Constructive Hypervolume Modeling

This paper deals with modeling point sets with attributes. A point set in a geometric space of an arbitrary dimension is a geometric model of a real/abstract object or process under consideration. An attribute is a mathematical model of an object property of arbitrary nature (material, photometric, physical, statistical, etc.) defined at any point of the point set. We provide a brief survey of different modeling techniques related to point sets with attributes. It spans such different areas as solid modeling, heterogeneous objects modeling, scalar fields or “implicit surface” modeling and volume graphics. Then, on the basis of this survey we formulate requirements to a general model of hypervolumes (multidimensional point sets with multiple attributes). A general hypervolume model and its components such as objects, operations, and relations are introduced and discussed. A function representation (FRep) is used as the basic model for the point set geometry and attributes represented independently using real-valued scalar functions of several variables. Each function defining the geometry or an attribute is evaluated at the given point by a procedure traversing a constructive tree structure with primitives in the leaves and operations in the nodes of the tree. This reflects the constructive nature of the symmetric approach to modeling geometry and associated attributes in multidimensional space. To demonstrate a particular application of the proposed general model, we consider in detail the problem of texturing, introduce a model of constructive hypervolume texture, and then discuss its implementation, as well as the special modeling language we used for modeling hypervolume objects.     

Constructive sculpting of heterogeneous volumetric objects using trivariate B-splines

This paper deals with modeling heterogeneous volumetric objects as point sets with attributes using trivariate B-splines. In contrast to homogeneous volumes with uniform distribution of material and other properties, a heterogeneous volumetric object has a number of variable attributes assigned at each point. An attribute is a mathematical model of an object property of an arbitrary nature (material, photometric, physical, statistical, etc.). In our approach, the function representation (FRep) is used as the basic model for both object geometry and attributes represented independently using real-valued scalar functions of point coordinates. While FRep directly defines object geometry, for an attribute it specifies a space partition used to define the attribute function. We propose a volume sculpting scheme with multiresolution capability based on trivariate B-spline functions to define both object geometry and its attributes. A new trivariate B-spline primitive is proposed that can be used as a leaf in an FRep constructive tree. An interactive volume modeler based on trivariate B-splines and other simple primitives is described, with a real-time repolygonization of the surface during modeling. We illustrate that the space partition obtained in the modeling process can be applied to define attributes for the objects with an arbitrary geometry model such as BRep or homogeneous volume models.     

Geometric texture modeling

Texture mapping has become an essential tool in any synthetic rendering scheme that aims at photorealism. Texture mapping typically associates any point on the surface of the rendered object with a location in the texture space. The surface point is then assigned rendering attributes, such as color or translucency from the respective location found in the texture space. Texture mapping techniques have also been used in attempts to emulate highly detailed geometry on the surfaces of objects. The proposed surface detail synthesis approach closes the loop from modeling to rendering using computer graphics texture mapping techniques, bringing them back into the geometric modeling phase. This article focuses primarily on texturing techniques that relate to shape modeling and surface geometry alteration.     

High Dynamic Range Point Clouds for Real‐Time Relighting

Acquired 3D point clouds make possible quick modeling of virtual scenes from the real world. With modern 3D capture pipelines, each point sample often comes with additional attributes such as normal vector and color response. Although rendering and processing such data has been extensively studied, little attention has been devoted using the light transport hidden in the recorded per‐sample color response to relight virtual objects in visual effects (VFX) look‐dev or augmented reality (AR) scenarios. Typically, standard relighting environment exploits global environment maps together with a collection of local light probes to reflect the light mood of the real scene on the virtual object. We propose instead a unified spatial approximation of the radiance and visibility relationships present in the scene, in the form of a colored point cloud. To do so, our method relies on two core components: High Dynamic Range (HDR) expansion and real‐time Point‐Based Global Illumination (PBGI). First, since an acquired color point cloud typically comes in Low Dynamic Range (LDR) format, we boost it using a single HDR photo exemplar of the captured scene that can cover part of it. We perform this expansion efficiently by first expanding the dynamic range of a set of renderings of the point cloud and then projecting these renderings on the original cloud. At this stage, we propagate the expansion to the regions not covered by the renderings or with low‐quality dynamic range by solving a Poisson system. Then, at rendering time, we use the resulting HDR point cloud to relight virtual objects, providing a diffuse model of the indirect illumination propagated by the environment. To do so, we design a PBGI algorithm that exploits the GPU's geometry shader stage as well as a new mipmapping operator, tailored for G‐buffers, to achieve real‐time performances. As a result, our method can effectively relight virtual objects exhibiting diffuse and glossy physically‐based materials in real time. Furthermore, it accounts for the spatial embedding of the object within the 3D environment. We evaluate our approach on manufactured scenes to assess the error introduced at every step from the perfect ground truth. We also report experiments with real captured data, covering a range of capture technologies, from active scanning to multiview stereo reconstruction.     

