the multi-level shape representation for both sparse and dense range data.     

An adaptive Rothe method for the wave equation

The adaptive Rothe method approaches a time-dependent PDE as an ODE in function space. This ODE is solved virtually using an adaptive state-of-the-art integrator. The actual realization of each time-step requires the numerical solution of an elliptic boundary value problem, thus perturbing the virtual function space method. The admissible size of that perturbation can be computed a priori and is prescribed as a tolerance to an adaptive multilevel finite element code, which provides each time-step with an individually adapted spatial mesh. In this way, the method avoids the well-known difficulties of the method of lines in higher space dimensions. During the last few years the adaptive Rothe method has been applied successfully to various problems with infinite speed of propagation of information. The present study concerns the adaptive Rothe method for hyperbolic equations in the model situation of the wave equation. All steps of the construction are given in detail and a numerical example (diffraction at a corner) is provided for the 2D wave equation. This example clearly indicates that the adaptive Rothe method is appropriate for problems which can generally benefit from mesh adaptation. This should be even more pronounced in the 3D case because of the strong Huygens' principle. Accepted: 12 August 1997     

Implicit simplicial models for adaptive curve reconstruction

Parametric deformable models have been extensively and very successfully used for reconstructing free-form curves and surfaces, and for tracking nonrigid deformations, but they require previous knowledge of the topological type of the data, and good initial curve or surface estimates. With deformable models, it is also computationally expensive to check for and to prevent self-intersections while tracking deformations. The implicit simplicial models that we introduce in this paper are implicit curves and surfaces defined by piecewise linear functions. This representation allows for local deformations, control of the topological type, and prevention of self-intersections during deformations. As a first application, we also describe an algorithm for 2D curve reconstruction from unorganized sets of data points. The topology, the number of connected components, and the geometry of the data are all estimated using an adaptive space subdivision approach. The main four components of the algorithm are topology estimation, curve fitting, adaptive space subdivision, and mesh relaxation     

Distance functions and skeletal representations of rigid and non-rigid planar shapes

Shape skeletons are fundamental concepts for describing the shape of geometric objects, and have found a variety of applications in a number of areas where geometry plays an important role. Two types of skeletons commonly used in geometric computations are the straight skeleton of a (linear) polygon, and the medial axis of a bounded set of points in the k-dimensional Euclidean space. However, exact computation of these skeletons of even fairly simple planar shapes remains an open problem.In this paper we propose a novel approach to construct exact or approximate (continuous) distance functions and the associated skeletal representations (a skeleton and the corresponding radius function) for solid 2D semi-analytic sets that can be either rigid or undergoing topological deformations. Our approach relies on computing constructive representations of shapes with R-functions that operate on real-valued halfspaces as logic operations. We use our approximate distance functions to define a new type of skeleton, i.e, the C-skeleton, which is piecewise linear for polygonal domains, generalizes naturally to planar and spatial domains with curved boundaries, and has attractive properties. We also show that the exact distance functions allow us to compute the medial axis of any closed, bounded and regular planar domain. Importantly, our approach can generate the medial axis, the straight skeleton, and the C-skeleton of possibly deformable shapes within the same formulation, extends naturally to 3D, and can be used in a variety of applications such as skeleton-based shape editing and adaptive motion planning.     

Diffeomorphic 3D Image Registration via Geodesic Shooting Using an Efficient Adjoint Calculation

In the context of large deformations by diffeomorphisms, we propose a new diffeomorphic registration algorithm for 3D images that performs the optimization directly on the set of geodesic flows. The key contribution of this work is to provide an accurate estimation of the so-called initial momentum, which is a scalar function encoding the optimal deformation between two images through the Hamiltonian equations of geodesics. Since the initial momentum has proven to be a key tool for statistics on shape spaces, our algorithm enables more reliable statistical comparisons for 3D images.     

A Fast and Log-Euclidean Polyaffine Framework for Locally Linear Registration

In this article, we focus on the parameterization of non-rigid geometrical deformations with a small number of flexible degrees of freedom. In previous work, we proposed a general framework called polyaffine to parameterize deformations with a finite number of rigid or affine components, while guaranteeing the invertibility of global deformations. However, this framework lacks some important properties: the inverse of a polyaffine transformation is not polyaffine in general, and the polyaffine fusion of affine components is not invariant with respect to a change of coordinate system. We present here a novel general framework, called Log-Euclidean polyaffine, which overcomes these defects. We also detail a simple algorithm, the Fast Polyaffine Transform, which allows to compute very efficiently Log-Euclidean polyaffine transformations and their inverses on regular grids. The results presented here on real 3D locally affine registration suggest that our novel framework provides a general and efficient way of fusing local rigid or affine deformations into a global invertible transformation without introducing artifacts, independently of the way local deformations are first estimated.

