Point cloud registration using the quasi-Newton method

Geodesy

UDC:

528.063.1

DOI:

10.22389/0016-7126-2023-992-2-2-11

1 Sharafutdinova A.A.

2 Bryn M.Ya.

Year:

2023

№:

992

Pages:

2-11

Petersburg State Transport University

1,

2,

Abstract:

The method of point clouds registration using scanning points based on an iterative closest points’ algorithm is actively researched in the terrestrial laser scanning practice. One of this method’s tasks is calculating the datum transformation optimal values: three rotation angles, three translation parameters, and a scale factor. A way of calculating it based on the Broyden-Fletcher-Goldfarb-Shanno numerical optimization method has been developed to solve the matter. The advantage is absence of need for direct calculating the Hesse matrix containing the second derivatives. Within the framework of the developed methodology the following elements are proposed: pre-optimization based on two-point model mass centres; calculation of the target function value and the target function gradient on iteration through the vectoring operator; finding step lengths under strong Wolf Conditions; plotting to determine the optimal step length on iteration; retrying the process until the quotient of the difference between the values of the target function on two extreme iterations by the value of the target edge repetition function takes the value that satisfies the given accuracy. The conditions on which the positive definiteness of the Hesse matrix is preserved are explained, and it is the main point of the Broyden-Fletcher-Goldfarb-Shanno method for the correct calculation of the transformation datum. The algorithm was implemented in the Mathcad software environment to test the developed method. As a result, the superlinear convergence and self-correcting properties of the developed technique were noted.

Keywords:

BFGS, datum transformation, optimization, point cloud, registration, terrestrial laser scanning

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Citation:

Sharafutdinova A.A.,

Bryn M.Ya.,

(2023) Point cloud registration using the quasi-Newton method. Geodesy and cartography = Geodezia i Kartografia, 84(2), pp. 2-11. (In Russian). DOI: 10.22389/0016-7126-2023-992-2-2-11