Hierarchical Quad Meshing of 3D Scanned Surfaces

In this paper we present a novel method to reconstruct watertight quad meshes on scanned 3D geometry. There exist many different approaches to acquire 3D information from real world objects and sceneries. Resulting point clouds depict scanned surfaces as sparse sets of positional information. A common downside is the lack of normals, connectivity or topological adjacency data which makes it difficult to actually recover a meaningful surface. The concept described in this paper is designed to reconstruct a surface mesh despite all this missing information. Even when facing varying sample density, our algorithm is still guaranteed to produce watertight manifold meshes featuring quad faces only. The topology can be set‐up to follow superimposed regular structures or align naturally to the point cloud's shape. Our proposed approach is based on an initial divide and conquer subsampling procedure: Surface samples are clustered in meaningful neighborhoods as leafs of a kd‐tree. A representative sample of the surface neighborhood is determined for each leaf using a spherical surface approximation. The hierarchical structure of the binary tree is utilized to construct a basic set of loose tiles and to interconnect them. As a final step, missing parts of the now coherent tile structure are filled up with an incremental algorithm for locally optimal gap closure. Disfigured or concave faces in the resulting mesh can be removed with a constrained smoothing operator.     

Texturing 3D Models of Real World Objects from Multiple Unregistered Photographic Views

As the efficiency of computer graphic rendering methods is increasing, generating realistic models is now becoming a limiting factor. In this paper we present a new technique to enhance already existing geometry models of real world objects with textures reconstructed from a sparse set of unregistered still photographs. The aim of the proposed technique is the generation of nearly photo-realistic models of arbitrarily shaped objects with minimal effort. In our approach, we require neither a prior calibration of the camera nor a high precision of the user's interaction. Two main problems have to be addressed of which the first is the recovery of the unknown positions and parameters of the camera. An initial estimate of the orientation is calculated from interactively selected point correspondences. Subsequently, the unknown parameters are accurately calculated by minimising a blend of objective functions in a 3D-2D projective registration approach. The key point of the proposed method of registration is a novel filtering approach which utilises the spatial information provided by the geometry model. Second, the individual images have to be combined yielding a set of consistent texture maps. We present a robust method to recover the texture from the photographs thereby preserving high spatial frequencies and eliminating artifacts, particularly specular highlights. Parts of the object not seen in any of the photographs are interpolated in the textured model. Results are shown for three complex example objects with different materials and numerous self-occlusions.     

Simple parallel hierarchical and relaxation algorithms for segmenting noncausal markovian random fields

The modeling and segmentation of images by MRF's (Markov random fields) is treated. These are two-dimensional noncausal Markovian stochastic processes. Two conceptually new algorithms are presented for segmenting textured images into regions in each of which the data are modeled as one of C MRF's. The algorithms are designed to operate in real time when implemented on new parallel computer architectures that can be built with present technology. A doubly stochastic representation is used in image modeling. Here, a Gaussian MRF is used to model textures in visible light and infrared images, and an autobinary (or autoternary, etc.) MRF to model a priori information about the local geometry of textured image regions. For image segmentation, the true texture class regions are treated either as a priori completely unknown or as a realization of a binary (or ternary, etc.) MRF. In the former case, image segmentation is realized as true maximum likelihood estimation. In the latter case, it is realized as true maximum a posteriori likelihood segmentation. In addition to providing a mathematically correct means for introducing geometric structure, the autobinary (or ternary, etc.) MRF can be used in a generative mode to generate image geometries and artificial images, and such simulations constitute a very powerful tool for studying the effects of these models and the appropriate choice of model parameters. The first segmentation algorithm is hierarchical and uses a pyramid-like structure in new ways that exploit the mutual dependencies among disjoint pieces of a textured region.     

