Particle swarm optimization for non-uniform rational B-spline surface reconstruction from clouds of 3D data points

Reconstructing Dynamic 3D Models with Small Data by Integrating Position-Based Dynamics and PDE-Based Modelling

Simulation with position-based dynamics is very popular due to its high efficiency. However, it has the weaknesses of lacking details when too few vertices are involved in simulation and inefficiency when too many vertices are used for simulation. To tackle this problem, in this paper, we propose a new method of reconstructing dynamic 3D models with small data. The core elements of the proposed approach are a curve-represented geometric model and a physics-based mathematical model defined by dynamic partial differential equations. We first use the simulation method of position-based dynamics to generate a group of keyframe poses, which are used to create the deformation animation of a 3D model. Then, wireframe curves are extracted from skin deformation shapes of the 3D model at different keyframe poses. A physics-based mathematical model defined by dynamic partial differential equations is proposed. Its closed-form solution is obtained to represent the extracted curves, which are used to reconstruct the deformation models at different keyframe poses. Experimental examples and comparisons made in this paper indicate that the proposed method of reconstructing dynamic 3D models can greatly reduce data size while keeping good details.

Immunological Approach for Full NURBS Reconstruction of Outline Curves from Noisy Data Points in Medical Imaging

Curve reconstruction from data points is an important issue for advanced medical imaging techniques, such as computer tomography (CT) and magnetic resonance imaging (MRI). The most powerful fitting functions for this purpose are the NURBS (non-uniform rational B-splines). Solving the general reconstruction problem with NURBS requires computing all free variables of the problem (data parameters, breakpoints, control points, and their weights). This leads to a very difficult non-convex, nonlinear, high-dimensional, multimodal, and continuous optimization problem. Previous methods simplify the problem by guessing the values for some variables and computing only the remaining ones. As a result, unavoidable approximations errors are introduced. In this paper, we describe the first method in the literature to solve the full NURBS curve reconstruction problem in all its generality. Our method is based on a combination of two techniques: an immunological approach to perform data parameterization, breakpoint placement, and weight calculation, and least squares minimization to compute the control points. This procedure is repeated iteratively (until no further improvement is achieved) for higher accuracy. The method has been applied to reconstruct some outline curves from MRI brain images with satisfactory results. Comparative work shows that our method outperforms the previous related approaches in the literature for all instances in our benchmark.

Non-Contact Body Measurement for Qinchuan Cattle with LiDAR Sensor

The body dimension measurement of large animals plays a significant role in quality improvement and genetic breeding, and the non-contact measurements by computer vision-based remote sensing could represent great progress in the case of dangerous stress responses and time-costing manual measurements. This paper presents a novel approach for three-dimensional digital modeling of live adult Qinchuan cattle for body size measurement. On the basis of capturing the original point data series of live cattle by a Light Detection and Ranging (LiDAR) sensor, the conditional, statistical outliers and voxel grid filtering methods are fused to cancel the background and outliers. After the segmentation of K-means clustering extraction and the RANdom SAmple Consensus (RANSAC) algorithm, the Fast Point Feature Histogram (FPFH) is put forward to get the cattle data automatically. The cattle surface is reconstructed to get the 3D cattle model using fast Iterative Closest Point (ICP) matching with Bi-directional Random K-D Trees and a Greedy Projection Triangulation (GPT) reconstruction method by which the feature points of cattle silhouettes could be clicked and calculated. Finally, the five body parameters (withers height, chest depth, back height, body length, and waist height) are measured in the field and verified within an accuracy of 2 mm and an error close to 2%. The experimental results show that this approach could be considered as a new feasible method towards the non-contact body measurement for large physique livestock.

Surface Fitting for Quasi Scattered Data from Coordinate Measuring Systems

Non-uniform rational B-spline (NURBS) surface fitting from data points is wildly used in the fields of computer aided design (CAD), medical imaging, cultural relic representation and object-shape detection. Usually, the measured data acquired from coordinate measuring systems is neither gridded nor completely scattered. The distribution of this kind of data is scattered in physical space, but the data points are stored in a way consistent with the order of measurement, so it is named quasi scattered data in this paper. Therefore they can be organized into rows easily but the number of points in each row is random. In order to overcome the difficulty of surface fitting from this kind of data, a new method based on resampling is proposed. It consists of three major steps: (1) NURBS curve fitting for each row, (2) resampling on the fitted curve and (3) surface fitting from the resampled data. Iterative projection optimization scheme is applied in the first and third step to yield advisable parameterization and reduce the time cost of projection. A resampling approach based on parameters, local peaks and contour curvature is proposed to overcome the problems of nodes redundancy and high time consumption in the fitting of this kind of scattered data. Numerical experiments are conducted with both simulation and practical data, and the results show that the proposed method is fast, effective and robust. What’s more, by analyzing the fitting results acquired form data with different degrees of scatterness it can be demonstrated that the error introduced by resampling is negligible and therefore it is feasible.

Cuckoo search with Lévy flights for weighted Bayesian energy functional optimization in global-support curve data fitting

The problem of data fitting is very important in many theoretical and applied fields. In this paper, we consider the problem of optimizing a weighted Bayesian energy functional for data fitting by using global-support approximating curves. By global-support curves we mean curves expressed as a linear combination of basis functions whose support is the whole domain of the problem, as opposed to other common approaches in CAD/CAM and computer graphics driven by piecewise functions (such as B-splines and NURBS) that provide local control of the shape of the curve. Our method applies a powerful nature-inspired metaheuristic algorithm called cuckoo search, introduced recently to solve optimization problems. A major advantage of this method is its simplicity: cuckoo search requires only two parameters, many fewer than other metaheuristic approaches, so the parameter tuning becomes a very simple task. The paper shows that this new approach can be successfully used to solve our optimization problem. To check the performance of our approach, it has been applied to five illustrative examples of different types, including open and closed 2D and 3D curves that exhibit challenging features, such as cusps and self-intersections. Our results show that the method performs pretty well, being able to solve our minimization problem in an astonishingly straightforward way.

From nonlinear optimization to convex optimization through firefly algorithm and indirect approach with applications to CAD/CAM

Fitting spline curves to data points is a very important issue in many applied fields. It is also challenging, because these curves typically depend on many continuous variables in a highly interrelated nonlinear way. In general, it is not possible to compute these parameters analytically, so the problem is formulated as a continuous nonlinear optimization problem, for which traditional optimization techniques usually fail. This paper presents a new bioinspired method to tackle this issue. In this method, optimization is performed through a combination of two techniques. Firstly, we apply the indirect approach to the knots, in which they are not initially the subject of optimization but precomputed with a coarse approximation scheme. Secondly, a powerful bioinspired metaheuristic technique, the firefly algorithm, is applied to optimization of data parameterization; then, the knot vector is refined by using De Boor's method, thus yielding a better approximation to the optimal knot vector. This scheme converts the original nonlinear continuous optimization problem into a convex optimization problem, solved by singular value decomposition. Our method is applied to some illustrative real-world examples from the CAD/CAM field. Our experimental results show that the proposed scheme can solve the original continuous nonlinear optimization problem very efficiently.