CN-121120369-B - Method and system for determining central axis of revolution based on iterative projection optimization

CN121120369BCN 121120369 BCN121120369 BCN 121120369BCN-121120369-B

Abstract

The invention discloses a method and a system for determining a central axis of a revolving body based on iterative projection optimization, which comprise the steps of obtaining three-dimensional point cloud data of the surface of a revolving body part in a three-dimensional space, adopting multi-initial-point iterative optimization based on the three-dimensional point cloud data to obtain an overall optimal projection direction vector, wherein the direction is the direction of the central axis of the revolving body, calculating other geometric parameters of the revolving body based on the direction, and the iterative optimization process aims at searching a projection direction which can enable a projection point set of the three-dimensional point cloud data on an orthogonal projection plane to have maximum circular symmetry. The invention can still stably and accurately determine the central axis of the revolving body under the condition of incomplete data.

Inventors

XIE HAIBO
LIN XIAOHUI
WANG CHENG
LIU ZHIBIN
WANG CHENGZHEN
YANG HUAYONG

Assignees

浙江大学

Dates

Publication Date: 20260512
Application Date: 20251113

Claims (9)

1. The method for determining the central axis of the revolution body based on iterative projection optimization is characterized by comprising the following steps of: S1, acquiring three-dimensional point cloud data of the surface of a revolving body part in a three-dimensional space; s2, generating a group of widely distributed initial projection direction vectors on a unit sphere by adopting a multi-initial-point strategy based on the three-dimensional point cloud data, wherein each initial point corresponds to one initial projection direction vector; S3, carrying out iterative optimization on each initial point to obtain an optimal projection direction vector of the initial point, wherein the iterative optimization process aims at searching a projection direction which can enable a projection point set of the three-dimensional point cloud data on an orthogonal projection plane to have maximum circular symmetry; In the step S3, iterative optimization is performed for each initial point, including the following sub-steps: S3.1, parameterizing each initial projection direction vector through a spherical coordinate system; s3.2, orthogonally projecting the three-dimensional point cloud data onto a two-dimensional plane taking the current projection direction vector as a normal line to generate a two-dimensional projection point set P'; S3.3, performing geometric shape fitting on the two-dimensional projection point set P 'to obtain a circular or elliptical contour containing the most inner points, and integrating the inner points conforming to the circular or elliptical contour to obtain an inner point set I'; s3.4, calculating an objective function for measuring the circular symmetry of the circular or elliptical profile obtained by fitting; S3.5, updating the projection direction vector by adopting a derivative-free optimization algorithm according to the value of the objective function so as to enable the objective function value calculated in the subsequent iteration to be minimum; s3.6, repeating the steps S3.2-S3.5 until the convergence condition is met, and obtaining the optimal projection direction vector of the initial point; s4, comparing the optimal projection direction vectors of all initial points to obtain an overall optimal projection direction vector, namely the direction of the central axis of the revolving body, and calculating other geometric parameters of the revolving body based on the overall optimal projection direction vector.
2. The method for determining a center axis of a revolution based on iterative projection optimization according to claim 1, wherein in S1, preprocessing the obtained three-dimensional point cloud data comprises removing noise points by a statistical outlier removal filter; or down-sampling too dense a point cloud by a voxel grid filter.
3. The method for determining a central axis of a revolution based on iterative projection optimization according to claim 1, wherein the objective function is obtained by weighted summation of cost terms, and the cost terms comprise an interior point proportion penalty term and a geometric roundness error term; The interior point proportion punishment item is used for punishing points which do not belong to the interior point set I 'in the two-dimensional projection point set P', and the value of the punishment item is 1 minus the ratio of the total number of the interior points in the interior point set I 'to the total number of points in the two-dimensional projection point set P'; The geometric roundness error term is used for punishing out non-roundness of geometric shapes formed by inner points, and the value of the geometric roundness error term is the eccentricity of the circular or elliptical outline obtained by fitting.
4. The method for determining a central axis of a revolution based on iterative projection optimization according to claim 3, wherein the cost term further comprises a concentricity error term for realizing a measure of concentricity having a value of the square root of the average of the sum of squares of deviations of all concentric circle center coordinates and the ensemble average center coordinates.
5. The method for determining a central axis of a revolution based on iterative projection optimization according to claim 3, wherein the cost term further comprises a multi-layer circle center parallelism error term for realizing a measure of parallelism, the value of which is a cross product square of a multi-layer circle center fitting straight line direction vector and a current projection direction vector.
6. The method for determining a central axis of a revolution based on iterative projection optimization according to claim 1, wherein in S3.5, the derivative-free optimization algorithm adopts a Nelder-Mead simplex method or a Powell conjugate direction method.
7. The method for determining a central axis of revolution based on iterative projection optimization according to claim 1, wherein in S3.3, a random sampling coincidence algorithm is used to perform geometric fitting on the two-dimensional projection point set P'.
8. The method for determining a central axis of revolution based on iterative projection optimization of claim 7, wherein in a single iteration of the random sample consensus algorithm, a fitting method for calculating geometric parameters from sample points employs Taubin algebraic fitting.
9. A system for determining a central axis of revolution based on iterative projection optimization, comprising a memory and one or more processors, the memory having executable code stored therein, the one or more processors being coupled to the memory, the executable code, when executed, for implementing the method for determining a central axis of revolution based on iterative projection optimization of any of claims 1-8.

