Method for solving three-dimensional similarity transformation parameter of model based on fitting plane normal vector direction

Abstract

The invention discloses a method for solving a three-dimensional similarity transformation parameter of a model based on a fitting plane normal vector direction. The method comprises the following steps: firstly, selecting N (N is greater than or equal to 3) pairs of corresponding points in a three-dimensional model and a real model as directional reference points, completing the coordinate centralization of the directional reference points under each model, solving the coordinates of the directional reference points after coordinate centralization, and further calculating a zoom factor lambda between the three-dimensional model and the real model; then obtaining optimal fitting planes of the directional reference points in the three-dimensional model and the real model by using an overall least square method, and performing further calculation so as to obtain the normal vectors of the two optimal fitting planes; finally calculating a three-dimensional rotary matrix R between the three-dimensional model and the real model, and calculating the translation vector t of similarity transformation. The method disclosed by the invention can realize the direct solution of the three-dimensional rotary parameters between the models without providing an initial value in advance, so that the dependence on the initial values of the parameters is reduced, and the method is suitable for the solution of three-dimensional similarity transformation parameters under various rotary conditions.

Description

technical field [0001] The invention relates to a method for calculating three-dimensional similarity transformation parameters of a model, in particular to a method for calculating three-dimensional similarity transformation parameters of a model based on a fitting plane normal vector direction, belonging to the fields of surveying and mapping and computer vision. Background technique [0002] In the process of target three-dimensional space positioning, the conversion between different coordinate systems is often involved, such as the conversion between the local three-dimensional coordinate system and the earth coordinate system, the conversion between the photogrammetric image space coordinate system and the object space coordinate system, etc. The conversion between three-dimensional rectangular coordinate systems satisfies the rigid body transformation, and the solution of seven parameters needs to be completed, including the transformation scale coefficient, the transl...

AI Technical Summary

Problems solved by technology

[0003] Usually, the three-dimensional rotation angle is used to express the rotation relationship. According to the three-dimensional spatial similarity transformation relationship, the multivariate function of the three-dimensional similarity transformation parameters is expanded into a Taylor series. The precise parameters are solved by iteration, but a relatively accurate initial value of the unknown must be provided. Otherwise, the solution will not converge or converge to the wrong solution

When the rotation angle of the coordinate system is very large, it is very difficult to accurately predict the initial value of the rotation angle

In the field of computer vision, the method of solving the rotation relationship based on the unit quaternion is widely used, but there are problems such as the unclear physical meaning of the parameters and the difficulty in estimating the accuracy of the parameters.

Images