Generative Design of Origami-Inspired Mechanisms With a Variational Level Set Approach

2020 ◽  
Author(s):  
Qian Ye ◽  
Xianfeng David Gu ◽  
Shikui Chen
Keyword(s):  
Level Set ◽  
3D Structure ◽  
Level Set Function ◽  
Shell Models ◽  
Proposed Model ◽  
Out Of Plane ◽  
Variational Level Set ◽  
Systematic Solution ◽  
Set Function ◽  
Level Set Approach

Abstract Origami has inspired the engineering design of self-assemble and re-configurable devices. Under particular crease patterns, a 2D flatten object can be transformed into a complex 3D structure. This work intends to find out a systematic solution for topology optimization of origami structures. The origami mechanism is simulated using shell models where the in-plane membrane, out of plane bending, and shear deformation can be well captured. Moreover, the pattern of the folds is represented implicitly by the boundaries of the level set function. The topology of the folds is optimized by minimizing a new multiobjective function, aiming to balance the kinematic performance with the structural stiffness as well as the geometric requirements. Besides regular straight folds, our proposed model can mimic crease patterns with curved folds. With the folding curves implicitly represented, the curvature flow are utilized to control the complexity of the generated folds. The effectiveness of the proposed method is demonstrated through the computational generation and physical validation of a thin-shell origami gripper.

scholarly journals Variational Level Set Method for Two-Stage Image Segmentation Based on Morphological Gradients

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Zemin Ren
Keyword(s):  
Transition Region ◽  
Level Set ◽  
Indicator Function ◽  
External Energy ◽  
Level Set Function ◽  
Proposed Model ◽  
Variational Level Set ◽  
Variational Level Set Method ◽  
Set Function ◽  
Edge Indicator Function

We use variational level set method and transition region extraction techniques to achieve image segmentation task. The proposed scheme is done by two steps. We first develop a novel algorithm to extract transition region based on the morphological gradient. After this, we integrate the transition region into a variational level set framework and develop a novel geometric active contour model, which include an external energy based on transition region and fractional order edge indicator function. The external energy is used to drive the zero level set toward the desired image features, such as object boundaries. Due to this external energy, the proposed model allows for more flexible initialization. The fractional order edge indicator function is incorporated into the length regularization term to diminish the influence of noise. Moreover, internal energy is added into the proposed model to penalize the deviation of the level set function from a signed distance function. The results evolution of the level set function is the gradient flow that minimizes the overall energy functional. The proposed model has been applied to both synthetic and real images with promising results.

scholarly journals Automatic Global Level Set Approach for Lumbar Vertebrae CT Image Segmentation

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Yang Li ◽  
Wei Liang ◽  
Yinlong Zhang ◽  
Jindong Tan
Keyword(s):  
Image Segmentation ◽  
Level Set ◽  
Lumbar Vertebrae ◽  
Ct Image ◽  
Global Level ◽  
Level Set Function ◽  
Weak Boundary ◽  
Irregular Boundaries ◽  
Set Function ◽  
Level Set Approach

Vertebrae computed tomography (CT) image automatic segmentation is an essential step for Image-guided minimally invasive spine surgery. However, most of state-of-the-art methods still require human intervention due to the inherent limitations of vertebrae CT image, such as topological variation, irregular boundaries (double boundary, weak boundary), and image noise. Therefore, this paper intentionally designed an automatic global level set approach (AGLSA), which is capable of dealing with these issues for lumbar vertebrae CT image segmentation. Unlike the traditional level set methods, we firstly propose an automatically initialized level set function (AILSF) that comprises hybrid morphological filter (HMF) and Gaussian mixture model (GMM) to automatically generate a smooth initial contour which is precisely adjacent to the object boundary. Secondly, a regularized level set formulation is introduced to overcome the weak boundary leaking problem, which utilizes the region correlation of histograms inside and outside the level set contour as a global term. Ultimately, a gradient vector flow (GVF) based edge-stopping function is employed to guarantee a fast convergence rate of the level set evolution and to avoid level set function oversegmentation at the same time. Our proposed approach has been tested on 115 vertebrae CT volumes of various patients. Quantitative comparisons validate that our proposed AGLSA is more accurate in segmenting lumbar vertebrae CT images with irregular boundaries and more robust to various levels of salt-and-pepper noise.

scholarly journals A Global Inhomogeneous Intensity Clustering- (GINC-) Based Active Contour Model for Image Segmentation and Bias Correction

2020 ◽  
Vol 2020 ◽  
pp. 1-18 ◽  
Author(s):  
Chaolu Feng ◽  
Jinzhu Yang ◽  
Chunhui Lou ◽  
Wei Li ◽  
Kun Yu ◽  
...  
Keyword(s):  
Image Segmentation ◽  
Level Set ◽  
Bias Correction ◽  
Active Contour Model ◽  
Multiple Objects ◽  
Level Set Function ◽  
Proposed Model ◽  
Segmentation Accuracy ◽  
Term Energy ◽  
Set Function

Image segmentation is still an open problem especially when intensities of the objects of interest are overlapped due to the presence of intensity inhomogeneities. A bias correction embedded level set model is proposed in this paper where inhomogeneities are estimated by orthogonal primary functions. First, an inhomogeneous intensity clustering energy is defined based on global distribution characteristics of the image intensities, and membership functions of the clusters described by the level set function are then introduced to define the data term energy of the proposed model. Second, a regularization term and an arc length term are also included to regularize the level set function and smooth its zero-level set contour, respectively. Third, the proposed model is extended to multichannel and multiphase patterns to segment colorful images and images with multiple objects, respectively. Experimental results and comparison with relevant models demonstrate the advantages of the proposed model in terms of bias correction and segmentation accuracy on widely used synthetic and real images and the BrainWeb and the IBSR image repositories.

