Camera Parameter Estimation via Quartic Equation Depth Solving
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Solution Overview
Problem
Existing methods for estimating external camera parameters, such as those in Non-Patent Documents 1 and 2, face high computational loads and stability issues due to the use of singular value decomposition and require multiple steps for coordinate transformation.
Innovation Solution
A camera parameter estimation apparatus and method that transforms three-dimensional coordinates into a local coordinate system, calculates a linear transformation matrix, and solves a quartic equation to determine depths, allowing for direct calculation of the rotation matrix and translation vector without singular value decomposition in a single step.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If singular value decomposition is used to calculate external parameters, then measurement precision is improved, but computational load increases and calculation time increases
Solution Approach 1:
The patent replaces the mechanical/computational heavy singular value decomposition process with a mathematical algebraic approach using quartic equations. By transforming the coordinate system and deriving a quartic equation for depth calculation, the method eliminates the need for iterative numerical optimization and SVD, achieving both speed and precision.
Solution Approach 2:
The patent changes the mathematical parameters and formulation by introducing a local coordinate system and transforming the projection equations into a quartic equation form. This parameter transformation converts a complex matrix decomposition problem into a solvable algebraic equation, reducing computational complexity while maintaining accuracy.
2Measurement precision
If multiple steps of coordinate transformation are used, then measurement precision is improved, but device complexity increases
Solution Approach 1:
The patent merges multiple coordinate transformation steps into a single integrated process. By defining a local coordinate system that directly incorporates the necessary transformations and solving the quartic equation in one step, the method combines what were previously separate transformation operations into a unified calculation, reducing overall complexity.
Solution Approach 2:
The patent segments the calculation process into distinct functional modules: coordinate transformation to local system, linear transformation matrix calculation, quartic equation solving for depth, and final external parameter computation. This segmentation makes the complex process more manageable and implementable while maintaining precision.
Data Source
AI summary
A camera parameter estimation apparatus: takes three sets of three-dimensional coordinates pertaining to an object and two-dimensional coordinates corresponding to the three-dimensional coordinates, and transforms a coordinate system of the three-dimensional coordinates from a world coordinate system to a local coordinate system; calculates a linear transformation matrix based on a projection transformation expression from the transformed three-dimensional coordinates to the two-dimensional coordinates, calculates a coefficient of a quartic equation pertaining to any one of depths from a camera center to each three-dimensional coordinate, and calculates each depth; calculates the rotation matrix in the local coordinate system using each depth and the linear transformation matrix; calculates a translation vector in the local coordinate system from each depth based on the projection transformation expression; and calculates a rotation matrix and a translation vector in the world coordinate system by performing an inverse transform of the rotation matrix and the translation vector.