Interactive mesh deformation using equality-constrained least squares

Mesh deformation techniques that preserve the differential properties have been intensively studied. In this paper, we propose an equality-constrained least squares approach for stably deforming mesh models while approximately preserving mean curvature normals and strictly satisfying other constraints such as positional constraints. We solve the combination of hard and soft constraints by constructing a typical least squares system using QR decomposition. A well-known problem of hard constraints is over-constraints. We show that the equality-constrained least squares approach is useful for resolving such over-constrained situations. In our framework, the rotations of mean curvature normals are treated using the logarithms of unit quaternions in . During deformation, mean curvature normals can be rotated while preserving their magnitudes. In addition, we introduce a new modeling constraints called rigidity constraints and show that rigidity constraints can effectively preserve the shapes of feature regions during deformation. Our framework achieves good performance for interactive deformation of mesh models.     

Acquiring Both Constraint and Solution Preferences in Interactive Constraint Systems

Constraints are useful to model many real-life problems. Soft constraints are even more useful, since they allow for the use of preferences, which are very convenient in many real-life problems. In fact, most problems cannot be precisely defined by using hard constraints only.However, soft constraint solvers usually can only take as input preferences over constraints, or variables, or tuples of domain values. On the other hand, it is sometimes easier for a user to state preferences over entire solutions of the problem.In this paper, we define an interactive framework where it is possible to state preferences both over constraints and over solutions, and we propose a way to build a system with such features by pairing a soft constraint solver and a learning module, which learns preferences over constraints from preferences over solutions. We also describe a working system which fits our framework, and uses a fuzzy constraint solver and a suitable learning module to search a catalog for the best products that match the user's requirements.     

Interactive design exploration for constrained meshes

In architectural design, surface shapes are commonly subject to geometric constraints imposed by material, fabrication or assembly. Rationalization algorithms can convert a freeform design into a form feasible for production, but often require design modifications that might not comply with the design intent. In addition, they only offer limited support for exploring alternative feasible shapes, due to the high complexity of the optimization algorithm.We address these shortcomings and present a computational framework for interactive shape exploration of discrete geometric structures in the context of freeform architectural design. Our method is formulated as a mesh optimization subject to shape constraints. Our formulation can enforce soft constraints and hard constraints at the same time, and handles equality constraints and inequality constraints in a unified way. We propose a novel numerical solver that splits the optimization into a sequence of simple subproblems that can be solved efficiently and accurately.Based on this algorithm, we develop a system that allows the user to explore designs satisfying geometric constraints. Our system offers full control over the exploration process, by providing direct access to the specification of the design space. At the same time, the complexity of the underlying optimization is hidden from the user, who communicates with the system through intuitive interfaces.     

Deformation analysis of thin elastic membranes in multiple contact

This article presents the deformation analysis of thin elastic membranes, supported at the boundaries, and lifted by multiple rigid indentors. This study is motivated by a problem that is encountered in the design of flexible elastomeric surface tooling for prototyping free-form shapes made of composite materials. The deformation analysis was carried out using a mathematical programming approach and assuming contacts between the membrane and indentors to be frictionless. The Mooney form of strain energy function is used for potential energy calculations. The conjugate gradient method in the presence of contact constraints is used for energy minimization. The results are presented for three numerical examples describing the realizability of ruled and doubly curved surface shapes.     

Shape registration in implicit spaces using information theory and free form deformations

We present a novel, variational and statistical approach for shape registration. Shapes of interest are implicitly embedded in a higher-dimensional space of distance transforms. In this implicit embedding space, registration is formulated in a hierarchical manner: the mutual information criterion supports various transformation models and is optimized to perform global registration; then, a B-spline-based incremental free form deformations (IFFD) model is used to minimize a sum-of-squared-differences (SSD) measure and further recover a dense local nonrigid registration field. The key advantage of such framework is twofold: 1) it naturally deals with shapes of arbitrary dimension (2D, 3D, or higher) and arbitrary topology (multiple parts, closed/open) and 2) it preserves shape topology during local deformation and produces local registration fields that are smooth, continuous, and establish one-to-one correspondences. Its invariance to initial conditions is evaluated through empirical validation, and various hard 2D/3D geometric shape registration examples are used to show its robustness to noise, severe occlusion, and missing parts. We demonstrate the power of the proposed framework using two applications: one for statistical modeling of anatomical structures, another for 3D face scan registration and expression tracking. We also compare the performance of our algorithm with that of several other well-known shape registration algorithms.     

