B-spline Level Set Research Articles

Target positioning method based on B-spline level set and GC Yolo-v3

Target positioning method based on B-spline level set and GC Yolo-v3

Strength design of porous materials using B-spline based level set method

The inverse homogenization method can tailor some mechanical and physical effective properties by laying out materials in a periodic representative volume element. However, studies on strength design are yet to be developed because of the difficulties in numerically retrieving its value. Unlike traditional asymptotic homogenization, the fast Fourier transform-based homogenization method based on the augmented Lagrangian approach uses a Green operator in the frequency domain to replace time-consuming finite element analysis and inherently meet the periodic boundary conditions. Thus, it is developed in this work to retrieve material strength in terms of the von Mises yield criterion. The zero-level contour of a linear combination of cubic B-spline basis functions with repeated knots is used to represent the microstructure profile in the design of material strength. The effective strength or its squared difference with a prescribed target is minimized within the framework of the reaction diffusion-based B-spline level set method. The filtered, non-consistent discrete Green operator is adopted to avoid slow convergence of porous material. Examples of porous material demonstrate that the proposed method guarantees surface smoothness, optimization flexibility, and structural periodicity in strength design.

Bayesian Shape Reconstruction Using B-Spline Level Set in Electrical Impedance Tomography

A new shape reconstruction framework that incorporates sparse Bayesian learning (SBL) and the B-spline level set (BLS) is proposed for difference electrical impedance tomography (EIT). To begin with, the conductivity distribution to be reconstructed is assumed to be piecewise constant under the BLS framework. Second, the boundaries of the inclusions are represented by the B-spline curves in a parametric and explicit way. Next, the optimal shapes are found by solving the unknown variables using the SBL method. Then, the proposed method takes full advantage of B-spline flexible representation and Bayesian learning capability, resulting in improvements in reconstruction performance, noise robustness, and computational efficiency. Finally, a series of numerical and experimental tests are performed to verify the feasibility of the proposed method. Furthermore, the robustness studies are also investigated considering the inhomogeneous background, different numbers of control points, and different initial guesses. The results show that the proposed method leads to reliable and robust shape reconstructions, as evaluated by several quantitative metrics. Specifically, the forced vital capacity (FVC) tests of ten healthy volunteers show that the mean error in the 1-s rate of the shape reconstructions is less than 5% compared with simultaneous spirometry measurements. Hence, the proposed method is promising in providing an effective assessment for lung imaging.

A reaction diffusion-based B-spline level set (RDBLS) method for structural topology optimization

This work uses the zero-level contour of a parameterized level set function, a linear combination of cubic B-spline basis functions, to express the structural profile in structural topology optimization. Together with mean compliance, diffusion energy is minimized under a volume constraint to control the structural complexity. The design variables, namely the coefficients of cubic B-spline basis functions, are updated by solving the reaction–diffusion equation within a finite element analysis framework. The bisectional algorithm accurately calculates the Lagrangian multiplier of the volume constraint in each iteration. In addition to expressing the optimized structure smoothly, the proposed method is highly efficient. For instance, it only takes 20 iterations to solve the cantilever and MBB beams in 2D. For 3D optimization, we obtain several elegant bridge designs using nearly one million elements, demonstrating the great potential of the proposed method for practical applications.

Biological Image Segmentation Using Region-Scalable Fitting Energy with B-Spline Level Set Implementation and Watershed

ObjectivesImage segmentation plays an important role in the analysis and understanding of the cellular process. However, this task becomes difficult when there is intensity inhomogeneity between regions, and it is more challenging in the presence of the noise and clustered cells. The goal of the paper is propose an image segmentation framework that tackles the above cited problems. Material and methodsA new method composed of two steps is proposed: First, segment the image using B-spline level set with Region-Scalable Fitting (RSF) active contour model, second apply the Watershed algorithm based on new object markers to refine the segmentation and separate clustered cells. The major contributions of the paper are: 1) Use of a continuous formulation of the level set in the B-spline basis, 2) Develop the energy function and its derivative by introducing the RSF model to deal with intensity inhomogeneity, 3) For the Watershed, propose a relevant choice of markers that considers the cell properties. ResultsExperimental results are performed on widely used synthetic images, in addition to simulated and real biological images, without and with additive noise. They attest the high quality of segmentation of the proposed method in terms of quantitative and qualitative evaluation. ConclusionThe proposed method is able to tackle many difficulties at the same time: overlapped intensities, noise, different cell sizes and clustered cells. It provides an efficient tool for image segmentation especially biological ones.