Approximate Symmetry Detection in Partial 3D Meshes

Symmetry is a common characteristic in natural and man‐made objects. Its ubiquitous nature can be exploited to facilitate the analysis and processing of computational representations of real objects. In particular, in computer graphics, the detection of symmetries in 3D geometry has enabled a number of applications in modeling and reconstruction. However, the problem of symmetry detection in incomplete geometry remains a challenging task. In this paper, we propose a vote‐based approach to detect symmetry in 3D shapes, with special interest in models with large missing parts. Our algorithm generates a set of candidate symmetries by matching local maxima of a surface function based on the heat diffusion in local domains, which guarantee robustness to missing data. In order to deal with local perturbations, we propose a multi‐scale surface function that is useful to select a set of distinctive points over which the approximate symmetries are defined. In addition, we introduce a vote‐based scheme that is aware of the partiality, and therefore reduces the number of false positive votes for the candidate symmetries. We show the effectiveness of our method in a varied set of 3D shapes and different levels of partiality. Furthermore, we show the applicability of our algorithm in the repair and completion of challenging reassembled objects in the context of cultural heritage.     

Lazy Solid Texture Synthesis

Existing solid texture synthesis algorithms generate a full volume of color content from a set of 2D example images. We introduce a new algorithm with the unique ability to restrict synthesis to a subset of the voxels, while enforcing spatial determinism. This is especially useful when texturing objects, since only a thick layer around the surface needs to be synthesized. A major difficulty lies in reducing the dependency chain of neighborhood matching, so that each voxel only depends on a small number of other voxels. Our key idea is to synthesize a volume from a set of pre‐computed 3D candidates, each being a triple of interleaved 2D neighborhoods. We present an efficient algorithm to carefully select in a pre‐process only those candidates forming consistent triples. This significantly reduces the search space during subsequent synthesis. The result is a new parallel, spatially deterministic solid texture synthesis algorithm which runs efficiently on the GPU. Our approach generates high resolution solid textures on surfaces within seconds. Memory usage and synthesis time only depend on the output textured surface area. The GPU implementation of our method rapidly synthesizes new textures for the surfaces appearing when interactively breaking or cutting objects.     

Alignment of continuous video onto 3D point clouds

We propose a general framework for aligning continuous (oblique) video onto 3D sensor data. We align a point cloud computed from the video onto the point cloud directly obtained from a 3D sensor. This is in contrast to existing techniques where the 2D images are aligned to a 3D model derived from the 3D sensor data. Using point clouds enables the alignment for scenes full of objects that are difficult to model; for example, trees. To compute 3D point clouds from video, motion stereo is used along with a state-of-the-art algorithm for camera pose estimation. Our experiments with real data demonstrate the advantages of the proposed registration algorithm for texturing models in large-scale semi-urban environments. The capability to align video before a 3D model is built from the 3D sensor data offers new practical opportunities for 3D modeling. We introduce a novel modeling-through-registration approach that fuses 3D information from both the 3D sensor and the video. Initial experiments with real data illustrate the potential of the proposed approach.     

Modeling Complex Unfoliaged Trees from a Sparse Set of Images

We present a novel image‐based technique for modeling complex unfoliaged trees. Existing tree modeling tools either require capturing a large number of views for dense 3D reconstruction or rely on user inputs and botanic rules to synthesize natural‐looking tree geometry. In this paper, we focus on faithfully recovering real instead of realistically‐looking tree geometry from a sparse set of images. Our solution directly integrates 2D/3D tree topology as shape priors into the modeling process. For each input view, we first estimate a 2D skeleton graph from its matte image and then find a 2D skeleton tree from the graph by imposing tree topology. We develop a simple but effective technique for computing the optimal 3D skeleton tree most consistent with the 2D skeletons. For each edge in the 3D skeleton tree, we further apply volumetric reconstruction to recover its corresponding curved branch. Finally, we use piecewise cylinders to approximate each branch from the volumetric results. We demonstrate our framework on a variety of trees to illustrate the robustness and usefulness of our technique.     

