Scalar Image Reconstruction via Surjective Vector Mapping
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Solution Overview
Problem
Existing image reconstruction methods in the gradient domain often introduce artefacts such as smoothed and smeared edges due to the inherent ill-posedness of reintegrating non-integrable gradient fields, particularly in applications like data fusion where multichannel images are converted to scalar images.
Innovation Solution
A method that avoids integration by using a surjective function class to map each vector image to a unique scalar value, allowing for the selection of a function that approximates the derivative field closest to the original, thereby reducing edge artefacts and smearing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If a naive Poisson solver or robust techniques are used to reintegrate the gradient field, then the reconstruction process can be completed, but serious image artefacts remain (edge smearing and bending in flat regions)
Solution Approach 1:
Instead of reintegrating the gradient field to recover the image (forward approach), the patent inverts the process by differentiating the input image to compute gradients, manipulating these gradients, and then using a modified Poisson equation to directly solve for the output image. This inversion avoids the ill-posed reintegration step that causes artefacts.
Solution Approach 2:
The patent modifies the Poisson equation by introducing a regularization term with parameter λ that balances gradient fidelity and solution smoothness. By adjusting this parameter, the method controls the trade-off between preserving edge details and avoiding artefacts, fundamentally changing the mathematical parameters of the reconstruction process.
2Manufacturing precision
If complex reintegration techniques are used to diminish artefacts, then image quality improves slightly, but the process becomes more complex and computationally expensive
Solution Approach 1:
The patent extracts and removes the problematic reintegration step from the traditional gradient domain pipeline. By eliminating this complex, artefact-prone step and replacing it with a direct Poisson-based formulation, the method achieves comparable or better quality with simpler, more efficient algorithms.
3Ease of operation
If traditional gradient field reintegration is used, then the process follows the standard three-step workflow, but the ill-posed nature of reintegrating non-integrable fields cannot be overcome
Solution Approach 1:
The patent performs preliminary computation of the gradient field from the input image before any manipulation occurs. By pre-computing gradients and storing them, the method avoids the need to reintegrate during the reconstruction phase, thereby eliminating the ill-posed reintegration problem while maintaining a clear, reliable workflow.
Data Source
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AI summary
A method and system for producing a scalar image from a derivative field and a vector image is disclosed. A function class c is selected, where all members of the class c are functions which map each vector of the vector image to a unique scalar value. A function f is selected from the class c which maps the vector image to a scalar image, the derivative of which is closest to the derivative field. The scalar image is generated from the vector image by using f to calculate each scalar value in the scalar image from a corresponding vector in the vector image.