Object Detection Based on Deep Learning and B-Spline Level Set in Color Images

Object detection based on deep learning is a popular trend, and it includes object recognition and positioning. This paper proposes a method that can accurately obtain object type and accurate three-dimensional position. The method is divided into three parts: object recognition and coarse positioning based on deep learning, precise positioning based on deep learning combined with B-spline level set in color images, and precise three-dimensional positioning with depth information of RGB-D camera. The precise positioning of the object provides accurate end pose information for the autonomous grasping of the robotic arm, and it has great significance to the gripping of the robotic arm. Performance metrics include mAP (mean average precision) and IOU (intersection of a union). Experimental results show that the mAP value of Yolo-v3 in this paper can reach 87.62%, the average IOU of Yolo-v3 in this paper can reach 66.74%, the average IOU of Yolo-v3 and B-spline level set can reach 100%, and can get accurate 3D location in the real scene. In addition, the experiments comparisons between VOC dataset and our own dataset validate that our dataset can take higher mAP and average IOU values.

Stress-based shape and topology optimization with cellular level set in B-splines

A parametric level set approach based on B-splines is developed for the stress-based shape and topology optimization of cellular structures. In this method, the whole design domain is divided into a set of non-overlapping sub-domains, within each of which the structure is represented by an implicit B-spline level set function. This parameterization scheme ensures that the adjacent cells can be smoothly connected. The stress value of the structure is computed by using a p-norm function-based aggregation. The extended finite element method is implemented to calculate the structural stress. Moreover, a new optimization strategy based on a two-field formulation is proposed to eliminate numerical instability in the optimization process. A continuity scheme based on the least square method is proposed to guarantee the high-order connectivity at the adjacent cell boundary. In addition, optimized cellular structures with different cell partitions are obtained and discussed. Several numerical examples are presented to illustrate the applicability of the approach.

Multiphase Conductivity Imaging With Electrical Impedance Tomography and B-Spline Level Set Method

This article presents a B-spline level set (BLS)-based reconstruction scheme for multiphase conductivity imaging with electrical impedance tomography (EIT). The EIT inverse problem is recast as a shape reconstruction problem where both the inclusion interface and conductivity values are the unknown. In using this scheme, the unknown conductivity to be reconstructed is assumed to be piecewise constant while the inclusion interface is represented by the zero level set of a BLS surface, which, in turn, is represented as a linear combination of B-spline basis functions. Through such a low-order representation technique, the number of unknowns in the reconstruction problem is significantly reduced compared with the traditional pixel-/voxel-based reconstruction methods. The performance of the BLS scheme is tested with heart-and-lungs phantom studies and the cross section of the industrial pipeline phantom studies. The results demonstrate that the BLS scheme is capable of preserving sharp features of inclusions and providing estimates to both the interface locations and unknown conductivity values with reliable accuracy. In addition, we also found that the BLS scheme is quite robust to the selection of the regularization weighting parameter in the least-square-based optimization regime and the additional parameter in the Heaviside function used for modeling the conductivity profile.

B-Spline Level Set Method for Shape Reconstruction in Electrical Impedance Tomography.

A B-spline level set (BLS) based method is proposed for shape reconstruction in electrical impedance tomography (EIT). We assume that the conductivity distribution to be reconstructed is piecewise constant, transforming the image reconstruction problem into a shape reconstruction problem. The shape/interface of inclusions is implicitly represented by a level set function (LSF), which is modeled as a continuous parametric function expressed using B-spline functions. Starting from modeling the conductivity distribution with the B-spline based LSF, we show that the shape modeling allows us to compute the solution by restricting the minimization problem to the space spanned by the B-splines. As a consequence, the solution to the minimization problem is obtained in terms of the B-spline coefficients. We illustrate the behavior of this method using simulated as well as water tank data. In addition, robustness studies considering varying initial guesses, differing numbers of control points, and modeling errors caused by inhomogeneity are performed. Both simulation and experimental results show that the BLS-based approach offers clear improvements in preserving the sharp features of the inclusions in comparison to the recently published parametric level set method.

