Deep learning-based 3D mesh segmentation methods typically rely on dense annotations and fully supervised training, which are costly and difficult to scale to diverse scenarios. This work proposes a light-weight labeling scheme and a corresponding weakly supervised learning framework that significantly reduces annotation cost while maintaining competitive performance. First, we project pixel-level labels from 2D rendered images back onto mesh faces, generating two weakly labeled datasets. We then introduce an instance-specific label propagation method that leverages geometric and topological cues to generate dense pseudo-labels from sparse annotations. Finally, we propose a robust label learning strategy that progressively exploits increasingly reliable samples and introduces a noise-suppression loss to improve pseudo-label quality during self-training. Extensive experiments on two widely used benchmarks, i.e. , COSEG and Human Body dataset, demonstrate that our method achieves performance comparable to state-of-the-art fully supervised approaches with 2% ∼ 5% annotation cost.

Topology optimization (TO) yields structurally optimal designs, but the output is typically represented by faceted, poor-quality surface meshes that are inadequate for high-fidelity simulation and downstream design and manufacturing. This paper proposes an automated framework for transforming raw TO results into smooth, watertight, and CAD-compatible B-rep models that can be directly integrated for subsequent product design. The method capitalizes on the underlying structural topology by first extracting a curve skeleton, which acts as a high-level descriptor of the design’s form and connectivity. This skeleton guides a structured, block-based reconstruction, where junction orientations are determined and branch cross-sections are profiled via ray-casting. A manifold, pure quadrilateral mesh is then generated through a skeletal-driven extrusion process. To ensure high quality resulting surfaces, the initial quad-dominant layout is regularized and subsequently represented by an initial smooth subdivision surface. The geometry is further aligned with the target TO output through a subdivision-based surface reconstruction algorithm, enhanced by a curvature-driven fairness energy. The final output is a geometrically faithful representation of the input raw TO mesh model with a high-level smooth surface, designed for direct integration into downstream workflows. The effectiveness of the method is validated on benchmark compliance minimization problems, demonstrating its capacity to transform intricate, optimized topological structures into manufacturable, high-quality surface models. • Present a robust and automated framework for TO-to-CAD construction. • It converts raw TO results into watertight, high-quality subdivision surface models. • Develop an algorithm for efficient sparse anisotropic quad mesh generation. • The quad mesh is well suited for Catmull-Clark subdivision surface recon- struction. • Produce a CAD-compatible B-rep model for downstream design and man- ufacturing.

We propose a unified tuning framework for primal subdivision schemes that are generalizations of odd-degree uniform B-spline surfaces for unstructured quadrilateral meshes of arbitrary topology. The subdivision of the resulting tuned primal subdivision (TPS) schemes is performed through efficient repeated local refinement operations. One level of subdivision of TPS-schemes is decomposed into one step of simple topological splitting plus an additional series of repeated local smoothing operations. The unified tuning framework optimizes subdivision rules for both topological splitting and smoothing operations near extraordinary vertices by minimizing the curvature fluctuation of the second-order characteristic maps of the respective TPS-scheme. To validate the limit surface quality of TPS-schemes in extraordinary regions, a mesh-independent metric is also devised to estimate local curvature variation in addition to highlight lines and direct curvature evaluation. With (p - 1)/2 steps of smoothing operations in each level of subdivision, the respective TPS-scheme is termed as a degree-p scheme that produces global C p -1 limit surfaces everywhere except at a finite number of extraordinary positions where near- G 2 continuity is achieved. The limit surface of TPS-schemes in extraordinary regions also exhibits appealing highlight lines, and the larger the number of smoothing operations applied in each level of subdivision, the better the final limit surface quality. One of the key advantages of the proposed tuning framework for TPS-schemes is that the optimization of relevant subdivision rules is performed by tuning structured operations of topological splitting and repeated smoothing that involve direct neighbors of an extraordinary vertex only without the need of tuning large subdivision stencils. All subdivision operations of TPS-schemes are local, involving one-ring of neighboring vertices only, which is efficient for high-degree surface subdivision and convenient for practical implementation. Numerical examples also validate the superiority of TPS-schemes over other state-of-the-art subdivision methods in terms of both highlight lines and various curvature measures.

