2900427
Reconstructing B-spline Curves from Point Clouds--A Tangential Flow Approach Using Least Squares Minimization
We present a novel algorithm based on least-squares minimization to approximate point cloud data in 2D plane with a smooth B-spline curve. The point cloud data may represent an open curve with self intersection and sharp corner. Unlike other existing methods, such as the moving least-squares method and the principle curve method, our algorithm does not need a thinning process. The idea of our algorithm is intuitive and simple - we make a B-spline curve grow along the tangential directions at its two end-points following local geometry of point clouds. Our algorithm generates appropriate control points of the fitting B-spline curve in the least squares sense. Although presented for the 2D case, our method can be extended in a straightforward manner to fitting data points by a B-spline curve in higher dimensions
181647
Geometric modeling with conical meshes and developable surfaces
In architectural freeform design, the relation between shape and fabrication poses new challenges and requires more sophistication from the underlying geometry. The new concept of conical meshes satisfies central requirements for this application: They are quadrilateral meshes with planar faces, and therefore particularly suitable for the design of freeform glass structures. Moreover, they possess a natural offsetting operation and provide a support structure orthogonal to the mesh. Being a discrete analogue of the network of principal curvature lines, they represent fundamental shape characteristics. We show how to optimize a quad mesh such that its faces become planar, or the mesh becomes even conical. Combining this perturbation with subdivision yields a powerful new modeling tool for all types of quad meshes with planar faces, making subdivision attractive for architecture design and providing an elegant way of modeling developable surfaces.
18042921
Transforming Least Squares to Weighted Least Squares for Accurate Range Image Registration
The traditional ICP algorithm is a de facto standard approach for range image registration. While it assumes that one data set is a subset of another, this assumption is often violated in practice. As a result, a number of algorithms have been developed to first eliminate false matches due to occlusion, appearance and disappearance of points and then estimate the camera motion parameters in the least squares sense. Instead of eliminating outliers in the process of image registration, we in this paper use the generalised entropy to estimate the probability of correspondences established using the traditional closest point criterion, leading camera motion parameters to be estimated in the weighted least squares sense. For more accurate registration results, we also learn from the probability of correspondences estimated in the past. Since one point in one data set can only correspond to a single point in another, the two way constraint is also imposed. Finally the cam era motion parameters are optimized using the powerful mean field annealing scheme. A comparative study based on real images has shown that the proposed algorithm produces promising automatic range image registration results.
11535936
Efficient implementation of tuple pattern based retrieval
Tuple pattern based retrieval is a language construct that matches a tuple pattern against a set of tuples to retrieve components of those tuples. This high-level abstraction allows programs to be written more easily and clearly than otherwise. This paper describes a clean and automatic method for transforming tuple pattern based retrievals into efficient implementations. The paper also presents two systems that implement the method, and describes successful experience and experiments in generating efficient implementations for graph algorithms, program analysis, security, and other applications.
36759557
Geometrical analysis of two sets of 3D correspondence data patterns
Given two sets of image correspondence data, the analysis of the corresponding rigid body transformation that accurately describes the object's motion in 3D space is a fundamental problem in image understanding. While many methods have been put forward to analyse 3D transformations, such methods do not make use of the vector distance between feature points and angular information as constraints to analyse transformation parameters. Current methods and algorithms have also suffered from the problems of lack of efficiency, sensitivity to noise, and multiplicity of solutions. In this paper we present a novel geometrical analysis of rigid body transformations and a novel algorithm to calibrate transformation parameters based on image correspondence. The algorithm is validated through experimental calibration and a comparison is made with calibration implemented by the least squares method. We demonstrate that the proposed algorithm works well in the presence of noise and that its performance is in general superior to algorithms based on the least squares method.
45330274
Time Series Prediction by Using Negatively Correlated Neural Networks
Negatively correlated neural networks (NCNNs) have been proposed to design neural network (NN) ensembles [1]. The idea of NCNNs is to encourage different individual NNs in the ensemble to learn different parts or aspects of a training data so that the ensemble can learn the whole training data better. The cooperation and specialisation among different individual NNs are considered during the individual NN design. This provides an opportunity for different NNs to interact with each other and to specialise. In this paper, NCNNs are applied to two time series prediction problems (i.e., the Mackey-Glass differential equation and the chlorophyll-a prediction in Lake Kasumigaura). The experimental results show that NCNNs can produce NN ensembles with good generalisation ability.
18963770
A quasi-Monte Carlo method for computing areas of point-sampled surfaces
A novel and efficient quasi-Monte Carlo method for computing the area of a point-sampled surface with associated surface normal for each point is presented. Our method operates directly on the point cloud without any surface reconstruction procedure. Using the Cauchy-Crofton formula, the area of the point-sampled surface is calculated by counting the number of intersection points between the point cloud and a set of uniformly distributed lines generated with low-discrepancy sequences. Based on a clustering technique, we also propose an effective algorithm for computing the intersection points of a line with the point-sampled surface. By testing on a number of point-based models, experiments suggest that our method is more robust and more efficient than those conventional approaches based on surface reconstruction.