FBSLS model for image segmentation

To achieve quick and accurate segmentations for intensity inhomogeneous images, the model named fractional B-spline level set (FBSLS) is proposed in this study. The core of FBSLS method is that the LS function is expressed as the line combination of FBS basis in continuous forms. In this expression, the evolution of the energy function can be seen as a variation problem on the space spanned by the FBSs. As a result, the minimum value of energy function can be obtained directly from the coefficient of FBSs. Furthermore, every minimisation step can be considered as a convolution operation, and the evolution of the process of energy function may be regarded as the filtering operation whose kernel function is defined by the fractional order BS function. The filtering operation induces an intrinsic algorithm of smoothing which may be controlled explicitly by the order of the chosen FBS function. At the last, the morphological operator was used as the step of post-processing to get better segmentation. The obtained experimental results demonstrate that the proposed model has better segment results than the traditional ones on segmentation time, Dice coefficient, precision, and recall and F-measure metrics.

Automatic crack detection from 2D images using a crack measure-based B-spline level set model

A method is proposed for automatic detection of cracks extracted from 2D images of damaged structures. In the 2D images, the cracks are treated as tree-like topological dark objects of which each tree branch is assumed to be line-like and have local symmetry across the crack center axis. Utilizing the geometric features of the cracks, a novel level set model in which the level set function comprises a set of B-spline basis functions is established to automatically extract the level set function from the 2D crack image with intensity inhomogeneity for crack detection. A new energy functional together with a crack measure technique is introduced to derive an iterative procedure for obtaining the exact level set function of the crack image via an optimization approach. In the iteration process, the level set model can produce smooth and continuous boundaries of the cracks with fast convergence speed. In a comparative study, it has been shown that the proposed method can extract cracks from several real noisy crack images of damaged structures made of various materials more accurate than those determined using the existing crack detection methods which use either different level set models or other image processing techniques in extracting the cracks.

Image-based goal-oriented adaptive isogeometric analysis with application to the micro-mechanical modeling of trabecular bone

Isogeometric analysis (IGA) of geometrically complex three-dimensional objects is possible when used in combination with the Finite Cell method (FCM). In this contribution we propose a computational methodology to automatically analyze the effective elastic properties of scan-based volumetric objects of arbitrary geometric and topological complexity. The first step is the reconstruction of a smooth geometry from scan-based voxel data using a B-spline level set function. The second step is a goal-oriented adaptive isogeometric linear elastic analysis. Elements are selected for refinement using dual-weighted residual shape function indicators, and hierarchical splines are employed to construct locally refined spline spaces. The proposed methodology is studied in detail for various numerical test cases, including the computation of the effective Young’s modulus of a trabecular bone micro-structure reproduced from μCT-scan data.

Multiphase B-spline level set and incremental shape priors with applications to segmentation and tracking of left ventricle in cardiac MR images

This paper presents a new multiphase active contour model for object segmentation and tracking. The paper introduces an energy functional which incorporates image feature information to drive contours toward desired boundaries, and shape priors to constrain the evolution of the contours with respect to reference shapes. The shape priors, in the model, are constructed by performing the incremental principal component analysis (iPCA) on a set of training shapes and newly available shapes which are the resulted shapes derived from preceding segmented images. By performing iPCA, the shape priors are updated without repeatedly performing PCA on the entire training set including the existing shapes and the newly available shapes. In addition, by incrementally updating the resulted shape information of consecutive frames, the approach allows to encode shape priors even when the database of training shapes is not available. Moreover, in shape alignment steps, we exploit the shape normalization procedure, which takes into account the affine transformation, to directly calculate pose transformations instead of solving a set of coupled partial differential equations as in gradient descent-based approaches. Besides, we represent the level set functions as linear combinations of continuous basic functions expressed on B-spline basics for a fast convergence to the segmentation solution. The model is applied to simultaneously segment/track both the endocardium and epicardium of left ventricle from cardiac magnetic resonance (MR) images. Experimental results show the desired performances of the proposed model.

Moment-based alignment for shape prior with variational B-spline level set

This paper presents a new shape prior-based implicit active contour model for image segmentation. The paper proposes an energy functional including a data term and a shape prior term. The data term, inspired from the region-based active contour approach, evolves the contour based on the region information of the image to segment. The shape prior term, defined as the distance between the evolving shape and a reference shape, constraints the evolution of the contour with respect to the reference shape. Especially, in this paper, we present shapes via geometric moments, and utilize the shape normalization procedure, which takes into account the affine transformation, to align the evolving shape with the reference one. By this way, we could directly calculate the shape transformation, instead of solving a set of coupled partial differential equations as in the gradient descent approach. In addition, we represent the level-set function in the proposed energy functional as a linear combination of continuous basic functions expressed on a B-spline basic. This allows a fast convergence to the segmentation solution. Experiment results on synthetic, real, and medical images show that the proposed model is able to extract object boundaries even in the presence of clutter and occlusion.