Unlabeled data is often used to improve the generalization ability of one segmentation model. However, it tends to neglect the inherent difficulty of unlabeled samples, and then produces inaccurate pseudo masks in some unseen scenes, resulting in severe confirmation bias and potential performance degradation. These motivate two unexplored questions for new-coming data: (1) How many images do we need to annotate; and (2) how to annotate them? In this paper, two kinds of shadow detectors (i.e., SDTR and SDTR+) based on the Transformer and self-training scheme are successively proposed. The main difference between them is whether weak annotations are required for partial unlabeled data. Specifically, in SDTR, we first introduce an image-level sample selection scheme to separate the unlabeled data into reliable and unreliable samples from the holistic prediction-level stability. Then, we perform selective retraining to exploit the unlabeled images progressively in a curriculum learning manner. While in SDTR+, we further provide various weak labels (i.e., point, box and scribble) for the rest unreliable samples and design corresponding loss functions. By doing this, it can achieve a better trade-off between performance improvement and annotation cost. Experimental results on public benchmarks (i.e., SBU, UCF and ISTD) show that both SDTR and SDTR+ can be favorable against state-of-the-art methods.

We propose an unified λ -subdivision scheme with a continuous family of tuned subdivisions for quadrilateral meshes. Main subdivision stencil parameters of the unified scheme are represented as spline functions of the subdominant eigenvalue λ of respective subdivision matrices and the λ value can be selected within a wide range to produce desired properties of refined meshes and limit surfaces with optimal curvature performance in extraordinary regions. Spline representations of stencil parameters are constructed based on discrete optimized stencil coefficients obtained by a general tuning framework that optimizes eigenvectors of subdivision matrices towards curvature continuity conditions. To further improve the quality of limit surfaces, a weighting function is devised to penalize sign changes of Gauss curvatures on respective second order characteristic maps. By selecting an appropriate λ , the resulting unified subdivision scheme produces anticipated properties towards different target applications, including nice properties of several other existing tuned subdivision schemes. Comparison results also validate the advantage of the proposed scheme with higher quality surfaces for subdivision at lower λ values, a challenging task for other related tuned subdivision schemes.

Cloud native computing featured by microservice has been regarded as a compelling trend in cloud application development. Edge computing, as an alternative or complemen-tary to cloud computing, is potential to expand the microservice to edge computing, simplifying the development and deployment of edge applications. Despite that, there is still a challenge on how to manage the microservices efficiently in the open and heterogeneous distributed environment. To this end, service mesh provides a potential solution in efficient microservices management. However, as a traditional cloud-oriented architecture, it can not be applied into edge computing directly since the centralized controller policy. To address this problem, in this paper, we propose an edge service mesh architecture with distributively deployed controllers for edge native computing. We further inves-tigate the problem on how to deploy these distributive controllers in a cost efficient manner with the consideration of control cost and the synchronization cost. The problem is formulated into a non-linear optimization form and then linearized into an integer linear programming (ILP) problem. To tackle the computation complexity, we then come up with a customized k-means based algorithm (i.e., ck-means) in polynomial computation complexity. The experimental results verify the efficiency of our ck-means algorithm in comparison with the traditional k-means algorithm.

With the development of deep neural networks (DNNs), more complex accelerators have been designed for more sophisticated networks. Naturally, the complexity of accelerators makes them vulnerable to transient errors. Also, some DNN accelerators are widely used the safety-critical systems, such as autonomous vehicles. Therefore, the susceptibility to transient errors makes research on mitigation techniques more significant, and errors of accelerators should be limited to none. Some researchers proposed the modular redundancy method, which offers a highly reliable way but also considerably increases overhead. In this regard, algorithm-based solutions offer cheaper solutions. However, their implementation is primarily observed in software-based error injections. In this study, we propose a novel approach that focuses on implementing algorithm-based error detection (ABED) for RTL-level (hardware-based) error injections. Previous studies generally focused on the impact of soft errors in memory structures of embedded system-based accelerators. However, the main goal of this research is to study the impact of soft errors in processing elements and how to mitigate them. We implement an algorithm-based error detection that utilizes checksums for verifying convolution operations with low overhead. We first explain how to overcome the challenges of implementing ABED on FPGA-based accelerators, then how to implement it. We implement and evaluate our solution on an industry-level DNN accelerator called NVIDIA deep learning accelerator (NVDLA). In this study, our error injection method is constructed to test the most common soft error scenarios in processing units. The results of the research show that algorithm-based fault tolerance can detect all silent data corruptions (SDC) while maintaining a very low overhead (6-23%) on runtime.

