Fast character modeling with sketch-based PDE surfaces

You, Lihua; Yang, Xiaosong; Pan, Junjun; Lee, Tong‐Yee; Bian, Shaojun; Qian, Kun; Habib, Zulfiqar; Sargano, Allah Bux; Kazmi, Ismail Khalid; Zhang, Jian Jun

doi:10.1007/s11042-020-09060-9

Cited by 6 publications

(11 citation statements)

References 45 publications

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“…Wang et al investigate how to optimally convert PDE surface-represented high-speed train heads into NURBS surfaces [33]. You et al introduce partial differential equations to develop a physics-based deformation method for creating detailed three-dimensional virtual character models [34]. Wang et al integrate partial differential equation-based geometric modelling and boundary-based surface creation to obtain the first analytical C 0 continuous four-sided PDE patches [35].…”

Section: Pde-based Geometric Modellingmentioning

confidence: 99%

Improving Realism of Facial Interpolation and Blendshapes with Analytical Partial Differential Equation-Represented Physics

Day,

Xiao,

Chaudhry

et al. 2024

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How to create realistic shapes by interpolating two known shapes for facial blendshapes has not been investigated in the existing literature. In this paper, we propose a physics-based mathematical model and its analytical solutions to obtain more realistic facial shape changes. To this end, we first introduce the internal force of elastic beam bending into the equation of motion and integrate it with the constraints of two known shapes to develop the physics-based mathematical model represented with dynamic partial differential equations (PDEs). Second, we propose a unified mathematical expression of the external force represented with linear and various nonlinear time-dependent Fourier series, introduce it into the mathematical model to create linear and various nonlinear dynamic deformations of the curves defining a human face model, and derive analytical solutions of the mathematical model. Third, we evaluate the realism of the obtained analytical solutions in interpolating two known shapes to create new shape changes by comparing the shape changes calculated with the obtained analytical solutions and geometric linear interpolation to the ground-truth shape changes and conclude that among linear and various nonlinear PDE-based analytical solutions named as linear, quadratic, and cubic PDE-based interpolation, quadratic PDE-based interpolation creates the most realistic shape changes, which are more realistic than those obtained with the geometric linear interpolation. Finally, we use the quadratic PDE-based interpolation to develop a facial blendshape method and demonstrate that the proposed approach is more efficient than numerical physics-based facial blendshapes.

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Section: Pde-based Geometric Modellingmentioning

confidence: 99%

Improving Realism of Facial Interpolation and Blendshapes with Analytical Partial Differential Equation-Represented Physics

Day,

Xiao,

Chaudhry

et al. 2024

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“…Differential (partial and ordinary) equation model approach is effective in a wide range of applications ranging from up-to-date texture image classification [ 42 , 43 ] (SVM) to data-driven and physics-informed neural networks (PINNs) involving inverse problems [ 50 ] and machine learning for fluid mechanics [ 8 ]. In [ 77 ], the authors propose a new physics-based deformation method and efficient character that uses PDE surfaces for an improved modeling framework for creation of detailed 3D virtual geometric models of characters. In [ 6 ], the authors used a differential equation inspired by Newton’s law of motion for accurate coarse soft tissue modeling using finite element method-based fine simulation.…”

Section: Related Workmentioning

confidence: 99%

“…In [12] is presented a fractional-order differential equation for modeling of COVID-19 infection of epithelial cells. We refer the interested reader to [1,6,8,26,42,43,45,50,70,77] and the references cited therein for a survey on the partial differential equation modeling approaches along with several fine tuning tools as such as physics-informed, physicallybased simulation, data-driven method and data-driven enrichment for state-of-the-art ideas on development methods of multimedia applications involving differential equation as a crucial tool.…”

Section: Related Workmentioning

confidence: 99%

Texture image classification based on a pseudo-parabolic diffusion model

Vieira

Abreu

Florindo

2022

Multimed Tools Appl

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This work proposes a novel method based on a pseudo-parabolic diffusion process to be employed for texture recognition. The proposed operator is applied over a range of time scales giving rise to a family of images transformed by nonlinear filters. Therefore each of those images are encoded by a local descriptor (we use local binary patterns for that purpose) and they are summarized by a simple histogram, yielding in this way the image feature vector. Three main novelties are presented in this manuscript: (1) The introduction of a pseudo-parabolic model associated with the signal component of binary patterns to the process of texture recognition and a real-world application to the problem of identifying plant species based on the leaf surface image. (2) We also introduce a simple and efficient discrete pseudo-parabolic differential operator based on finite differences as texture descriptors. While the work in [ 26 ] uses complete local binary patterns, here we use the original version of the local binary pattern operator. (3) We also discuss, in more general terms, the possibilities of exploring pseudo-parabolic models for image analysis as they balance two types of processing that are fundamental for pattern recognition, i.e., they smooth undesirable details (possibly noise) at the same time that highlight relevant borders and discontinuities anisotropically. Besides the practical application, the proposed approach is also tested on the classification of well established benchmark texture databases. In both cases, it is compared with several state-of-the-art methodologies employed for texture recognition. Our proposal outperforms those methods in terms of classification accuracy, confirming its competitiveness. The good performance can be justified to a large extent by the ability of the pseudo-parabolic operator to smooth possibly noisy details inside homogeneous regions of the image at the same time that it preserves discontinuities that convey critical information for the object description. Such results also confirm that model-based approaches like the proposed one can still be competitive with the omnipresent learning-based approaches, especially when the user does not have access to a powerful computational structure and a large amount of labeled data for training.

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“…PDEs have been widely used to describe various physical phenomena, and the shape deformations using PDEs can be regarded as physics-based technique [29]. PDE-based modelling is to describe surfaces by resolving a PDE subjected to a set of suitably defined boundary conditions, and it is a powerful technique to create and manipulate 3D models.…”

Section: Pde-based Modellingmentioning

confidence: 99%

Real-time surface manipulation with $$C^{1}$$ continuity through simple and efficient physics-based deformations

et al. 2021

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We present a novel but simple physics-based method to interactively manipulate surface shapes of 3D models with $$ C^1 $$ C 1 continuity in real time. A fourth-order partial differential equation involving a sculpting force originating from elastic bending of thin plates is proposed to define physics-based deformations and achieve $$ C^1 $$ C 1 continuity at the boundary of deformation regions. In order to obtain real-time physics-based surface manipulation, we construct a mapping relationship between a deformation region in a 3D coordinate space and a unit circle on a 2D parametric plane, formulate corresponding $$ C^1 $$ C 1 continuous boundary conditions for the unit circle, and obtain a simple analytical solution to describe the physics-based deformation in the unit circle caused by a sculpting force. After that, the obtained physics-based deformation is mapped back to the 3D coordinate space, and added to the original surface to create a new surface shape with $$ C^1 $$ C 1 continuity at the boundary of the deformation region. We also develop an interactive user interface as a plug-in of the 3D modelling software package Maya to achieve real-time surface manipulation. The effectiveness, easiness, real-time performance, and better realism of our proposed method is demonstrated by testing surface deformations on several 3D models and comparing with other methods and ground-truth deformations.

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Fast character modeling with sketch-based PDE surfaces

Cited by 6 publications

References 45 publications

Improving Realism of Facial Interpolation and Blendshapes with Analytical Partial Differential Equation-Represented Physics

Improving Realism of Facial Interpolation and Blendshapes with Analytical Partial Differential Equation-Represented Physics

Texture image classification based on a pseudo-parabolic diffusion model

Real-time surface manipulation with $$C^{1}$$ continuity through simple and efficient physics-based deformations

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