Realistic human reconstruction embraces an extensive range of applications as depth sensors advance.However,current stateof-the-art methods with RGB-D input still suffer from artefacts,such as noisy surfaces,non-human...Realistic human reconstruction embraces an extensive range of applications as depth sensors advance.However,current stateof-the-art methods with RGB-D input still suffer from artefacts,such as noisy surfaces,non-human shapes,and depth ambiguity,especially for the invisible parts.The authors observe the main issue is the lack of geometric semantics without using depth input priors fully.This paper focuses on improving the representation ability of implicit function,exploring an effective method to utilise depth-related semantics effectively and efficiently.The proposed geometry-enhanced implicit function enhances the geometric semantics with the extra voxel-aligned features from point clouds,promoting the completion of missing parts for unseen regions while preserving the local details on the input.For incorporating multi-scale pixel-aligned and voxelaligned features,the authors use the Squeeze-and-Excitation attention to capture and fully use channel interdependencies.For the multi-view reconstruction,the proposed depth-enhanced attention explicitly excites the network to“sense”the geometric structure for a more reasonable feature aggregation.Experiments and results show that our method outperforms current RGB and depth-based SOTA methods on the challenging data from Twindom and Thuman3.0,and achieves a detailed and completed human reconstruction,balancing performance and efficiency well.展开更多
Surface-based geometric modeling has many advantages in terms of visualization and traditional subtractive manufacturing using computer-numerical-control cutting-machine tools.However,it is not an ideal solution for a...Surface-based geometric modeling has many advantages in terms of visualization and traditional subtractive manufacturing using computer-numerical-control cutting-machine tools.However,it is not an ideal solution for additive manufacturing because to digitally print a surface-represented geometric object using a certain additive manufacturing technology,the object has to be converted into a solid representation.However,converting a known surface-based geometric representation into a printable representation is essentially a redesign process,and this is especially the case,when its interior material structure needs to be considered.To specify a 3D geometric object that is ready to be digitally manufactured,its representation has to be in a certain volumetric form.In this research,we show how some of the difficulties experienced in additive manufacturing can be easily solved by using implicitly represented geometric objects.Like surface-based geometric representation is subtractive manufacturing-friendly,implicitly described geometric objects are additive manufacturing-friendly:implicit shapes are 3D printing ready.The implicit geometric representation allows to combine a geometric shape,material colors,an interior material structure,and other required attributes in one single description as a set of implicit functions,and no conversion is needed.In addition,as implicit objects are typically specified procedurally,very little data is used in their specifications,which makes them particularly useful for design and visualization with modern cloud-based mobile devices,which usually do not have very big storage spaces.Finally,implicit modeling is a design procedure that is parallel computing-friendly,as the design of a complex geometric object can be divided into a set of simple shape-designing tasks,owing to the availability of shape-preserving implicit blending operations.展开更多
In this paper, the well known implicit function theorem was applied to study existence and uniqueness of periodic solution of Duffing-type equation. Un-der appropriate conditions around the origin, a unique periodic s...In this paper, the well known implicit function theorem was applied to study existence and uniqueness of periodic solution of Duffing-type equation. Un-der appropriate conditions around the origin, a unique periodic solution was obtained.展开更多
We prove a global version of the implicit function theorem under a special condition and apply this result to the proof of a modified Hyers-Ulam-Rassias stability of exact differential equations of the form, g（x, y）...We prove a global version of the implicit function theorem under a special condition and apply this result to the proof of a modified Hyers-Ulam-Rassias stability of exact differential equations of the form, g（x, y） ＋ h（x, y）y＇ =0.展开更多
In this paper we shall study the solvability of discontinuous functional equations, and apply the so-obtained results to discontinuous implicit initial value problems in ordered Banach spaces. The proofs are based on ...In this paper we shall study the solvability of discontinuous functional equations, and apply the so-obtained results to discontinuous implicit initial value problems in ordered Banach spaces. The proofs are based on fixed point results in ordered spaces proved recently by the author. A concrete example is solved to demonstrate the obtained results.展开更多
In this paper,we present an approach for smooth surface reconstructions interpolating triangular meshes with ar- bitrary topology and geometry.The approach is based on the well-known radial basis functions (RBFs) and ...In this paper,we present an approach for smooth surface reconstructions interpolating triangular meshes with ar- bitrary topology and geometry.The approach is based on the well-known radial basis functions (RBFs) and the constructed surfaces are generalized thin-plate spline surfaces.Our algorithm first defines a pair of offset points for each vertex of a given mesh to en- hance the controUability of local geometry and to assure stability of the construction.A linear system is then solved by LU decomposi- tion and the implicit governing equation of interpolating surface is obtained.The constructed surfaces finally are visualized by a Marching Cubes based polygonizer.The approach provides a robust and efficient solution for smooth surface reconstruction from various 3 D meshes.展开更多
This paper proposes a 3D 2-node element for beams and cables. Main improvements of the element are two new interpolation functions for beam axis and cross-sectional rotation. New interpolation functions employ implici...This paper proposes a 3D 2-node element for beams and cables. Main improvements of the element are two new interpolation functions for beam axis and cross-sectional rotation. New interpolation functions employ implicit functions to simulate large deformations. In the translational interpolation function, two parameters which affect lateral deflection geometry are defined implicitly through nonlinear equations. The proposed translational interpolation function is shown to be more accurate than Hermitian function at large deformations. In the rotational interpolation function, twist rate is defined implicitly through a torsional continuity equation. Cross-sectional rotation which is strictly consistent to beam axis is obtained through separate bending rotation interpolation and torsional rotation interpolation. The element model fully accounts for geometric nonlinearities and coupling effects,and thus,can simulate cables with zero bending stiffness. Stiffness matrix and load vector have been derived using symbolic computation. Source code has been generated automatically.Numerical examples show that the proposed element has significantly higher accuracy than conventional 2-node beam elements under the same meshes for geometrically nonlinear problems.展开更多
In this paper,we prove the converse of gem is right equivalent is also true in[1] and[2],obtain the necessary and sufficient conditions of equivalence of a class gems of C∞ function on Banach spaces.
