A PDE‐based head visualization method with CT data

Chen, Congkun; Yu, Shengkai; Li, Fang; Zhang, Guixu; Ugail, Hassan

doi:10.1002/cav.1683

Cited by 5 publications

(6 citation statements)

References 44 publications

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“…Pan et al combine geometric partial differential equations with surface subdivision to develop a unified method for freeform surface design [31]. Chen et al visualise computed tomography data of human heads through partial differential equation-based surface reconstruction [32]. Wang et al investigate how to optimally convert PDE surface-represented high-speed train heads into NURBS surfaces [33].…”

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

Axioms

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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

Axioms

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show abstract

“…Surface generation from cross-sections is used in many applications, especially in medical visualization. Some illustrative examples include human body 3D visualization with 2D computed tomography (CT) slices [22] or magnetic resonance imaging (MRI) data [23]. Different methods have been developed to reconstruct 3D models or surfaces from cross sections or point clouds [24][25][26][27].…”

Section: Related Workmentioning

confidence: 99%

“…Solving Equation ( 21), we obtain the undetermined constants a P1 w0,i (w = x, y, z; i = 0, 1, 2, 3, 4, 5). Solving Equation (22), we obtain the undetermined constants a P1 wn,i (w = x, y; n = 1, 2, . .…”

Section: Pde Surface Patch 1 Creationmentioning

confidence: 99%

3D Modelling with C2 Continuous PDE Surface Patches

Bian

et al. 2022

Mathematics

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In this paper, we present a new modelling method to create 3D models. First, characteristic cross section curves are generated and approximated by generalized elliptic curves. Then, a vector-valued sixth-order partial differential equation is proposed, and its closed form solution is derived to create PDE surface patches from cross section curves where two adjacent PDE-surface patches are automatically stitched together. With the approach presented in this paper, C2 continuity between adjacent surface patches is well-maintained. Since surface creation of the model is transformed into the generation of cross sectional curves and few undetermined constants are required to describe cross sectional curves accurately, the proposed approach can save manual operations, reduce information storage, and generate 3D models quickly.

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“…Freedom in the evolution of a smooth topology can be achieved using methods with various degrees of complexity. If the generation of the interface is viewed as a boundary-value problem, the solution of a system of partial differential equations can be used to define a smooth interface ( [20,21,22,23]). Here, a set of parameters control the geometry through boundary conditions along the interface.…”

Section: Introductionmentioning

confidence: 99%

Ambiguous phase assignment of discretized 3D geometries in topology optimization

Barrera,

Maute

2020

Preprint

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Level set-based immersed boundary techniques operate on nonconforming meshes while providing a crisp definition of interface and external boundaries. In such techniques, an isocontour of a level set field interpolated from nodal level set values defines a problem's geometry. If the interface is explicitly tracked, the intersected elements are typically divided into sub-elements to which a phase needs to be assigned. Due to loss of information in the discretization of the level set field, certain geometrical configurations allow for ambiguous phase assignment of sub-elements, and thus ambiguous definition of the interface. The study presented here focuses on analyzing these topological ambiguities in embedded geometries constructed from discretized level set fields on hexahedral meshes. The analysis is performed on threedimensional problems where several intersection configurations can significantly affect the problem's topology. This is in contrast to two-dimensional problems where ambiguous topological features exist only in one intersection configuration and identifying and resolving them is straightforward. A set of rules that resolve these ambiguities for two-phase problems is proposed, and algorithms for their implementations are provided. The influence of these rules on the evolution of the geometry in the optimization process is investigated with linear elastic topology optimization problems. These problems are solved by an explicit level set topology optimization framework that uses the extended finite element method to predict physical responses. This study shows that the choice of a rule to resolve topological features can result in drastically different final geometries. However, for the problems studied in this paper, the performances of the optimized design do not differ.

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A PDE‐based head visualization method with CT data

Cited by 5 publications

References 44 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

3D Modelling with C2 Continuous PDE Surface Patches

Ambiguous phase assignment of discretized 3D geometries in topology optimization

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