Adaptive dimension splitting algorithm for three-dimensional elliptic equations

An adaptive dimension splitting algorithm for three-dimensional (3D) elliptic equations is presented in this paper. We propose residual and recovery-based error estimators with respect to X?Y plane direction and Z direction, respectively, and construct the corresponding adaptive algorithm. Two-sided bounds of the estimators guarantee the efficiency and reliability of such error estimators. Numerical examples verify their efficiency both in estimating the error and in refining the mesh adaptively. This algorithm can be compared with or even better than the 3D adaptive finite element method with tetrahedral elements in some cases. What is more, our new algorithm involves only two-dimensional mesh and one-dimensional mesh in the process of refining mesh adaptively, and it can be implemented in parallel.     

Automated adaptive 3D forming simulation processes

In this study, an automated adaptive mesh control scheme, based on local mesh modifications, is developed for the finite element simulations of 3D metal-forming processes. Error indicators are used to control the mesh discretization errors, and an h-adaptive procedure is conducted. The mesh size field used in the h-adaptive procedure is processed to control the discretization and geometric approximation errors of the evolving workpiece mesh. Industrial problems are investigated to demonstrate the capabilities of the developed scheme.     

Dense Non-Rigid Motion Estimation in Sequences of Medical Images Using Differential Constraints

We describe a new method for computing the displacement vector field in time sequences of 2D or 3D images (4D data). The method is energy-minimizing on the space of correspondence functions; the energy is split into two terms, with one term matching differential singularities in the images, and the other constraining the regularity of the field. In order to reduce the computational time of the motion estimation, we use an adaptive image mesh, the resolution of which depends on the value of the gradient intensity. We solve numerically the minimization problem with the finite element method which gives a continuous approximation of the solution. We present experimental results on synthetic data and on medical images and we show how to use these results for analyzing cardiac deformations.     

Silhouette-based occluded object recognition through curvature scale space

A complete and practical system for occluded object recognition has been developed which is very robust with respect to noise and local deformations of shape (due to weak perspective distortion, segmentation errors and non-rigid material) as well as scale, position and orientation changes of the objects. The system has been tested on a wide variety of free-form 3D objects. An industrial application is envisaged where a fixed camera and a light-box are utilized to obtain images. Within the constraints of the system, every rigid 3D object can be modeled by a limited number of classes of 2D contours corresponding to the object's resting positions on the light-box. The contours in each class are related to each other by a 2D similarity transformation. The Curvature Scale Space technique [26, 28] is then used to obtain a novel multi-scale segmentation of the image and the model contours. Object indexing [16, 32, 36] is used to narrow down the search space. An efficient local matching algorithm is utilized to select the best matching models. Received: 5 August 1996 / Accepted: 19 March 1997     

Placement of Deformable Objects

With the increasing complexity of photorealistic scenes, the question of building and placing objects in three‐dimensional scenes is becoming ever more difficult. While the question of placement of rigid objects has captured the attention of researchers in the past, this work presents an intuitive and interactive scheme to properly place deformable objects with the aid of free‐form deformation tools. The presented scheme can also be used to animate the locomotion of nonrigid objects, most noticeably animals, and adapt the motion to arbitrary terrain. The automatic construction of our free‐form deformation tool is completely hidden from the end user, and hence, circumvents the difficulties typically faced in manipulating these deformation functions. Further, a precise bound on the error that is introduced by applying free‐form deformations to polygonal models is presented, along with an almost‐optimal adaptive refinement algorithm to achieve a certain accuracy in the mapping.     

iLogDemons: A Demons-Based Registration Algorithm for Tracking Incompressible Elastic Biological Tissues

Tracking soft tissues in medical images using non-linear image registration algorithms requires methods that are fast and provide spatial transformations consistent with the biological characteristics of the tissues. LogDemons algorithm is a fast non-linear registration method that computes diffeomorphic transformations parameterised by stationary velocity fields. Although computationally efficient, its use for tissue tracking has been limited because of its ad-hoc Gaussian regularisation, which hampers the implementation of more biologically motivated regularisations. In this work, we improve the logDemons by integrating elasticity and incompressibility for soft-tissue tracking. To that end, a mathematical justification of demons Gaussian regularisation is proposed. Building on this result, we replace the Gaussian smoothing by an efficient elastic-like regulariser based on isotropic differential quadratic forms of vector fields. The registration energy functional is finally minimised under the divergence-free constraint to get incompressible deformations. As the elastic regulariser and the constraint are linear, the method remains computationally tractable and easy to implement. Tests on synthetic incompressible deformations showed that our approach outperforms the original logDemons in terms of elastic incompressible deformation recovery without reducing the image matching accuracy. As an application, we applied the proposed algorithm to estimate 3D myocardium strain on clinical cine MRI of two adult patients. Results showed that incompressibility constraint improves the cardiac motion recovery when compared to the ground truth provided by 3D tagged MRI.     

