Normal Vector Estimation for Projector Distortion Correction
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Solution Overview
Problem
Existing image display devices, such as projectors, face challenges in accurately calculating normal vectors for distortion correction due to insufficient transformation matrix accuracy, leading to keystone distortions on non-flat projection surfaces.
Innovation Solution
A method involving projecting a detectable pattern from a projector onto a planar surface, capturing images from multiple positions, calculating transformation matrices, and estimating normal vectors using internal parameters of the camera and projector to correct geometric distortions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a single transformation matrix is calculated from one picked-up image, then the calculation process is simple, but the calculation accuracy of the normal vector is insufficient
Solution Approach 1:
The patent divides the measurement process into multiple independent observations by capturing images from multiple different positions. Each position provides an independent transformation matrix calculation, and the normal vector is determined by synthesizing results from multiple positions rather than relying on a single observation. This segmentation of the measurement process improves accuracy without requiring complex single-observation measurement systems.
Solution Approach 2:
The patent performs more measurement actions than the minimum required by capturing images from multiple positions (excessive action) rather than just one position. This redundant measurement approach provides multiple data points for normal vector calculation, improving accuracy through oversampling while keeping each individual measurement simple.
2Measurement precision
If multiple normal vectors are calculated from one transformation matrix, then more solution candidates are obtained, but the calculation accuracy remains insufficient
Solution Approach 1:
The patent transitions from a two-dimensional single-image measurement to a three-dimensional multi-position measurement by adding the position dimension. Instead of trying to extract multiple normal vectors from a single transformation matrix (2D data), the system captures images from multiple positions in space (3D data), providing independent transformation matrices that collectively enable accurate normal vector calculation through spatial diversity.
3Reliability
If distortion correction is performed without accurate normal vector calculation, then the process is faster, but keystone distortion occurs on non-flat surfaces
Solution Approach 1:
The patent performs preliminary measurement and calculation actions by capturing multiple images and calculating transformation matrices before the final distortion correction is applied. This preliminary multi-position measurement establishes accurate normal vector information in advance, ensuring reliable distortion correction without requiring time-consuming iterative adjustments during the actual projection correction phase.
Data Source
AI summary
A calculation method is provided, the calculation method including calculation processing of calculating, for each picked-up image, a transformation matrix in which a first corresponding point set in advance in a pattern projected onto a projection surface by a projector and a second corresponding point corresponding to the first corresponding point in each of two or more picked-up images acquired by picking up an image of the projection surface where the pattern is projected, with a camera from two or more positions, are associated with each other, by using the first corresponding point, the second corresponding point, an estimated value of an internal parameter of the camera, and an internal parameter of the projector, and comparing normal vectors of the projection surface calculated from the respective transformation matrices calculated for each picked-up image, thus estimating a normal vector of the projection surface.