Unified Radial Distortion and Motion Model for Image Tracking
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Solution Overview
Problem
Current motion models and alignment techniques fail to accurately track point regions in images with radial distortion, such as those from cameras with fish-eye lenses or medical endoscopes, due to the inability to account for radial distortion, leading to localization drifts and reduced tracking accuracy and repeatability.
Innovation Solution
The method extends perspective motion models and alignment techniques to include radial distortion models, using Inverse Compositional Alignment and the Schur Complement Method to efficiently estimate parameters and account for distortion, enabling accurate tracking and calibration of radial distortion and zoom variations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional motion models and alignment techniques are used for tracking in images with radial distortion, then the tracking process is computationally simple and fast, but the tracking accuracy and repeatability deteriorate due to localization drifts
Solution Approach 1:
The patent combines the radial distortion model with the perspective motion model into a unified warp model. The distortion model parameters (alpha, beta, gamma) are integrated with the motion model parameters (translation, rotation, scaling) to create a composite transformation model that simultaneously accounts for both radial distortion effects and camera motion, thereby improving tracking accuracy without requiring separate processing steps
Solution Approach 2:
The extended motion model serves multiple functions: it corrects radial distortion, models camera motion (translation, rotation, scaling), and enables tracking of point regions in distorted images. This multi-functional approach eliminates the need for separate distortion correction and motion tracking steps, resolving the contradiction between model complexity and tracking performance
2Reliability
If radial distortion correction is applied through image pre-processing, then the distortion effect is removed, but the computational cost increases due to interpolation and the reliability decreases due to artificially interpolated pixel intensities
Solution Approach 1:
The patent performs preliminary estimation of distortion parameters using a subset of tracked points, then applies these parameters to correct the warp model for all points. This preliminary action allows the system to establish accurate distortion compensation without requiring computationally expensive per-point optimization, thereby reducing overall computational cost while maintaining reliability
Solution Approach 2:
The patent introduces distortion parameter estimation as an intermediary step between raw image input and final tracking output. By estimating global distortion parameters (alpha, beta, gamma) from the motion of tracked points, the system creates an intermediate representation that enables accurate tracking without requiring direct interpolation of pixel intensities, thus avoiding the reliability issues of synthetic correction
3Measurement precision
If the warp model includes both local motion parameters and global distortion parameters, then the tracking accuracy improves, but the computational complexity and memory management become more difficult
Solution Approach 1:
The patent segments the parameter estimation process into two stages: first estimating global distortion parameters (alpha, beta, gamma) from the motion of tracked points, then estimating local motion parameters (translation, rotation, scaling) using the corrected distortion model. This segmentation reduces the computational complexity by breaking down the joint estimation problem into manageable sub-problems that can be solved sequentially
Solution Approach 2:
The patent changes the parameter representation by expressing the warp model in terms of distortion parameters (alpha, beta, gamma) that capture the radial distortion effect, combined with motion parameters. This parameterization allows the model to adapt to different distortion levels while maintaining a consistent mathematical framework, simplifying the estimation process and memory management compared to more complex general transformation models
Data Source
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AI summary
The present invention relates to a method for matching point regions in images with radial distortion that, given two frames acquired by a camera with radial distortion, estimates the global image distortion and the local transformations undergone by the image regions between frames, with the objective of accurately tracking an aligning these image regions in a sequence of frames, calibrating the radial distortion using only moving image points, or estimating the relative change in focal length in cameras with radial distortion and variable zoom using only moving image points, and that comprises the following steps: extracting local image features; tracking local features; and determining the radial distortion calibration based on a computational efficient procedure that uses the information for all local features being tracked.