基金supported by the National Key R&D Programme of China(2022YFF0902200).
文摘Realistic human reconstruction embraces an extensive range of applications as depth sensors advance.However,current stateof-the-art methods with RGB-D input still suffer from artefacts,such as noisy surfaces,non-human shapes,and depth ambiguity,especially for the invisible parts.The authors observe the main issue is the lack of geometric semantics without using depth input priors fully.This paper focuses on improving the representation ability of implicit function,exploring an effective method to utilise depth-related semantics effectively and efficiently.The proposed geometry-enhanced implicit function enhances the geometric semantics with the extra voxel-aligned features from point clouds,promoting the completion of missing parts for unseen regions while preserving the local details on the input.For incorporating multi-scale pixel-aligned and voxelaligned features,the authors use the Squeeze-and-Excitation attention to capture and fully use channel interdependencies.For the multi-view reconstruction,the proposed depth-enhanced attention explicitly excites the network to“sense”the geometric structure for a more reasonable feature aggregation.Experiments and results show that our method outperforms current RGB and depth-based SOTA methods on the challenging data from Twindom and Thuman3.0,and achieves a detailed and completed human reconstruction,balancing performance and efficiency well.
基金supported by the National Natural Science Foundation of China(Grant No.61502402 and 61379080)the Natural Science Foundation of Fujian Province of China(Grant No.2015J05129).
文摘Surface-based geometric modeling has many advantages in terms of visualization and traditional subtractive manufacturing using computer-numerical-control cutting-machine tools.However,it is not an ideal solution for additive manufacturing because to digitally print a surface-represented geometric object using a certain additive manufacturing technology,the object has to be converted into a solid representation.However,converting a known surface-based geometric representation into a printable representation is essentially a redesign process,and this is especially the case,when its interior material structure needs to be considered.To specify a 3D geometric object that is ready to be digitally manufactured,its representation has to be in a certain volumetric form.In this research,we show how some of the difficulties experienced in additive manufacturing can be easily solved by using implicitly represented geometric objects.Like surface-based geometric representation is subtractive manufacturing-friendly,implicitly described geometric objects are additive manufacturing-friendly:implicit shapes are 3D printing ready.The implicit geometric representation allows to combine a geometric shape,material colors,an interior material structure,and other required attributes in one single description as a set of implicit functions,and no conversion is needed.In addition,as implicit objects are typically specified procedurally,very little data is used in their specifications,which makes them particularly useful for design and visualization with modern cloud-based mobile devices,which usually do not have very big storage spaces.Finally,implicit modeling is a design procedure that is parallel computing-friendly,as the design of a complex geometric object can be divided into a set of simple shape-designing tasks,owing to the availability of shape-preserving implicit blending operations.
文摘In this paper, the well known implicit function theorem was applied to study existence and uniqueness of periodic solution of Duffing-type equation. Un-der appropriate conditions around the origin, a unique periodic solution was obtained.
文摘We prove a global version of the implicit function theorem under a special condition and apply this result to the proof of a modified Hyers-Ulam-Rassias stability of exact differential equations of the form, g（x, y） ＋ h（x, y）y＇ =0.
文摘In this paper we shall study the solvability of discontinuous functional equations, and apply the so-obtained results to discontinuous implicit initial value problems in ordered Banach spaces. The proofs are based on fixed point results in ordered spaces proved recently by the author. A concrete example is solved to demonstrate the obtained results.
文摘In this paper,we present an approach for smooth surface reconstructions interpolating triangular meshes with ar- bitrary topology and geometry.The approach is based on the well-known radial basis functions (RBFs) and the constructed surfaces are generalized thin-plate spline surfaces.Our algorithm first defines a pair of offset points for each vertex of a given mesh to en- hance the controUability of local geometry and to assure stability of the construction.A linear system is then solved by LU decomposi- tion and the implicit governing equation of interpolating surface is obtained.The constructed surfaces finally are visualized by a Marching Cubes based polygonizer.The approach provides a robust and efficient solution for smooth surface reconstruction from various 3 D meshes.
基金Sponsored by the National Natural Science Foundation of China(Grant No.91215302)
文摘This paper proposes a 3D 2-node element for beams and cables. Main improvements of the element are two new interpolation functions for beam axis and cross-sectional rotation. New interpolation functions employ implicit functions to simulate large deformations. In the translational interpolation function, two parameters which affect lateral deflection geometry are defined implicitly through nonlinear equations. The proposed translational interpolation function is shown to be more accurate than Hermitian function at large deformations. In the rotational interpolation function, twist rate is defined implicitly through a torsional continuity equation. Cross-sectional rotation which is strictly consistent to beam axis is obtained through separate bending rotation interpolation and torsional rotation interpolation. The element model fully accounts for geometric nonlinearities and coupling effects,and thus,can simulate cables with zero bending stiffness. Stiffness matrix and load vector have been derived using symbolic computation. Source code has been generated automatically.Numerical examples show that the proposed element has significantly higher accuracy than conventional 2-node beam elements under the same meshes for geometrically nonlinear problems.
基金Supported by the National Science Foundation of China（60802045） Supported by the Science and Technology Foundation of Guizhou（20052004） Supported by the Science Foundation of Qiannan Normal College for Nationalities
文摘In this paper,we prove the converse of gem is right equivalent is also true in[1] and[2],obtain the necessary and sufficient conditions of equivalence of a class gems of C∞ function on Banach spaces.
