Relative orientation method based on axial angle vector

Abstract

The invention relates to a relative orientation method based an axial angle vector. The method comprises the steps of firstly utilizing the axial angle vector to parameterize a rotation matrix, and deducing the differential relation between the rotation matrix and the axial angle vector; then establishing a coplanar condition equation, and deducing a relative orientation adjustment model based on the axial angle vector according to the property of the parameterized rotation matrix and the property of an antisymmetric matrix; finally utilizing an indirect-method adjustment principle to solve a relative orientation parameter. According to the method, the axial angle vector is utilized to replace a traditional eulerian angle to construct the rotation matrix, so the singularity possibly happening in a traditional attitude parameter resolving process is avoided; only the sine trigonometric function operation and the cosine trigonometric function operation of one rotation angle are related in adjustment resolving, so the calculation cost is effectively reduced; the property of the antisymmetric matrix is fully utilized, and the obtained mathematic model is precise and concise in form; compared with a traditional relative orientation element resolving algorithm, the method is quick in calculation speed, good in stability and high in numerical resolving accuracy.

Description

technical field [0001] The invention belongs to the field of photogrammetry and computer vision, in particular to a relative orientation method based on an axis-angle vector. Background technique [0002] The relative orientation of the three-dimensional model is one of the basic problems in photogrammetry and computer vision. Its purpose is to use the internal geometric relationship of the three-dimensional model to determine the relative position and relative attitude parameters of the left and right photos in the three-dimensional model. It is mainly used for the target geometry. Positioning and 3D model reconstruction. In the traditional relative orientation, Euler angles are often used to describe the pose of the photo. Although the geometric meaning is more obvious, a large number of trigonometric function operations will affect the calculation speed and accuracy, and the singularity of the numerical solution may appear; in addition, The unit quaternion has 4 degrees ...

AI Technical Summary

Problems solved by technology

In the traditional relative orientation, Euler angles are often used to describe the pose of the photo. Although the geometric meaning is more obvious, a large number of trigonometric function operations will affect the calculation speed and accuracy, and the singularity of the numerical solution may appear; in addition, The unit quaternion has 4 degrees of freedom, and a constraint must be added when describing the attitude, which increases the complexity of the solution

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