Two-view curve reconstruction based on the snake model

Reconstruction of 3D curves from their stereo images is an important issue in computer vision. Based on deformation of the snake model and NURBS representation, we evolve the curve in the view of inverse optimization to finish reconstruction. This manner can reduce the need of matching multi-view space curve projections, meanwhile improve the reconstruction precision. Considering that the 2D data reconstruction exists error inevitably, based on two cameras, a discussion on its influence to stereo reconstruction is given next. Finally, the proposed approach is experimented with artificial and real data, and gains a satisfying reconstruction effect.     

Depth Map Reconstruction Based on Features Formed by Descriptor of Stereo Color Pairs

Doklady Mathematics - An approach to depth map reconstruction from stereo pairs of color images in visualization of three-dimensional objects is proposed and substantiated for the first time. The...     

A unified framework for 3D reconstruction

3D reconstruction is a branch of computer vision with a broad range of applications like computer aided design, animation, medicine and many others. In this talk we use continuous linear functionals for characterizing different kinds of 3D data. These problems can be tackled in the framework of Reproducing Kernel Hilbert Spaces and regularization of inverse problems. It can be said that 3D reconstruction is the general problem of estimating or finding functional dependencies from a three-dimensional data set. The origin of these data covers a wide range that includes tomography, surface reconstruction from point clouds or image and signal processing. Usually the problem of reconstruction has a very close relationship with scientific visualization and computer graphics. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fast surface reconstruction and hole filling using positive definite radial basis functions

Surface reconstruction from large unorganized data sets is very challenging, especially if the data present undesired holes. This is usually the case when the data come from laser scanner 3D acquisitions or if they represent damaged objects to be restored. An attractive field of research focuses on situations in which these holes are too geometrically and topologically complex to fill using triangulation algorithms. In this work a local approach to surface reconstruction from point-clouds based on positive definite Radial Basis Functions (RBF) is presented that progressively fills the holes by expanding the neighbouring information. The method is based on the algorithm introduced in [7] which has been successfully tested for the smooth multivariate interpolation of large scattered data sets. The local nature of the algorithm allows for real time handling of large amounts of data, since the computation is limited to suitable small areas, thus avoiding the critical efficiency problem involved in RBF multivariate interpolation. Several tests on simulated and real data sets demonstrate the efficiency and the quality of the reconstructions obtained using the proposed algorithm. AMS subject classification 65D17, 65D05, 65Y20     

Random change on a Lie group and mean glaucomatous projective shape change detection from stereo pair images

In this article we develop a nonparametric methodology for estimating the mean change for matched samples on a Lie group. We then notice that for k≥5, a manifold of projective shapes of k-ads in 3D has the structure of a 3k−15 dimensional Lie group that is equivariantly embedded in a Euclidean space, therefore testing for mean change amounts to a one sample test for extrinsic means on this Lie group. The Lie group technique leads to a large sample and a nonparametric bootstrap test for one population extrinsic mean on a projective shape space, as recently developed by Patrangenaru, Liu and Sughatadasa. On the other hand, in the absence of occlusions, the 3D projective shape of a spatial k-ad can be recovered from a stereo pair of images, thus allowing one to test for mean glaucomatous 3D projective shape change detection from standard stereo pair eye images.     

Wave Surface Identification Based on Stereo Vision and Wave Theory: an Initial Attempt北大核心CSCD

波高是波浪信息最基本的元素,对波高的精确测量无论是对波浪理论的研究还是数值方法的拓展,都起着指导和验证的作用。文中基于双目立体视觉原理自主搭建了波面光学测量系统,突破了传统测量设备如浪高仪等单点测量的局限性,并将波浪理论融入到数据后处理方法中,对常用的单纯依赖图像的光学测量方法进行了改进。通过在拖曳水池中对单向规则波瞬时波面的识别和重构,并将结果与浪高仪以及理论来波参数进行了对比验证,结果表明该测量系统在大范围波面的测量中误差在1%左右,最后对其在非规则的来波下进行了初步尝试。     

基于离散点和法矢的曲线重构算法

This paper presents a curve reconstruction algorithm based on discrete data points and normal vectors using B-splines.The proposed algorithm has been improved in three steps:parameterization of the discrete data points with tangent vectors,the B-spline knot vector determination by the selected dominant points based on normal vectors,and the determination of the weight to balancing the two errors of the data points and normal vectors in fitting model.Therefore,we transform the B-spline fitting problem into three sub-problems,and can obtain the B-spline curve adaptively.Compared with the usual fitting method which is based on dominant points selected only by data points,the B-spline curves reconstructed by our approach can retain better geometric shape of the original curves when the given data set contains high strength noises.     