Feature sensitive deformation for triangular mesh models

Shape deformation is a useful tool for shape modeling and animation in computer graphics. In this paper, we propose a novel surface deformation method based on a feature sensitive (FS) metric. Firstly, taking unit normal vectors into account, we derive a FS Laplacian operator, which is more sensitive to featured regions of mesh models than existing operators. Secondly, we use the 1‐ring tetrahedron in the dual mesh, a volumetric structure, to encode geometric details. To preserve the shape of the tetrahedron, we introduce linear tetrahedron constraints minimizing both the distortion of the base triangle and the change of the corresponding height. These ensure that geometric details are accurately preserved during deformation. The time complexity of our new method is similar to that of existing linear Laplacian methods. Examples are included to show that our FS deformation method better preserves mesh details, especially features, than existing Laplacian methods. Copyright © 2010 John Wiley & Sons, Ltd.     

基于物理的准D—NURBS造型方法

该文提出了基于物理的推Ｄ－ＮＵＲＢＳ的概念。ＮＵＲＢＳ由于既能够表示自由形状，又能够表示标准解析形状（即初等曲线曲面）而成为商业造型系统的标准。但直到目前，ＮＵＲＢＳ仍被看成是纯几何的设计工具，它要求我们手工调整控制顶点和相应权值来设计满足要求的形状。准Ｄ－ＮＵＲＢＳ则基于物理定律，将物体的质量分布，阻尼，内部变形能和其它物理特性与普通ＮＵＲＢＳ基结合，这使得我们不仅可以使用手工调整控制顶点和相应权值的传统方法，也可以施加模拟的外力和局部与全局几何约束而使设计形状依时间动态变形的方法来设计出满足要求的形状，通过物理变形的方法得到要求的形状使得设计更加直观，高效。同时，基于物理的准Ｄ－ＮＵＲＢＳ模型还用于柔性物体的运动、变形仿真。     

Constrained Modelling of 3‐Valent Meshes Using a Hyperbolic Deformation Metric

Polygon meshes with 3‐valent vertices often occur as the frame of free‐form surfaces in architecture, in which rigid beams are connected in rigid joints. For modelling such meshes, it is desirable to measure the deformation of the joints' shapes. We show that it is natural to represent joint shapes as points in hyperbolic 3‐space. This endows the space of joint shapes with a geometric structure that facilitates computation. We use this structure to optimize meshes towards different constraints, and we believe that it will be useful for other applications as well.     

Vesicles and Amoebae: On Globally Constrained Shape Deformation

Modeling the deformation of shapes under constraints on both perimeter and area is a challenging task due to the highly nontrivial interaction between the need for flexible local rules for manipulating the boundary and the global constraints. We propose several methods to address this problem and generate “random walks” in the space of shapes obeying quite general possibly time varying constraints on their perimeter and area. Design of perimeter and area preserving deformations are an interesting and useful special case of this problem. The resulting deformation models are employed in annealing processes that evolve original shapes toward shapes that are optimal in terms of boundary bending-energy or other functionals. Furthermore, such models may find applications in the analysis of sequences of real images of deforming objects obeying global constraints as building blocks for registration and tracking algorithms.     