Abstract This paper presents subdivision schemes with subdivision stencils near an extraordinary vertex that are free from or with substantially reduced polar artifact in extraordinary regions while maintaining the best possible bounded curvature at extraordinary positions. The subdivision stencils are firstly constructed to meet tangent plane continuity with bounded curvature at extraordinary positions. They are further optimized towards curvature continuity at an extraordinary position with additional measures for removing or for minimizing the polar artifact in extraordinary regions. The polar artifact for subdivision stencils of lower valences is removed by applying an additional constraint to the subdominant eigenvalue to be the same as that of subdivision at regular vertices, while the polar artifact for subdivision stencils of higher valances is substantially reduced by introducing an additional thin‐plate energy function and a penalty function for maintaining the uniformity and regularity of the characteristic map. A new tuned subdivision scheme is introduced by replacing subdivision stencils of Catmull‐Clark subdivision with that from this paper for extraordinary vertices of valences up to nine. We also compare the refined meshes and limit surface quality of the resulting subdivision scheme with that of Catmull‐Clark subdivision and other tuned subdivision schemes. The results show that subdivision stencils from our method produce well behaved subdivision meshes with the least polar artifact while maintaining satisfactory limit surface quality.

Abstract We present a novel method to construct subdivision stencils near extraordinary vertices with limit surfaces having optimal bounded curvature at extraordinary positions. With the proposed method, subdivision stencils for newly inserted and updated vertices near extraordinary vertices are first constructed to ensure subdivision with G1 continuity and bounded curvature at extraordinary positions. The remaining degrees of freedom of the constructed subdivision stencils are further used to optimize the eigenbasis functions corresponding to the subsubdominant eigenvalues of the subdivision with respect to G2 continuity constraints. We demonstrate the method by replacing subdivision stencils near extraordinary vertices for Catmull‐Clark subdivision and compare the results with the original Catmull‐Clark subdivision and previous tuning schemes known with small curvature variation near extraordinary positions. The results show that the proposed method produces subdivision schemes with better or comparable curvature behavior around extraordinary vertices with comparatively simple subdivision stencils.

Traditional 3D model-based bas-relief modeling methods are often limited to model-dependent and monotonic relief styles. This paper presents a novel method for digital bas-relief modeling with intuitive style control. Given a composite normal image, the problem discussed in this paper involves generating a discontinuity-free depth field with high compression of depth data while preserving or even enhancing fine details. In our framework, several layers of normal images are composed into a single normal image. The original normal image on each layer is usually generated from 3D models or through other techniques as described in this paper. The bas-relief style is controlled by choosing a parameter and setting a targeted height for them. Bas-relief modeling and stylization are achieved simultaneously by solving a sparse linear system. Different from previous work, our method can be used to freely design bas-reliefs in normal image space instead of in object space, which makes it possible to use any popular image editing tools for bas-relief modeling. Experiments with a wide range of 3D models and scenes show that our method can effectively generate digital bas-reliefs.

The L2-norm method is often used in the multi-degree reduction problem of Bezier curves, which achieves an approximation order of m+1 by using polynomials of degree m. This paper presents a tangent method for achieving a higher approximation order, in which a system of linear equations in the unknown control points of the resulting approximation Bezier curve is derived. Given the degrees of the given and the approximation Bezier curves, i.e., n and m, the control points of the approximation curve can be explicitly expressed. In principle, when the given Bezier curve geometrically coincides with a cubic Bezier curve, the new method can exactly recover the cubic Bezier curve. Numerical examples show that the new method can achieve a better approximation effect than that of the L2-norm method for degree reduction.

