Projective Transformation Matrix Determination for Non-Planar Surfaces
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Solution Overview
Problem
Existing methods for determining a projective transformation matrix fail when feature points in a projection image are projected onto a three-dimensional object instead of a planar surface, as they require feature points to be projected on the same planar surface to accurately associate projector and camera coordinates.
Innovation Solution
A method and system that adjust the positional relationship of feature points in the projection image by receiving a change instruction, projecting the feature points onto the same area, and determining the projective transformation matrix based on the new coordinates in both the projection and captured images, ensuring all feature points are projected on a planar surface.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If feature points are projected using a standard projection image, then the projection can be displayed on the display surface, but the feature points may be projected onto a three-dimensional object instead of the planar display surface, making it impossible to determine the projective transformation matrix
Solution Approach 1:
The patent makes the feature point positions dynamic by allowing their coordinates to be changed between a first projection image and a second projection image. The determination section uses feature points from the second projection image that have different positional relationships compared to the first projection image, enabling the system to adapt to different projection scenarios and ensure feature points are projected onto the planar display surface rather than three-dimensional objects.
2Measurement precision
If the positional relationship among feature points is changed from the first projection image to the second projection image, then feature points can be ensured to be projected on the same planar display surface, but this requires receiving change instructions and projecting multiple images
Solution Approach 1:
The patent applies preliminary action by preparing a second projection image in advance with feature points positioned at coordinates that will ensure projection onto the planar display surface. The determination section is pre-configured to use feature points from this second projection image rather than the first projection image, allowing the system to proactively avoid the problem of feature points being projected onto three-dimensional objects before the determination process begins.
Data Source
AI summary
A projective transformation matrix determination method includes receiving a change instruction to change a positional relationship among four feature points in a situation in which a projector projects a first projection image showing the four feature points onto a first area, causing the projector to project a second projection image showing the four feature points onto the first area in response to the change instruction, and determining a projective transformation matrix based on the coordinates of the four feature points in the second projection image and the coordinates of the four feature points in a first captured image generated by capturing, with a camera, an image of the first area where the second projection image is projected, the projective transformation matrix associating a projector coordinate system which defining the coordinates in an image projected by the projector with a camera coordinate system defining the coordinates in an image generated by the camera.