On-line handwritten Chinese character recognition via a fuzzy attribute representation

Chinese characters are constructed by strokes according to structural rules. Therefore, the geometric configurations of characters are important features for character recognition. In handwritten characters, stroke shapes and their spatial relations may vary to some extent. The attribute value of a structural identification is then a fuzzy quantity rather than a binary quantity. Recognizing these facts, we propose a fuzzy attribute representation (FAR) to describe the structural features of handwritten Chinese characters for an on-line Chinese character recognition (OLCCR) system. With a FAR. a fuzzy attribute graph for each handwritten character is created, and the character recognition process is thus transformed into a simple graph matching problem. This character representation and our proposed recognition method allow us to relax the constraints on stroke order and stroke connection. The graph model provides a generalized character representation that can easily incorporate newly added characters into an OLCCR system with an automatic learning capability. The fuzzy representation can describe the degree of structural deformation in handwritten characters. The character matching algorithm is designed to tolerate structural deformations to some extent. Therefore, even input characters with deformations can be recognized correctly once the reference dictionary of the recognition system has been trained using a few representative learning samples. Experimental results are provided to show the effectiveness of the proposed method.     

Unsupervised Template Warp Consistency for Implicit Surface Correspondences

Unsupervised template discovery via implicit representation in a category of shapes has recently shown strong performance. At the core, such methods deform input shapes to a common template space which allows establishing correspondences as well as implicit representation of the shapes. In this work we investigate the inherent assumption that the implicit neural field optimization naturally leads to consistently warped shapes, thus providing both good shape reconstruction and correspondences. Contrary to this convenient assumption, in practice we observe that such is not the case, consequently resulting in sub-optimal point correspondences. In order to solve the problem, we re-visit the warp design and more importantly introduce explicit constraints using unsupervised sparse point predictions, directly encouraging consistency of the warped shapes. We use the unsupervised sparse keypoints in order to further condition the deformation warp and enforce the consistency of the deformation warp. Experiments in dynamic non-rigid DFaust and ShapeNet categories show that our problem identification and solution provide the new state-of-the-art in unsupervised dense correspondences.     

Simultaneous oblique impacts and contacts in multibody systems with friction

This paper presents a new dissipation principle for resolving post-impact tangential velocities after simultaneous impact events on a system composed of interconnected rigid bodies. In this work, contact is considered as a succession of impacts so that simultaneous contacts and impacts can be treated using the same framework. This treatment includes Coulomb friction and considers hard impacts where deformation of the impacting surfaces is negligible. The impact problem is addressed using the complementarity conditions which lead to an investigation of the relationship between post-impact velocities and feasible coefficients of friction. These conditions do not define a unique post-impact velocity so a dissipation principle is proposed which is encoded as an optimization problem. This solution preserves the discontinuity between the static and dynamic coefficients of friction. The approach is illustrated on a bicycle-like structure with elliptical wheels.     

Effective segmentation and classification for HCC biopsy images

Accurate grading for hepatocellular carcinoma (HCC) biopsy images is important to prognosis and treatment planning. In this paper, we propose an automatic system for grading HCC biopsy images. In preprocessing, we use a dual morphological grayscale reconstruction method to remove noise and accentuate nuclear shapes. A marker-controlled watershed transform is applied to obtain the initial contours of nuclei and a snake model is used to segment the shapes of nuclei smoothly and precisely. Fourteen features are then extracted based on six types of characteristics for HCC classification. Finally, we propose a SVM-based decision-graph classifier to classify HCC biopsy images. Experimental results show that 94.54% of classification accuracy can be achieved by using our SVM-based decision-graph classifier while 90.07% and 92.88% of classification accuracy can be achieved by using k-NN and SVM classifiers, respectively.     

用弹簧分子系统进行弹性医学图像配准

将源图像Delaunay三角化,用弹簧分子系统模拟网格形变,网格点在系统力的作用下移动去拟合待配准的目标图像.力由互信息梯度定义,并利用已知解剖结构特征的对应关系对形变过程进行约束.经过一段时间,网格点停止运动,对每一个Delaunay三角形计算局部仿射变换.实验结果表明,该算法能够快速准确地实现弹性医学图像配准.     

