Plane Tracking via Dual-Angle Camera Rotation and Affine Transformation
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Solution Overview
Problem
Existing methods for tracking a plane using a single camera rely on projective transformations, which are complex and difficult to handle due to their non-linear nature and limited applicability, failing to effectively preserve parallelism and requiring iterative processes like RANSAC.
Innovation Solution
A method involving two cameras capturing a plane from different angles, using inertial measurement units to calculate rotation transformations, and applying affine and projective transformations to simulate a parallel plane, allowing for linearization of the tracking problem and efficient feature matching.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If projective transformation is used to track a plane with a single camera, then the transformation can handle general perspective changes, but the complexity of calculation increases and parallelism is not preserved
Solution Approach 1:
The patent segments the transformation process into two distinct stages: first applying a rotation transformation to align the captured frame with a simulated top-down view, then applying an affine transformation for feature matching. This segmentation separates the complex projective transformation into manageable components, reducing overall calculation complexity while maintaining adaptability to perspective changes.
Solution Approach 2:
The patent introduces an intermediary simulated top-down view frame as an intermediate representation between the captured perspective view and the final matched features. This intermediary frame serves as a mediator that simplifies subsequent affine transformations by providing a normalized coordinate system where parallelism is preserved and calculations are more tractable.
2Adaptability or versatility
If projective transformation is used for plane tracking, then general transformations are handled, but the transformation is not defined on all of the plane and parallelism is not preserved
Solution Approach 1:
The patent segments the transformation into a rotation component that handles perspective distortion and an affine component that preserves parallelism. By separating these functions, the rotation transformation manages the coverage of general perspective changes while the subsequent affine transformation ensures parallelism is maintained in the final coordinate system.
Solution Approach 2:
The patent applies a rotation transformation that goes beyond the minimal necessary adjustment by fully normalizing the view to a simulated top-down perspective. This excessive action of completely reorienting the frame provides a standardized intermediate representation that guarantees parallelism preservation in subsequent processing, even though a smaller rotation might have sufficed for basic alignment.
3Manufacturing precision
If affine transformation is applied directly to captured frames from different angles, then parallelism is preserved, but the transformation cannot handle perspective distortions
Solution Approach 1:
The patent performs a preliminary rotation transformation on the captured frame before applying the affine transformation. This preliminary action of rotating the frame to a simulated top-down view removes perspective distortions in advance, creating a normalized input for the affine transformation that can then focus solely on preserving parallelism without being confounded by perspective effects.
Solution Approach 2:
The simulated top-down view frame acts as an intermediary that receives the perspective-distorted captured frame and transforms it into a form suitable for affine operations. This intermediary representation serves as a bridge between the perspective view and the parallelism-preserving affine coordinate system, enabling both perspective handling and parallelism preservation in sequence.
Data Source
AI summary
A method of plane tracking comprising: capturing by a camera a reference frame of a given plane from a first angle; capturing by the camera a destination frame of the given plane from a second angle different than the first angle; defining coordinates of matching points in the reference frame and the destination frame; calculating, using the first and second angles, first and second respective rotation transformations to a simulated plane parallel to the given plane; applying an affine transformation between the reference frame coordinate on the simulated plane and the destination frame coordinate on the simulated plane; and applying a projective transformation on the simulated plane destination frame coordinate to calculate the destination frame coordinate.