Crossing Point Detector Subpixel Precision via Function Model
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Solution Overview
Problem
Existing crossing point detectors in camera calibration methods suffer from low detection precision, especially when dealing with checker patterns that have edges along directions other than horizontal and vertical directions, due to aliasing effects and noise, which affects the accuracy of camera calibration.
Innovation Solution
A crossing point detector that uses a processor to detect crossing points by optimizing parameters of a function model or numerical model, which expresses pixel values with a curved surface, allowing for subpixel precision detection even when the checker pattern is tilted or rotated, and effectively handles aliasing by simulating pixel integration effects.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional crossing point detection methods are used, then the detection process is simple, but the detection precision is low due to aliasing effects and noise
Solution Approach 1:
The patent changes the parameter representation by using a function model with continuous parameters (a, b, c, d, θ, φ, σ) instead of discrete pixel values. This allows subpixel precision detection by optimizing these parameters to minimize the sum of squared differences between the function model and actual image data, thereby improving crossing point detection precision while managing algorithm complexity through systematic optimization.
Solution Approach 2:
The patent introduces a function model as an intermediary between the raw image data and the crossing point detection. This function model (Equation 1) acts as a mediator that represents the checker pattern with continuous mathematical functions, allowing for precise crossing point calculation by finding where the gradient components become zero, thus improving precision without directly processing noisy pixel data.
2Measurement precision
If the checker pattern is tilted or rotated, then the detection algorithm becomes more complex, but the detection precision deteriorates due to aliasing effects
Solution Approach 1:
The patent applies curvature by using a function model with sinusoidal components (involving cos(θ) and sin(θ)) that can represent tilted and rotated checker patterns. The parameters θ and φ represent the orientation angles of the boundary lines, allowing the model to adapt to any rotation angle while maintaining detection precision through continuous parameter optimization rather than discrete pixel sampling.
Solution Approach 2:
The patent introduces orientation parameters (θ and φ) that can be optimized to match any rotation angle of the checker pattern. By changing the parameter space to include these angular parameters, the algorithm can handle tilted and rotated patterns of any orientation while maintaining subpixel detection precision, resolving the contradiction between adaptability and precision.
3Measurement precision
If subpixel precision detection is implemented, then the detection precision improves, but the computational complexity increases
Solution Approach 1:
The patent replaces the mechanical pixel-based detection system with a mathematical function model approach. Instead of physically sampling pixels at discrete locations, the system uses continuous mathematical functions (Equation 1) and finds crossing points by solving for where the gradient components become zero. This substitution enables subpixel precision while reducing computational complexity through analytical solutions rather than exhaustive pixel search.
Solution Approach 2:
The patent creates a mathematical copy (function model) of the physical checker pattern in the image. This function model replicates the essential characteristics of the checker pattern using parameters that can be optimized to match the actual pattern. By working with this mathematical copy instead of the raw pixel data, the system achieves subpixel precision with reduced computational requirements through parameter optimization rather than fine-grained pixel analysis.
Data Source
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AI summary
A crossing point detector includes a memory and a crossing point detection unit that reads out a square image from a captured image in the memory, and detects a crossing point of two boundary lines in a checker pattern depicted in the square image. The crossing point detection unit decides multiple parameters of a numerical model, the parameters optimizing an evaluation value based on a difference between corresponding pixel values represented by the numerical model and the square image, respectively, and computes the position of a crossing point of two straight lines expressed by the decided multiple parameters to thereby detect the crossing point with subpixel precision. The numerical model is a model that simulates a pixel integration effect when imaging a step edge by assigning pixel values to respective regions inside a pixel divided by a straight line, and deciding a pixel value of the overall pixel.