A modified iterative closest point algorithm for shape registration

The most popular algorithm for aligning of three-dimensional point data is the iterative closest point (ICP). In this paper, a new algorithm for orthogonal registration of point clouds based on the point-to-plane ICP algorithm is proposed.The algorithm consists of three steps: first, a matrix of affine transformation between two given point clouds are calculated; second, the affine transformation matrix is projected onto the manifold SO(3) of orthonormal matrices; finally, a translation vector is reestimated. The proposed algorithm does not require an approximate initial estimate. At each iterative step of the ICP algorithm, an approximated closed-form solution for the orthogonal transformation is derived.The performance of the proposed algorithm is compared with that of common algorithms for the geometrical transformations estimation. KEYWORDS exact solution, ICP, point-to-plane, registration, variational problem 9218The variational problem point-to-point for orthogonal transformations is mathematically equivalent to the absolute orientation problem in photogrammetry. 4 In this case, the closed-form solution was obtained by Horn. 5,6 The solution in the earlier work of Horn 5 is expressed with quaternions, whereas the solution in his other work 6 uses orthogonal matrices. Note that the computational complexity of the solutions is linear with respect to the number of point pairs.The original ICP algorithm is widely used for registration of rigid objects, but it often fails for the case of nonrigid objects. Recently, an extension of the ICP algorithm for scaling has been proposed. 7 An efficient algorithm for arbitrary affine transformations was proposed. 8,9 A closed-form solution to the point-to-point problem was also derived. 10,11 The aforementioned approaches for the variational ICP problem are based on the point-to-point metric. It has been shown that the point-to-plane metric is better than the point-point metric in terms of accuracy and convergence rate. 12 Search for the closed-form solution to the point-to-plane case for orthogonal transformations is an open problem. Instead, iterative methods based on the Levenberg-Marquardt 13 linear least squares optimization or closed-form methods for small angles only are often used. 12 Note that all iterative solutions require an initial approximation of the geometrical transformation, and they usually possess poor convergence, sometimes converge to a local minimum, and sometimes do not converge.A closed-form solution to the point-to-plane problem for an arbitrary affine transformation was proposed. [14][15][16] The affine approach works well when the correspondence between point clouds is good. In this case, the affine point-to-plane algorithm precisely reconstructs the original geometric transformation for arbitrary affine transformations, particularly for orthogonal transformations. 15,16 When the correspondence between clouds is poor, the affine approach is unable to recover the original orthogonal transformation. Note that the variational problem for orthogona...

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“…An efficient algorithm for arbitrary affine transformations was proposed . A closed‐form solution to the point‐to‐point problem was also derived …”

Section: Introductionmentioning

confidence: 99%

A non‐iterative method for approximation of the exact solution to the point‐to‐plane variational problem for orthogonal transformations

Makovetskii

Voronin

Kober

et al. 2018

Math Methods in App Sciences

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“…Building dense 3D maps of environments is an important task for mobile robotics, with applications in navigation, manipulation, semantic mapping, face recognition [9,10,11,12,13,14,15,16,17], and in augmented reality applications, surveillance systems, medical applications [18,19,20,21,22].…”

Section: Introductionmentioning

confidence: 99%

Accurate reconstruction of the 3D indoor environment map with a RGB-D camera based on multiple ICP

Ruchay

Dorofeev

Kober³

2018

Collection of Selected Papers of the IV International Conference on Information Technology and Nanotechnology

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In this paper, we propose a new method for 3D map reconstruction using the Kinect sensor based on multiple ICP. The Kinect sensor provides RGB images as well as depth images. Since the depth and RGB color images are captured by one Kinect sensor with multiple views, each depth image should be related to the color image. After matching of the images (registration), point-to-point corresponding between two depth images is found, and they can be combined and represented in the 3D space. In order to obtain a dense 3D map of the 3D indoor environment, we design an algorithm to combine information from multiple views of the Kinect sensor. First, features extracted from color and depth images are used to localize them in a 3D scene. Next, Iterative Closest Point (ICP) algorithm is used to align all frames. As a result, a new frame is added to the dense 3D model. However, the spatial distribution and resolution of depth data affect to the performance of 3D scene reconstruction system based on ICP. In this paper we automatically divide the depth data into sub-clouds with similar resolution, to align them separately, and unify in the entire points cloud. This method is called the multiple ICP. The presented computer simulation results show an improvement in accuracy of 3D map reconstruction using real data.

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“…A generalization of this algorithm to the case of an arbitrary affine transformation was done [10,11]. A closed-form solution to the point-to-point problem was derived [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

“…A closed-form solution to the point-to-plane case for orthogonal transformations is an open problem. Instead, iterative methods based on the linear least-squares optimization or closed-form methods for small angles only are often used [12]. Iterative solutions require an initial approximate estimate of the transformation parameters, and the iterations might converge slowly, converge to a local optimum or not converge at all.…”

Section: Introductionmentioning

confidence: 99%

Point clouds registration based on the point-to-plane approach for orthogonal transformations

Makovetskii

Voronin

Kober

et al. 2018

Collection of Selected Papers of the IV International Conference on Information Technology and Nanotechnology

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A modified iterative closest point algorithm for shape registration

Cited by 8 publications

References 10 publications

A non‐iterative method for approximation of the exact solution to the point‐to‐plane variational problem for orthogonal transformations

A non‐iterative method for approximation of the exact solution to the point‐to‐plane variational problem for orthogonal transformations

Accurate reconstruction of the 3D indoor environment map with a RGB-D camera based on multiple ICP

Point clouds registration based on the point-to-plane approach for orthogonal transformations

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