Facial geometry parameterisation based on Partial Differential Equations

Yu, Shengkai; Willis, Philip; Castro, Gabriela; Ugail, Hassan

doi:10.1016/j.mcm.2011.04.025

Cited by 17 publications

(12 citation statements)

References 30 publications

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“…The fundamental reason is that the visual attention mechanism can quickly find the area we hope to get from the massive amount of data. After Sheng et al [18] first proposed the ITTI algorithm, scholars have successively constructed many visual saliency algorithms based on the ITTI algorithm. These algorithms are inspired by the ITTI model in their fundamental ideas.…”

Section: Related Workmentioning

confidence: 99%

Image Segmentation Method for an Illumination Highlight Region of Interior Design Effects Based on the Partial Differential Equation

Wang¹,

Liu

Qian

2021

Advances in Mathematical Physics

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The saliency calculation model based on the principle of partial differential equations sometimes highlights areas with high contrast in the background, and the salient targets obtained occasionally have holes. The above problems can be solved by combining the improved convex hull calculation center saliency map. This paper designs a single-target color image segmentation algorithm based on partial differential equations. First, we calculate the basic saliency map according to the uniqueness of the color and the spatial distribution of the color; second, we then use the superpixel to improve the convex hull and calculate the central saliency map according to the principle; finally, the basic saliency map and the central saliency map are calculated. The weighted fusion is used to obtain the comprehensive saliency map, and the threshold method is used to segment the comprehensive saliency map to obtain the final target image. This paper designs an evaluation standard suitable for the segmentation of the illuminated highlight area of the effect image. It compares the experimental results of the segmentation method in this paper with the SLIC (Simple Linear Iterative Clustering) method and the traditional superpixel method to segment the illuminated highlight area. The segmentation method is applied to the image enhancement experiment. Based on the fuzzy means clustering algorithm, a fuzzy clustering objective function including brightness, color, and distance parameters is designed, which improves the weight of the brightness value in the clustering and improves the edge fit of the segmentation of the lighting highlight area of the rendering. The segmentation method produced by combining the clustering method with the superpixel biased clustering method can improve the output effect of the illuminated highlight area of the effect image after segmentation. We perform color equalization processing on the image to be segmented to reduce the impact of light, then set the closed value of the brightness information component, perform segmentation judgment, and expand the long and short axes of the ellipse model in the high-brightness area to further reduce the impact of light. The experimental results prove that the above method has a better segmentation effect than the traditional ellipse model and can accurately segment the gesture image. Compared with the existing mainstream saliency calculation models, this algorithm is closer to the true value image in terms of visual effects and has obvious advantages in terms of accuracy.

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Section: Related Workmentioning

confidence: 99%

Image Segmentation Method for an Illumination Highlight Region of Interior Design Effects Based on the Partial Differential Equation

Wang¹,

Liu

Qian

2021

Advances in Mathematical Physics

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“…end while return S; e 3D = Estimate error (S est = S, S GT , P store ); %use Eq. (53) Note that C provides the information about the subspace, not the vectorial points. However, we have the chart of the trajectories and its corresponding subspace.…”

Section: Solutionmentioning

confidence: 99%

Dense Non-Rigid Structure from Motion: A Manifold Viewpoint

Kumar,

Van Gool,

de Oliveira

et al. 2020

Preprint

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Non-Rigid Structure-from-Motion (NRSfM) problem aims to recover 3D geometry of a deforming object from its 2D feature correspondences across multiple frames. Classical approaches to this problem assume a small number of feature points and, ignore the local non-linearities of the shape deformation, and therefore, struggles to reliably model non-linear deformations. Furthermore, available dense NRSfM algorithms are often hurdled by scalability, computations, noisy measurements and, restricted to model just global deformation. In this paper, we propose algorithms that can overcome these limitations with the previous methods and, at the same time, can recover a reliable dense 3D structure of a non-rigid object with higher accuracy. Assuming that a deforming shape is composed of a union of local linear subspace and, span a global low-rank space over multiple frames enables us to efficiently model complex nonrigid deformations. To that end, each local linear subspace is represented using Grassmannians and, the global 3D shape across multiple frames is represented using a low-rank representation. We show that our approach significantly improves accuracy, scalability, and robustness against noise. Also, our representation naturally allows for simultaneous reconstruction and clustering framework which in general is observed to be more suitable for NRSfM problems. Our method currently achieves leading performance on the standard benchmark datasets.

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“…Due to the advantages of PDE-based geometric modelling discussed above, they have been applied in many applications. For example, PDE-based geometric modelling has been used in parametric design and optimisation of solid pharmaceutical tablets in cylindrical and spherical shapes (Ahmat et al 2014), facial geometry parameterisation (Sheng et al 2011), cyclic animation (Gonzalez Castro et al 2010), and real-time aircraft design (Athan et al 2009).…”

Section: Pde-based Geometric Modellingmentioning

confidence: 99%

Optimal NURBS conversion of PDE surface-represented high-speed train heads

et al. 2019

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The head shape of high-speed trains has become a critical factor in boosting the speed further. Aerodynamic simulation-based optimization is a dominant method to obtain the optimal head shape which relies on detailed train head models defined by a lot of design variables. Since aerodynamic simulation-based optimization involves heavy calculations, too many design variables not only causes high computational costs, but also makes the optimal solution difficult to obtain. Therefore, how to use few design variables to define detailed train head model is the key to success. Partial differential equation (PDE)-based geometric modelling which creates a complicated PDE patch with few design variables provides an effective solution to this problem. In addition, it also has the advantage of naturally maintaining any high-order continuities between two adjacent surfaces which is very important in designing highly smooth train heads to achieve excellent aerodynamic performance. At the present time, PDE-based geometric modelling cannot be directly applied in computer-aided design (CAD), computer-aided manufacturing (CAM), and computer-aided engineering (CAE) since it has not become an industrial standard. In contrast, non-uniform rational B-splines (NURBS) are commonly used in CAD, CAM, CAE, and many other engineering fields. They have already become part of industry wide standards. In order to apply PDE-based geometric modelling in shape design of high-speed train heads for CAD etc., how to optimally convert PDE surfaces into NURBS surfaces must be addressed. In this paper, a new method of achieving optimal conversion of PDE surfaces representing high-speed train heads into NURBS surfaces is developed. It takes control points and weight deformations of NURBS surfaces to be design variables, and the error between NURBS surfaces and PDE surfaces as the objective function. The least squares fitting and the genetic algorithm are combined to obtain the optimal conversion between PDE surfaces and NURBS surfaces. The application examples demonstrate the effectiveness of the developed method.

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Facial geometry parameterisation based on Partial Differential Equations

Cited by 17 publications

References 30 publications

Image Segmentation Method for an Illumination Highlight Region of Interior Design Effects Based on the Partial Differential Equation

Image Segmentation Method for an Illumination Highlight Region of Interior Design Effects Based on the Partial Differential Equation

Dense Non-Rigid Structure from Motion: A Manifold Viewpoint

Optimal NURBS conversion of PDE surface-represented high-speed train heads

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