This paper presents some results on isogeometric analysis (IGA) using a new class of basis functions, named truncated interpolatory basis function (TIBF). While much work in IGA has been done based on approximating basis functions, such as B-splines, NURBS and T-splines, little work is reported so far using interpolatory schemes. In this article, a truncated interpolatory basis function is proposed for isogeometric analysis. The basis function has many nice properties which are desirable for both modeling and isogeometric analysis. It has also the potential to be used as an alternative basis for interpolatory subdivision schemes whose basis functions are often not explicitly available. Based on TIBF, a cut-off rule is also proposed for handling shapes with boundaries. The proposed interpolatory scheme based on TIBF exhibits modeling qualities that are pretty close to the Kobbelt subdivision scheme for a regular control mesh. Several examples on IGA based on TIBF are also presented in this article. Both the modeling and simulation examples show that TIBF provides a good alternative option for isogeometric analysis.

For approximating subdivision schemes, there are several unified frameworks for effectively constructing subdivision surfaces generalizing splines of an arbitrary degree. In this article, we present a similar unified framework for interpolatory subdivision schemes. We first decompose the 2 n -point interpolatory curve subdivision scheme into repeated local operations. By extending the repeated local operations to quadrilateral meshes, an efficient algorithm can be further derived for interpolatory surface subdivision. Depending on the number n of repeated local operations, the continuity of the limit curve or surface can be of an arbitrary order C L , except in the surface case at a limited number of extraordinary vertices where C 1 continuity with bounded curvature is obtained. Boundary rules built upon repeated local operations are also presented.

This paper presents an interpolatory subdivision scheme derived from the Doo-Sabin subdivision scheme. We first present the relations among three curve subdivision schemes, namely a four point interpolatory subdivision scheme, a cubic B-spline curve subdivision scheme, and the Chaikin's algorithm that generates uniform quadratic B-spline curves. By generalizing these relations to the surface case, we derive an interpolatory surface subdivision scheme from the Doo-Sabin subdivision scheme, a generalization of the Chaikin's algorithm to surface subdivision. In the new subdivision scheme, we also introduce a variable tension parameter that is dependent to local control vertices. The variable tension parameter can be used to effectively control the resulting limit surface of the proposed subdivision scheme.

An efficient scheme is introduced to construct interpolatory curves and surfaces passing through a set of given scattered data points. The scheme is based on an interpolatory basis derived from the sinc function with a Guassian multiplier previously applied in other fields for signal or function reconstruction. In connection with its application addressed in this article for spatial curve and surface construction, the interpolatory basis possesses various nice properties, such as partition of unity, linear precision, and local support, etc., under a small tolerance. By using these basis functions, free-form curves and surfaces can be conveniently constructed. A designer can adjust the shape of the constructed curve and surface by moving some interpolating points or by inserting new interpolating points. The resulting interpolatory curves and surfaces are C ∞ continuous. Smooth connection between curves or surfaces can easily be achieved. Closed curves and surfaces can also be expressed using the proposed interpolatory basis functions.

This paper describes an approach to the approximation of Loop subdivision surfaces for real-time rendering. The approach consists of two phases, which separately construct the approximation geometry and the normal field of a subdivision surface. It first exploits quartic triangular Bézier patches to approximate the geometry of the subdivision surface by interpolating a grid of sampled points. To remedy the artifact of discontinuity of normal fields between adjacent patches, a continuous normal field is then reconstructed by approximating the tangent vector fields of the subdivision surfaces with quartic triangular Bézier patches. For regular triangles, the approach reproduces the associated subdivision patches, quartic three-directional box splines.

A method of blending circular quadrics with parametric patches is proposed in this paper. It needs n rational bicubic Bezier patches and two S-patches to blend n (n > 2) quadrics. The blend is G1continuous. Explicit formulae of control points of both Beacutezier patches and S-patches are derived from the corresponding G1-continuity conditions. In addition, the shape can be intuitively modified by adjusting the free parameters of the blending surfaces.

This paper applies a modified composite radic(2) subdivision framework to an extensive family of box splines, and therefore generalizes these box splines to irregular control meshes. Particularly, a variant of the quad subdivision of Peters and Shiue (2004) is shown as a special case of the new framework. In addition, a new dual subdivision scheme is also derived, as a generalization of some special box splines. Towards the practical use, the unified framework is also extended for modelling boundary and crease features.