Curve reconstruction: Connecting dots with good reason

Curve reconstruction algorithms are supposed to reconstruct curves from point samples. Recent papers present algorithms that come with a guarantee: Given a sufficiently dense sample of a closed smooth curve, the algorithms construct the correct polygonal reconstruction. Nothing is claimed about the output of the algorithms, if the input is not a dense sample of a closed smooth curve, e.g., a sample of a curve with endpoints. We present an algorithm that comes with a guarantee for any set P of input points. The algorithm constructs a polygonal reconstruction G and a smooth curve Γ that justifies G as the reconstruction from P.     

On the Reconstruction and Computation of Dual-Phase Steel Microstructures Based on 3D EBSD Data

In this contribution we reconstruct the three dimensional microstructure of a dual-phase steel based on the tomographic experimental data provided by the 3D electron backscatter diffraction (3D EBSD) method. The cross sections of the resulting microstructure are compared to the 2D reconstruction, which are obtained directly from the 3D EBSD data. We also perform FE-simulations based on these geometries and observe comparable results in 2D and 3D. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Reconstruction of the Linear Ordinary Differential System Based on Discrete Points

In this paper, we discuss an inverse problem, i.e., the reconstruction of a linear differential dynamic system from the given discrete data of the solution. We propose a model and a corresponding algorithm to recover the coefficient matrix of the differential system based on the normal vectors from the given discrete points, in order to avoid the problem of parameterization in curve fitting and approximation. We also give some theoretical analysis on our algorithm. When the data points are taken from the solution curve and the set composed of these data points is not degenerate, the coefficient matrix $A$ reconstructed by our algorithm is unique from the given discrete and noisefree data. We discuss the error bounds for the approximate coefficient matrix and the solution which are reconstructed by our algorithm. Numerical examples demonstrate the effectiveness of the algorithm.     

Vector field reconstruction via quaternionic setting

We propose the reconstruction of the solenoidal part of a vector field supported in the unit ball in 3 dimensions by using cone beam data from a curve surrounding it, and this curve satisfies the Tuy's condition of order 3. We use the quaternionic inversion formula to decompose the solenoidal part of a vector field into 2 parts. To recover the first one, which is the main part of the solenoidal component, another definition of a cone beam transform containing both Doppler and transverse data will be introduced. The second part will be reconstructed by using information from the first part as in Katsevich and Schuster's work with less data.     

Regular and non-regular point sets: Properties and reconstruction

In this paper, we address the problem of curve and surface reconstruction from sets of points. We introduce regular interpolants, which are polygonal approximations of curves and surfaces satisfying a new regularity condition. This new condition, which is an extension of the popular notion of r-sampling to the practical case of discrete shapes, seems much more realistic than previously proposed conditions based on properties of the underlying continuous shapes. Indeed, contrary to previous sampling criteria, our regularity condition can be checked on the basis of the samples alone and can be turned into a provably correct curve and surface reconstruction algorithm. Our reconstruction methods can also be applied to non-regular and unorganized point sets, revealing a larger part of the inner structure of such point sets than past approaches. Several real-size reconstruction examples validate the new method.     

Reconstructing 3D compact sets

Reconstructing a 3D shape from sample points is a central problem faced in medical applications, reverse engineering, natural sciences, cultural heritage projects, etc. While these applications motivated intense research on 3D surface reconstruction, the problem of reconstructing more general shapes hardly received any attention. This paper develops a reconstruction algorithm changing the 3D reconstruction paradigm as follows.First, the algorithm handles general shapes, i.e. compact sets, as opposed to surfaces. Under mild assumptions on the sampling of the compact set, the reconstruction is proved to be correct in terms of homotopy type. Second, the algorithm does not output a single reconstruction but a nested sequence of plausible reconstructions. Third, the algorithm accommodates topological persistence so as to select the most stable features only. Finally, in case of reconstruction failure, it allows the identification of under-sampled areas, so as to possibly fix the sampling.These key features are illustrated by experimental results on challenging datasets, and should prove instrumental in enhancing the processing of such datasets in the aforementioned applications.     

Shape recovery for sparse‐data tomography

A two‐dimensional sparse‐data tomographic problem is studied. The target is assumed to be a homogeneous object bounded by a smooth curve. A nonuniform rational basis splines (NURBS) curve is used as a computational representation of the boundary. This approach conveniently provides the result in a format readily compatible with computer‐aided design software. However, the linear tomography task becomes a nonlinear inverse problem because of the NURBS‐based parameterization. Therefore, Bayesian inversion with Markov chain Monte Carlo sampling is used for calculating an estimate of the NURBS control points. The reconstruction method is tested with both simulated data and measured X‐ray projection data. The proposed method recovers the shape and the attenuation coefficient significantly better than the baseline algorithm (optimally thresholded total variation regularization), but at the cost of heavier computation.     