An adaptive method for the determination of the order of element for acquiring the desired accuracy in 3D elastostatic FEM analysis

An adaptive method for the determination of the order of element (or element order) was developed for the finite element analysis of 3D elastostatic problems. Here the order of element means the order of polynomial function, which interpolates the displacement distribution in the element. This method was based on acquiring the desired accuracy for each finite element. From the numerical experiments, the relationship ξ=k(1/p)^β was deduced, where ξ is the error of the result of the finite element analysis relative to the exact value, p is the order of element, and k and β are constants. Applying this relationship to the two results of computations with different orders of element, the order of element for the third computation was deduced. A computer program using this adaptive determination method for the order of element was developed and applied to several 3D elastostatic problems of various shapes. The usefulness of the method was illustrated by these application results.     

Edge Detection by Adaptive Splitting

In this paper we propose an algorithm (EDAS-d) to approximate the jump discontinuity set of functions defined on subsets of ℝ ^d . We have limited our study to the 1D (EDAS-1) and 2D (EDAS-2) versions of the algorithm. Theoretical and computational results prove its effectiveness in the case of piecewise continuous 1D functions and piecewise constant 2D functions. The algorithm is based on adaptive splitting of the domain of the function guided by the value of an average integral. EDAS-d exhibits a number of attractive features: accurate determination of the jump points, fast processing, absence of oscillatory behavior, precise determination of the magnitude of the jumps, and ability to differentiate between real jumps (discontinuities) and steep gradients. Moreover, low-dimensional versions of EDAS-d can be used for solving higher dimensional problems. Computational experiments also show that EDAS-d can be applied to solve some problems involving general piecewise continuous functions. EDAS-1 and EDAS-2 have been used to determine edges in 2D-images. The results are quite satisfactory for practical purposes.     

Adaptive marching cubes

The marching cubes algorithm (MC) is a powerful technique for surface rendering that can produce very high-quality images. However, it is not suitable for interactive manipulation of the 3D surfaces constructed from high-resolution volume datasets in terms of both space and time. In this paper, we present an adaptive version of MC called adaptive marching cubes (AMC). It significantly reduces the number of triangles representing the surface by adapting the size of the triangles to the shape of the surface. This improves the performance of the manipulation of the 3D surfaces. A typical example with the volume dataset of size 256×256×113 shows that the number of triangles is reduced by 55%. The quality of images produced by AMC is similar to that of MC. One of the fundamental problems encountered with adaptive algorithms is thecrack problem. Cracks may be created between two neighboring cubes processed with different levels of subdivision. We solve the crack problem by patching the cracks using polygons of the smae shape as those of the cracks. We propose a simple, but complete, method by first abstracting 22 basic configurations of arbitrarily sized cracks and then reducing the handling of these configurations to a simple rule. It requires onlyO(n ²) working memory for an×n×n volume data set.     

autoC: an efficient translator for model checking deterministic scheduler based OSEK/VDX applications

The measurement of the vessel pattern in fingers is a superior method for identifying individuals owing to its convenience and the security it offers. We introduce in this paper a new perspective to accomplish finger vein recognition. This method, which regards deformations as discriminative information, is distinct from existing methods that attempt to prevent the influence of deformations. The proposed technique is based on the observation that regular deformation, which corresponds to a posture change, can only exist in genuine vein patterns. In terms of methodology, we incorporate optimized matching to generate pixelbased 2D displacements that correspond to deformations. The texture of uniformity extracted from the displacement fields is taken as the final matching score. Evaluated on two publicly available databases, PolyU and SDU-MLA, extensive experiments demonstrated that the discriminability of the new feature derived from deformations is preferable. The equal error rate (EER) achieved is the lowest compared to that of state-of-the-art techniques.

     

Facetons: face primitives for building 3D architectural models in virtual environments

We present facetons, geometric modeling primitives designed for building architectural models especially effective for a virtual environment where six degrees of freedom input devices are available. A faceton is an oriented point floating in the air and defines a plane of infinite extent passing through the point. The polygonal mesh model is constructed by taking the intersection of the planes associated with the facetons. With the simple interaction of faceton, users can easily create 3D architecture models. The faceton primitive and its interaction reduce the overhead associated with standard polygonal mesh modeling, where users have to manually specify vertexes and edges which could be far away. The faceton representation is inspired by the research on boundary representations (B‐rep) and constructive solid geometry, but it is driven by a novel adaptive bounding algorithm and is specifically designed for 3D modeling activities in an immersive virtual environment. We describe the modeling method and our current implementation. The implementation is still experimental but shows potential as a viable alternative to traditional modeling methods. Copyright © 2014 John Wiley & Sons, Ltd.