Spectral Affine‐Kernel Embeddings

In this paper, we propose a controllable embedding method for high‐ and low‐dimensional geometry processing through sparse matrix eigenanalysis. Our approach is equally suitable to perform non‐linear dimensionality reduction on big data, or to offer non‐linear shape editing of 3D meshes and pointsets. At the core of our approach is the construction of a multi‐Laplacian quadratic form that is assembled from local operators whose kernels only contain locally‐affine functions. Minimizing this quadratic form provides an embedding that best preserves all relative coordinates of points within their local neighborhoods. We demonstrate the improvements that our approach brings over existing nonlinear dimensionality reduction methods on a number of datasets, and formulate the first eigen‐based as‐rigid‐as‐possible shape deformation technique by applying our affine‐kernel embedding approach to 3D data augmented with user‐imposed constraints on select vertices.     

Fourier domain representation of planar curves for recognition in multiple views

Recognition of planar shapes is an important problem in computer vision and pattern recognition. The same planar object contour imaged from different cameras or from different viewpoints looks different and their recognition is non-trivial. Traditional shape recognition deals with views of the shapes that differ only by simple rotations, translations, and scaling. However, shapes suffer more serious deformation between two general views and hence recognition approaches designed to handle translations, rotations, and/or scaling would prove to be insufficient. Many algebraic relations between matching primitives in multiple views have been identified recently. In this paper, we explore how shape properties and multiview relations can be combined to recognize planar shapes across multiple views. We propose novel recognition constraints that a planar shape boundary must satisfy in multiple views. The constraints are on the rank of a Fourier-domain measurement matrix computed from the points on the shape boundary. Our method can additionally compute the correspondence between the curve points after a match is established. We demonstrate the applications of these constraints experimentally on a number of synthetic and real images.     

Possibility theory in constraint satisfaction problems: Handling priority, preference and uncertainty

In classical Constraint Satisfaction Problems (CSPs) knowledge is embedded in a set of hard constraints, each one restricting the possible values of a set of variables. However constraints in real world problems are seldom hard, and CSP's are often idealizations that do not account for the preference among feasible solutions. Moreover some constraints may have priority over others. Lastly, constraints may involve uncertain parameters. This paper advocates the use of fuzzy sets and possibility theory as a realistic approach for the representation of these three aspects. Fuzzy constraints encompass both preference relations among possible instantiations and priorities among constraints. In a Fuzzy Constraint Satisfaction Problem (FCSP), a constraint is satisfied to a degree (rather than satisfied or not satisfied) and the acceptability of a potential solution becomes a gradual notion. Even if the FCSP is partially inconsistent, best instantiations are provided owing to the relaxation of some constraints. Fuzzy constraints are thus flexible. CSP notions of consistency and k-consistency can be extended to this framework and the classical algorithms used in CSP resolution (e.g., tree search and filtering) can be adapted without losing much of their efficiency. Most classical theoretical results remain applicable to FCSPs. In the paper, various types of constraints are modelled in the same framework. The handling of uncertain parameters is carried out in the same setting because possibility theory can account for both preference and uncertainty. The presence of uncertain parameters leads to ill-defined CSPs, where the set of constraints which defines the problem is not precisely known.     

Inverse Markov Process Based Constrained Dynamic Graph Layout

In online dynamic graph drawing,constraints over nodes and node pairs help preserve a coherent mental map in a sequence of graphs.Defining the constraints is challenging due to the requirements of both preserving mental map and satisfying the visual aesthetics of a graph layout.Most existing algorithms basically depend on local changes but fail to do proper evaluations on the global propagation when setting constraints.To solve this problem,we introduce a heuristic model derived from PageRank which simulates the node movement as an inverse Markov process hence to give a global analysis of the layout's change,according to which different constraints can be set.These constraints,along with stress function,generate layouts maintaining spatial positions and shapes of relatively stable substructures between adjacent graphs.Experiments demonstrate that our method preserves both structure and position similarity to help users track graph changes visually.