主成分分析在经济预测中的应用

在许多社会经济现象中，有这样的数学模型，它是不断地增长的，但又略有波浪式的起伏。要预测这类型的问题，既不能用一般的线性回归预测法，即使在ｎ＝２１时其相关系数高达０．９８８（甚至０．９９６），也能产生较大的预测误差。我们也不能用一般的曲线回归或多项式回归。包括很常用的龚珀资（Ｃｏｍｐｅｒｔｚ）曲线预测法也无济于事，因为龚法实际上是对具有Ｓ形数学模型的预测有效。它们都不符合波浪增长式且具有一定周期的数学模型。本文先就青岛市１９６２年至１９８２年这２１年人口资料进行分析探讨；再就１９７１年至１９９１年这２１年资料进行动态跟踪分析。并引进波浪增长曲线的作法。     

Hierarchical approach of seismic full waveform inversion

Full waveform inversion (FWI) of seismic traces recorded at the free surface allows the reconstruction of the physical parameters structure on the underlying medium. For such a reconstruction, an optimization problem is defined, where synthetic traces, obtained through numerical techniques as finite-difference or finite-element methods in a given model of the subsurface, should match the observed traces. The number of data samples is routinely around 1 billion for 2D problems and 1 trillion for 3D problems while the number of parameters ranges from 1 million to 10 million degrees of freedom. Moreover, if one defines the mismatch as the standard least-squares norm between values sampled in time/frequency and space, the misfit function has a significant number of secondary minima related to the ill-posedness and the nonlinearity of the inversion problem linked to the so-called cycle skipping. Taking into account the size of the problem, we consider a local linearized method where gradient is computed using the adjoint formulation of the seismic wave propagation problem. Starting for an initial model, we consider a quasi-Newtonian method, which allows us to formulate the reconstruction of various parameters such as P and S waves velocities or density or attenuation factors. A hierarchical strategy based on the incremental increase of the data complexity starting from low-frequency content to high-frequency content, from initial wavelets to later phases in the data space from narrow azimuths to wide azimuths and from simple observables to more complex ones. Different synthetic examples on realistic structures illustrate the efficiency of this strategy based on the data manipulation. This strategy related to the data space has to be inserted into a more global framework where we could improve significantly the probability to converge to the global minimum. When considering the model space, we may rely on the construction of the initial model or add constraints such as smoothness of the searched model and/or prior informations collected by other means. An alternative strategy concerns the building of the objective function and various possibilities must be considered, which may increase the linearity of the inversion procedure.     

Adaptive Surface Reconstruction Based on Tensor Product Algebraic Splines

Surface reconstruction from unorganized data points is a challenging problem in Computer Aided Design and Geometric Modeling. In this paper, we extend the mathematical model proposed by Juttler and Felis (Adv. Comput. Math., 17 (2002), pp. 135-152) based on tensor product algebraic spline surfaces from fixed meshes to adaptive meshes. We start with a tensor product algebraic B-spline surface defined on an initial mesh to fit the given data based on an optimization approach. By measuring the fitting errors over each cell of the mesh, we recursively insert new knots in cells over which the errors are larger than some given threshold, and construct a new algebraic spline surface to better fit the given data locally. The algorithm terminates when the error over each cell is less than the threshold. We provide some examples to demonstrate our algorithm and compare it with Jiittler's method. Examples suggest that our method is effective and is able to produce reconstruction surfaces of high quality.AMS subject classifications: 65D17     

A neural approach for obstacle detection with a linear stereoscopic sensor

A neural implementation for achieving real-time obstacle detection in front of a moving vehicle using a linear stereoscopic sensor is presented. The key problem is the so-called “correspondence problem” which consists in matching features in two stereo images that are projections of the same physical entity in the three-dimensional world. In our approach, the set of edge points extracted from each linear image is first split into two classes. Within each of these classes, the matching problem is turned into an optimization task where an energy function, which represents the constraints on the solution, is to be minimized. The optimization problem is then performed thanks to an analog Hopfield neural network. The preliminary discrimination of the edge points allows us to implement the matching process as two networks running in parallel. Experimental results are presented to demonstrate the effectiveness of the approach for 3-D reconstruction in real traffic conditions.     

Geometric Perception of Pose and Tracking

Object tracking and manipulation is an important process for many applications in robotics and computer vision. A novel 3D pose estimation of objects using reflectionally symmetry formulated in conformal geometric algebra (CGA) is proposed in this work. The synthesis of the kinematical model for robots using the CGA approach is described. Real time implementation results are presented for the pose estimation of object using a stereo vision system.