New non-iterative solution of the perspective 3-point problem

作者：Zeng, Huaien^*

来源：Journal of Computational Information Systems, 2012, 8(9): 3747-3755.

• Algebraic techniques
• Camera positions
• Collinearity equations
• Control point
• Explicit solutions
• Exterior orientation
• Ferrari
• Line element
• Multipolynomial resultant
• Non-iterative
• Perspective 3-Point problems
• Quartic equation
• Second orders
• Space resection

The perspective 3-point problem is a basic issue in computer vision and photogrammetry, and in photogrammetry is called space resection in the case of three control points. The problem is usually solved iteratively with collinearity equations, but it usually does not succeed in the case of large pose angles because of an improper starting estimate of exterior orientation elements. Instead, it can be solved non-iteratively and elegantly with the pyramid principle. This paper firstly solves the camerapoint (camera projective center to control point) distances equations, by resultant and Ferrari's solution of quartic equations, and then presents the explicit solution of the camera position and orientation based on algebraic techniques. Three images with large, medium and small pose angles are respectively simulated, and the exterior elements are recovered using the presented approach. The result shows the calculative errors of line elements are in 10-6-m order of magnitude, and the errors of pose angle elements are in 10-4-second order of magnitude for the three images. Thus the presented approach is correct and efficient.

• 出版日期2012
• 单位三峡大学