A Variational Level Set Remote Sensing SAR Image Segmentation Approach for Oil Spill Detecting Based on Fuzzy Cluster

2015 ◽  
Vol 719-720 ◽  
pp. 1049-1055 ◽  
Author(s):  
Jin Yu Liu ◽  
Zheng Ning Zhang ◽  
He Meng Yang
Keyword(s):  
Image Segmentation ◽  
Level Set ◽  
Oil Spill ◽  
Fuzzy Clustering ◽  
Sar Image ◽  
Segmentation Method ◽  
Level Set Function ◽  
Sar Image Segmentation ◽  
Variational Level Set ◽  
Set Function

Synthetic Aperture Radar (SAR) has become one of the important means for the ocean remote sensing detection of oil spills. The existing SAR image segmentation method has the issues of edge blur, poor contrast, non-uniform intensity image, so the segmentation effect is not ideal. This paper presents a variational level set SAR image of oil spill detection method based on fuzzy clustering. First of all, apply the threshold method on initial segmentation of the original SAR image to transform the initial segmented image as fuzzy clustering. Secondly, introduce the clustering results into the initial level set function to achieve the initial contour. Finally, add fuzzy clustering model in the level set energy function to complete the level set evolution process and get the final segmented image. This paper uses the threshold segmentation results to achieve the initialization of the variational level set function profile. In theory, it could improve the level set method for efficiency, and reduce the wrong segmentation phenomenon. The experimental results show that the SAR image segmentation method of oil spill has good segmentation qualities and is suitable for the edge complex image segmentation.

Numerical Simulation of Interface Time Evolution by Oriented Lagrangian Particles and Level-Set Method

2009 ◽  
Author(s):  
Sandro Ianniello ◽  
Andrea Di Mascio
Keyword(s):  
Level Set ◽  
Eikonal Equation ◽  
Evolution Equations ◽  
Normal Vector ◽  
Geometrical Properties ◽  
Level Set Function ◽  
Standard Level ◽  
Fundamental Vector ◽  
Set Function ◽  
Level Set Approach

A new computational approach for tracking evolving interfaces is proposed. The procedure is based on the copuling of lagrangian massless particles and the standard Level-Set methodology, and the use of evolution equations for fundamental vector and tensor quantities related to the geometrical properties of the interface Γ. In particular, the normal vector n and the second fundamental tensor ∇n are linked to the particles and advected with them; in this way, the particles can be located upon Γ and enable a step–by–step calculation of the Level–Set function φ through a direct solution of the eikonal equation. No transport equation and reinitialization procedure for φ have to be taken into account and the usual numerical diffusion affecting the Level–Set approach is removed. The method is easy to code and carries out an accurate reconstruction of the front, limited only by the spatial resolution of the mesh.

scholarly journals An Image Segmentation Method Based on Improved Regularized Level Set Model

2018 ◽  
Vol 8 (12) ◽  
pp. 2393 ◽  
Author(s):  
Lin Sun ◽  
Xinchao Meng ◽  
Jiucheng Xu ◽  
Shiguang Zhang
Keyword(s):  
Image Segmentation ◽  
Level Set ◽  
Energy Functional ◽  
External Energy ◽  
Regularization Term ◽  
Level Set Function ◽  
New Energy ◽  
Segmentation Approach ◽  
Set Function ◽  
Distance Regularization

When the level set algorithm is used to segment an image, the level set function must be initialized periodically to ensure that it remains a signed distance function (SDF). To avoid this defect, an improved regularized level set method-based image segmentation approach is presented. First, a new potential function is defined and introduced to reconstruct a new distance regularization term to solve this issue of periodically initializing the level set function. Second, by combining the distance regularization term with the internal and external energy terms, a new energy functional is developed. Then, the process of the new energy functional evolution is derived by using the calculus of variations and the steepest descent approach, and a partial differential equation is designed. Finally, an improved regularized level set-based image segmentation (IRLS-IS) method is proposed. Numerical experimental results demonstrate that the IRLS-IS method is not only effective and robust to segment noise and intensity-inhomogeneous images but can also analyze complex medical images well.

A Method for Tracking a Solid Body in a Fluid Field in Immersed Boundary Methods

2018 ◽  
Author(s):  
Guangfa Yao
Keyword(s):  
Level Set ◽  
Solid Body ◽  
Volume Fraction ◽  
Transformation Matrix ◽  
The Body ◽  
New Method ◽  
Immersed Boundary ◽  
Body Interaction ◽  
Level Set Function ◽  
Set Function

Immersed boundary method has got increasing attention in modeling fluid-solid body interaction using computational fluid dynamics due to its robustness and simplicity. It usually simulates fluid-solid body interaction by adding a body force in the momentum equation. This eliminates the body conforming mesh generation that frequently requires a very labor-intensive and challenging task. But accurately tracking an arbitrary solid body is required to simulate most real world problems. In this paper, a few methods that are used to track a rigid solid body in a fluid domain are briefly reviewed. A new method is presented to track an arbitrary rigid solid body by solving a transformation matrix and identifying it using a level set function. Knowing level set function, the solid volume fraction can be derived if needed. A three-dimensional example is used to study a few methods used to represent and solve the transformation matrix, and demonstrate the presented new method.

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