物联网需求驱动的服务组合方法

为实现依据用户需求动态地组合原子服务, 形成服务集合, 提出一种基于本体的服务组合方法。首先对物联网服务进行多视图建模, 使用服务交互模型描述服务与物理实体的交互过程, 服务功能模型刻画物理世界中服务的属性和行为, 服务状态模型表示服务引起的期望状态变化, 并采用扩展的OWL描述面向物理对象的服务。同时, 采用多维QoS模型对用户的需求进行建模, 使用语义的方法进行服务的匹配与组合, 并基于QoS选择满足约束的服务。最后, 通过案例研究和实验验证了所提方法的正确性和有效性。     

Constructing X-of-N Attributes for Decision Tree Learning

While many constructive induction algorithms focus on generating new binary attributes, this paper explores novel methods of constructing nominal and numeric attributes. We propose a new constructive operator, X-of-N. An X-of-N representation is a set containing one or more attribute-value pairs. For a given instance, the value of an X-of-N representation corresponds to the number of its attribute-value pairs that are true of the instance. A single X-of-N representation can directly and simply represent any concept that can be represented by a single conjunctive, a single disjunctive, or a single M-of-N representation commonly used for constructive induction, and the reverse is not true. In this paper, we describe a constructive decision tree learning algorithm, called XofN. When building decision trees, this algorithm creates one X-of-N representation, either as a nominal attribute or as a numeric attribute, at each decision node. The construction of X-of-N representations is carried out by greedily searching the space defined by all the attribute-value pairs of a domain. Experimental results reveal that constructing X-of-N attributes can significantly improve the performance of decision tree learning in both artificial and natural domains in terms of higher prediction accuracy and lower theory complexity. The results also show the performance advantages of constructing X-of-N attributes over constructing conjunctive, disjunctive, or M-of-N representations for decision tree learning.     

Attribute selection based on information gain ratio in fuzzy rough set theory with application to tumor classification

Tumor classification based on gene expression levels is important for tumor diagnosis. Since tumor data in gene expression contain thousands of attributes, attribute selection for tumor data in gene expression becomes a key point for tumor classification. Inspired by the concept of gain ratio in decision tree theory, an attribute selection method based on fuzzy gain ratio under the framework of fuzzy rough set theory is proposed. The approach is compared to several other approaches on three real world tumor data sets in gene expression. Results show that the proposed method is effective. This work may supply an optional strategy for dealing with tumor data in gene expression or other applications.     

Parameterized point pattern matching and its application torecognition of object families

The problem of recognizing and localizing objects that can vary in parameterized ways is considered. To achieve this goal, a concept of parameterized point pattern is introduced to model parameterized families of such objects, and a parameterized point pattern matching algorithm is proposed. A parameterized point pattern is a very flexible concept that can be used to model a large class of parameterized objects, such as a pair of scissors with rotating blades. The proposed matching algorithm is formulated as a tree search procedure, and it generates all maximum matchings satisfying a condition called δ-boundedness. Several pruning methods based on the condition of δ-boundedness and their efficient computing techniques are given. The proposed matching algorithm is applied to a real shape matching problem in order to check the validity of the approach     

Floating Textures

We present a novel multi‐view, projective texture mapping technique. While previous multi‐view texturing approaches lead to blurring and ghosting artefacts if 3D geometry and/or camera calibration are imprecise, we propose a texturing algorithm that warps (“floats”) projected textures during run‐time to preserve crisp, detailed texture appearance. Our GPU implementation achieves interactive to real‐time frame rates. The method is very generally applicable and can be used in combination with many image‐based rendering methods or projective texturing applications. By using Floating Textures in conjunction with, e.g., visual hull rendering, light field rendering, or free‐viewpoint video, improved rendering results are obtained from fewer input images, less accurately calibrated cameras, and coarser 3D geometry proxies.     

Heterogeneous object modeling through direct face neighborhood alteration

Two recent advances—the use of functionally gradient materials in parts and layered manufacturing technology—have brought to the forefront the need for design and fabrication methodologies for heterogeneous objects. However, current solid modeling systems, a core component of computer-aided design and fabrication tools, are typically purely geometry based, and only after the modeling of product geometry, can a part's non-geometric attributes such as material composition be modeled. This sequential order of modeling leads to unnecessary operations and over-segmented 3D regions during heterogeneous object modeling processes.

To enable an efficient design of heterogeneous objects, we propose a novel method, direct face neighborhood operation. This approach combines the geometry and material decisions into a common computational framework as opposed to separate and sequential operations in existing modeling systems. We present theories and algorithms for direction face neighborhood alteration, which enables direct alteration of face neighborhood before 3D regions are formed. This alteration is based on set membership classification (SMC) and region material semantics. The SMC is computationally enhanced by the usage of topological characteristics of heterogeneous objects. After the SMC, boundary evaluation is performed according to the altered face neighborhood. In comparison with other solid modeling methods, the direct face neighborhood alteration method is computationally effective, allows direct B-Rep operations, and is efficient for persistent region naming. A prototype system has been implemented to validate the method and some examples are presented.