30454395
Flag Guided Integration of Multiple Registered Range Images
Integration of multiple registered range images finds applications in numerous areas. While most existing integration algorithms detect corresponding points between neighbouring views based on interpoint distances, we define in this paper corresponding area for each point and then carry out geometrical, rigidity, and orientation tests for the same purpose, not only reflecting the scanning nature of sampling resolution, but also the geometry of object surface. To more accurately fuse corresponding points, while most existing algorithms consider the confidence of points, we consider an accumulative fusion scheme of confidences, reflecting the number of times of observation. The fused points are finally triangulated using the improved Delaunay triangulation method, guaranteeing a watertight surface. A comparative study based on real images shows that the proposed algorithm is accurate and efficient and is able to compensate both the accumulative registration errors and imaging noise
26921590
Evaluating structural constraints for accurate range image registration
New technological developments in optics and electronics are rendering laser scanning systems cheaper and more accurate. Such systems can directly capture depth information from objects simplifying range image analysis and enlarging their applications scope. Accurate image registration algorithms represent a pivotal aspect of range image analysis which still require substantial improvements. While a large number of algorithms have been proposed, it is very important to compare the performance of different registration algorithms so that good algorithms can be selected for real applications. Unfortunately, most of these algorithms are iterative with a number of parameters initialised by users. The main disadvantages of these methods are that these parameters are often context dependent. Thus, while aiming to develop automatic registration algorithms instead of comparing the registration algorithms themselves, we compare the structural constraints based on a single registration algorithm(GICP). A large number of experiments using real range images demonstrate their effectiveness on improving the GICP algorithm.
9293300
Automatic registration of overlapping 3D point clouds using closest points
Abstract While the SoftAssign algorithm imposes a two-way constraint embedded into the deterministic annealing scheme and the EMICP algorithm imposes a one-way constraint, they represent the state of the art technique for the automatic registration of overlapping free form shapes. They both have a time complexity of O ( n 2 ). While the former has a space complexity also of O ( n 2 ), the latter has a space complexity of O ( n ). The heavy demand for computation and storage memory renders either the SoftAssign or EMICP algorithm to hardly operate on whole shapes with thousands of points. In this case, they often have to reduce the number of points to an order of 100s on the free form shapes to be registered. This paper proposes using closest points in conjunction with either the one-way or two-way constraint for the automatic registration of overlapping 3D point clouds and thus, combining the accuracy of both the SoftAssign and EMICP algorithms with the efficiency of the traditional ICP algorithm. A comparative study based on both synthetic data and real images has shown that the proposed algorithm does not significantly sacrifice accuracy and stability of either the SoftAssign or EMICP algorithm, but gains remarkable efficiency of the traditional ICP algorithm for the automatic registration of overlapping 3D point clouds. Since, the proposed algorithm is of general use and has an advantage of easy implementation, it is likely to become in the future a benchmark for the automatic registration of overlapping 3D point clouds.
18654744
Evaluating collinearity constraint for automatic range image registration
While most of the existing range image registration algorithms either have to extract and match structural (geometric or optical) features or have to estimate the motion parameters of interest from outliers corrupted point correspondence data for the elimination of false matches in the process of image registration, the registration error and the collinearity error derived directly from the traditional closest point criterion are also capable of doing the same job. However, the latter has an advantage of easy implementation. The purpose of this paper is to investigate which definition of collinearity is more accurate and stable in eliminating false matches inevitably introduced by the closest point criterion. The experiments based on real images show the advantages and disadvantages of different definitions of collinearity.
14532857
Projecting registration error for accurate registration of overlapping range images
Abstract In this paper, we propose a novel algorithm for the automatic registration of two overlapping range images. Since it is relatively difficult to compare the registration errors of different point matches, we project them onto a virtual image plane for more accurate comparison using the classical pin-hole perspective projection camera model. While the traditional ICP algorithm is more interested in the points in the second image close to the sphere centred at the transformed point, the novel algorithm is more interested in the points in the second image as collinear as possible to the transformed point. The novel algorithm then extracts useful information from both the registration error and projected error histograms for the elimination of false matches without any feature extraction, image segmentation or the requirement of motion estimation from outliers corrupted data and, thus, has an advantage of easy implementation. A comparative study based on real images captured under typical imaging conditions has shown that the novel algorithm produces good registration results.
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.
39617215
Counting rooted near-triangulations on the sphere
This paper provides the results on the enumerations of rooted simple outerplanar maps, rooted outerplanar near-triangulations, rooted 2-connected near-triangulations, rooted strict 2-connected near-triangulations and rooted simple 2-connected near-triangulations. The answer to an open problem proposed by one of the authors is also provided.
1265218
Solving Regular Tree Grammar Based Constraints
This paper describes the precise specification, design, analysis, implementation, and measurements of an efficient algorithm for solving regular tree grammar based constraints. The particular constraints are for dead-code elimination on recursive data, but the method used for the algorithm design and complexity analysis is general and applies to other program analysis problems as well. The method is centered around Paige's finite differencing, i.e., computing expensive set expressions incrementally, and allows the algorithm to be derived and analyzed formally and implemented easily. We propose higher-level transformations that make the derived algorithm concise and allow its complexity to be analyzed accurately. Although a rough analysis shows that the worst-case time complexity is cubic in program size, an accurate analysis shows that it is linear in the number of live program points and in other parameters, including mainly the arity of data constructors and the number of selector applications into whose arguments the value constructed at a program point might flow. These parameters explain the performance of the analysis in practice. Our implementation also runs two to ten times as fast as a previous implementation of an informally designed algorithm.
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.
19566771
Nowhere-Zero 4-Flows and Cayley Graphs on Solvable Groups
We prove that every Cayley graph on a finite solvable group admits a nowhere-zero 4-flow. In particular, every cubic Cayley graph on a solvable group is 3-edge-colorable.
31965236
Iterate, Incrementalize, and Implement: A systematic approach to efficiency improvement and guarantees
People may more easily specify what they would like to compute if not concerned with how to compute efficiently. Given descriptions that may lead to inefficient computations, can we systematically obtain efficient algorithms and implementations? Can we further have efficiency guarantees for them? We give an overview of a general and systematic method for achieving efficiency improvement and providing efficiency guarantees. The method is centered around incrementalization: making computation proceed repeatedly on small incremented inputs and effectively maintaining and using previously computed results. The method has three steps: iterate, incrementalize, and implement. Step 1 determines a minimum step to be taken repeatedly. Step 2 makes each step compute incrementally, particularly by using and maintaining and appropriate additional values. Step 3 designs appropriate data structures for storing and accessing the values maintained. The central step of incrementalization [4] is: given a program f and an increment operation +, derive an incremental program that computes f(x+y) efficiently by using the result of f(x) [13], the intermediate results of f(x) [11], and auxiliary information of f(x) that can be inexpensively maintained [12]. This unifies existing approaches to incremental computation and is generally applicable; it exploits many existing program analysis and transformation techniques and can be systematically applied. The method has been used successfully in optimizing expensive recursive Electronic Notes in Theoretical Computer Science 90 (2003) 45–47