Abstract This article presents an efficient construction of biorthogonal wavelets built upon an interpolatory subdivision for quadrilateral meshes. The interpolatory subdivision scheme is first turned into a scheme for reversible primitive wavelet synthesis. Some desired properties are then incorporated in the primitive wavelet using the lifting scheme. The analysis and synthesis algorithms of the resulting new wavelet are finally obtained as local and in‐place lifting operations. The wavelet inherits the advantage of refinement with added levels of resolution. Numerical experiments show that the lifted wavelet built upon interpolatory subdivision has sufficient stability and better performance in dealing with closed or open semi‐regular quadrilateral meshes compared with other existing wavelets for quadrilateral manifold meshes.

Abstract This paper presents a universal method for constructing interpolatory subdivision schemes from known approximatory subdivisions. The method establishes geometric rules of the associated interpolatory subdivision through addition of further weighted averaging operations to the approximatory subdivision. The paper thus provides a novel approach for designing new interpolatory subdivision schemes. In addition, a family of subdivision surfaces varying from the given approximatory scheme to its associated interpolatory scheme, namely the blending subdivisions, can also be established. Based on the proposed method, variants of several known interpolatory subdivision schemes are constructed. A new interpolatory subdivision scheme is also developed using the same technique. Brief analysis of a family of blending subdivisions associated with the Loop subdivision scheme demonstrates that this particular family of subdivisions are globally C1 continuous while maintaining bounded curvature for regular meshes. As a further extension of the blending subdivisions, a volume‐preserving subdivision strategy is also proposed in the paper.

This paper presents a novel approach for constructing a piecewise triangular cubic polynomial surface with C/sup 1/ continuity around a common corner vertex. A C/sup 1/ continuity condition between two cubic triangular patches is first derived using mixed directional derivatives. An approach for constructing a surface with C/sup 1/ continuity around a corner is then developed. Our approach is easy and fast with the virtue of cubic reproduction, local shape controllability, C/sup 2/ continuous at the corner vertex. Some experimental results are presented to show the applicability and flexibility of the approach.

Abstract This paper presents a new interpolatory subdivision scheme for quadrilateral meshes based on a 1–4 splitting operator. The scheme generates surfaces coincident with those of the Kobbelt interpolatory subdivision scheme for regular meshes. A new group of rules are designed for computing newly inserted vertices around extraordinary vertices. As an extension of the regular masks,the new rules are derived based on a reinterpretation of the regular masks. Eigen‐structure analysis demonstrates that subdivision surfaces generated using the new scheme are C1continuous and, in addition, have bounded curvature.

This paper presents a new interpolatory subdivision for quadrilateral meshes. The proposed scheme employs a /spl radic/2 split operator to refine a given control mesh such that the face number of the refined mesh is doubled after each refinement. For regular meshes, the smallest mask is chosen to calculate newly inserted vertices and special rules are developed to compute the F-vertices for irregular faces based on the Fourier analysis of block circulant matrices. Numerical analysis manifests that the scheme yields globally C1 continuous limit surfaces. Finally, an extension to arbitrary polygonal meshes is considered.

A hierarchically structured constraint-based data model for solid modelling in a virtual reality environment is presented. The data model integrates a high-level constraint-based model for precise object definition, a mid-level CSG/Brep hybrid solid model for supporting hierarchical geometry abstractions and object creation, and a low-level polygon model for real-time visualization and interaction in the virtual reality environment. Constraints are embedded in the solid model and organized at different levels to reflect the entire solid modelling process from features and parts, to assemblies. This model not only provides precise object definition, but also supports real-time visualization and interaction in the VR environment. Furthermore, it has the potential to obtain precise 3D interactions and precise constraint-based manipulations can be deduced from the data model to carry out precise solid modelling in the VR environment.

This paper presents a new approach for fitting a subdivision surface from an irregular and dense triangle mesh of arbitrary topological type. All feature edges and feature vertices of the original mesh model are first identified. A topology- and feature-preserving mesh simplification algorithm is developed to further simplify the dense triangle mesh into a coarse mesh. A subdivision surface with exactly the same topology and sharp features as that of the simplified mesh is finally fitted from a subset of the vertices of the original dense mesh. During the fitting process, both the position masks and subdivision rules are used for setting up the fitting equation. Examples are provided to demonstrate the proposed approach.