Description

Method and system for determining central axis of revolution based on iterative projection optimization Technical Field The invention relates to the field of three-dimensional computer vision and point cloud processing, in particular to a method and a system for determining a central axis of a revolving body based on iterative projection optimization, which are used for robustly and accurately extracting geometric parameters of the revolving body (such as a cone, a cylinder, a round table and the like) with a central revolving shaft, in particular to a method and a system for the central revolving shaft of the revolving body from incomplete or noisy three-dimensional point cloud data. The invention can be widely applied to the scenes such as reverse engineering, industrial automatic detection, robot vision navigation, digital protection of cultural relics and the like. Background In the fields of modern industrial manufacturing, quality control, three-dimensional reconstruction, etc., it is a fundamental and critical task to identify and fit geometric primitives from three-dimensional point cloud data acquired by means of laser scanners, structured light cameras, etc. In particular to a revolving body formed by revolving a curved surface around a straight line, the central revolving shaft and the profile parameters of the revolving body are accurately determined, and the method has important significance in evaluating the processing precision of parts, realizing object grabbing and assembling and the like. Existing geometric fitting methods, such as algorithms implemented in a mainstream point cloud processing library (such as Point Cloud Library, hereinafter referred to as PCL), typically employ a strategy that directly performs model parameter fitting in three-dimensional space. Such methods, such as random sample consensus (RANSAC) based algorithms, assume a three-dimensional model (e.g., vertex, axis and half apex angle of a cone, or axis and radius of a cylinder) with multiple degrees of freedom by randomly sampling the set of points, and then evaluate the model's conformity to the entire point cloud. However, these direct three-dimensional fitting methods have significant limitations in processing incomplete data common in the real world. In many application scenarios, due to occlusion, limitation of scanning angle, or characteristics of the object itself, the collected point cloud data often only covers a local area of the surface of the revolution body. For such partial point cloud data, it becomes very difficult to directly fit a high-degree-of-freedom three-dimensional model. Because sparse or unevenly distributed point sets may not provide sufficient geometric constraints for all model parameters, the fitting process is unstable, the result accuracy is low, and even fails entirely. In addition, noise and outliers commonly existing in the point cloud data can further interfere with the fitting process, and robustness of the algorithm is reduced. Therefore, how to robustly and accurately extract the central revolution axis from the incomplete, noisy partial revolution surface point cloud is a challenge in the current technology. Disclosure of Invention Aiming at the technical problems of poor robustness, low precision and easy failure when the revolving body is fitted from partial or noisy three-dimensional point cloud data in the prior art, the invention provides a method and a system for determining the central axis of the revolving body based on iterative projection optimization, which are used for stably and accurately determining the central axis of the revolving body under the condition of incomplete data. The specific technical scheme is as follows: a method for determining a central axis of a revolution body based on iterative projection optimization comprises the following steps: S1, acquiring three-dimensional point cloud data of the surface of a revolving body part in a three-dimensional space; s2, generating a group of widely distributed initial projection direction vectors on a unit sphere by adopting a multi-initial-point strategy based on the three-dimensional point cloud data, wherein each initial point corresponds to one initial projection direction vector; S3, carrying out iterative optimization on each initial point to obtain an optimal projection direction vector of the initial point, wherein the iterative optimization process aims at searching a projection direction which can enable a projection point set of the three-dimensional point cloud data on an orthogonal projection plane to have maximum circular symmetry; s4, comparing the optimal projection direction vectors of all initial points to obtain an overall optimal projection direction vector, namely the direction of the central axis of the revolving body, and calculating other geometric parameters of the revolving body based on the overall optimal projection direction vector. Further, in the step S1, preprocessing the obtai