The absence of constraints is one of the major limitations in current Virtual Reality (VR) environments. Without constraints, it is difficult to perform precise 3D interactive manipulations in VR environments and precise solid modelling in VR environments cannot be guaranteed. In this paper, constraints are incorporated into the VR environment for intuitive and precise solid modelling. A hierarchically structured constraint-based data model is developed to support solid modelling in the VR environment. Solid modelling in the VR environment is precisely performed in an intuitive manner through constraint-based manipulations. Constraint-based manipulations are accompanied with automatic constraint recognition and precise constraint satisfaction to establish the hierarchically structured constraint-based data model and are realized by allowable motions for precise 3D interactions in the VR environment. The allowable motions are represented as a mathematical matrix for conveniently deriving allowable motions from constraints. A procedure-based degree-of-freedom incorporation approach for 3D constraint solving is presented for deriving the allowable motions. A rule-based constraint recognition engine is developed for both constraint-based manipulations and implicitly incorporating constraints into the VR environment. A prototype system has been implemented for precise solid modelling in an intuitive manner through constraint-based manipulations in the VR environment.

With today's virtual reality systems, it is difficult to directly and precisely create and modify complex objects in a virtual reality environment. One of the most important reasons is the absence of a suitable model representation that can efficiently support solid modelling in a virtual reality environment. A hierarchically structured constraint-based data model for solid modelling in the virtual reality environment is presented in this paper. The data model integrates a high-level constraint-based model for precise object definition, a mid-level CSG/B rep hybrid solid model for supporting hierarchical geometry abstractions and object creation, and a low-level polygon model for real-time visualization and interaction in the virtual reality environment. Constraints are embedded in the solid model and are organized at different levels to reflect the process of solid modelling. This data model not only provides precise object definition, but also supports real-time visualization and interaction in the virtual reality environment.

Based on the semantic equivalence degree the formal definitions of fuzzy functional dependencies (FFDs) and fuzzy multivalued dependencies (FMVDs) are first introduced to the fuzzy relational databases, where fuzziness of data appears in attribute values in the form of possibility attributions, as well as resemblance relations in attribute domain elements, called extended possibility-based fuzzy relational databases. A set of inference rules for FFDs and FMVDs is then proposed. It is shown that FFDs and FMVDs are consistent and the inference rules are sound and complete, just as Armstrong's axioms for classic cases. © 2002 Wiley Periodicals, Inc.

Entity-relationship–extended entity-relationship models play a crucial role in the conceptual design of relational databases as well as object-oriented databases. Recently, several approaches have been proposed to enhance object-oriented databases (OODBs) using fuzzy set theory. In this paper, we introduce a fuzzy extended entity-relationship model to cope with imperfect as well as complex objects in the real world at a conceptual level. In particular, we provide the formal approach to mapping a fuzzy extended entity-relationship model to a fuzzy object-oriented database schema. © 2001 John Wiley & Sons, Inc.

Reverse engineering is an approach for reconstructing a computer model from physical object through dimensional measurement and surface modelling. Various mathematical models have be discussed for the representation of free form surfaces in the context of reverse engineering applications. Most of the existing algorithms are, however, mainly developed for fitting isolated surfaces and one must smoothly connect these surfaces afterwards. This paper presents a procedure for simultaneously fitting smoothly connected multiple surfaces from point clouds with arbitrary topology. The final fitted surfaces are represented as Catmull-Clark surfaces, a network of smoothly connected bicubic B-spline surfaces with a finite number of B-spline subdivision surface patches next to extraordinary corner points. The final fitted surfaces are perfect G2 continuous across all surface boundaries except at a finite number of extraordinary points where G1 continuity is obtained. The algorithm is purely a linear least squares fitting procedure without any constraints.

Fuzzy conceptual data modeling is concentrated on in this paper. Based on possibility theory, A conceptual data model IFO is extended. Different levels of fuzziness are introduced and the corresponding graphical representations are given. IFO data model is this extended to fuzzy IFO data model, denoted IF/sub 2/O in the paper. Attention is paid to the fuzzification of objects and relationships, specially on that of ISA relationships.

In this paper, we propose notions of equivalence and inclusion of fuzzy data in relational databases for measuring their semantic relationship. The fuzziness of data appears in attribute values in forms of possibility distribution as well as resemblance relations in attribute domain elements. An approach for evaluating semantic measures is presented. With the proposal, one can remove fuzzy data redundancy and define fuzzy functional dependency. © 2000 John Wiley & Sons, Inc.