Image Upsampling via Sparse Derivative Priors
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Solution Overview
Problem
Existing image upsampling methods often produce unnatural-looking results with blurred edges due to the under-constrained nature of the problem, and current solutions are either simple but produce blocky images or complex and artifact-prone.
Innovation Solution
A system and method that evaluates potential upsampling solutions using an objective function dependent on sparse derivative priors, particularly on first and second derivatives, to identify a higher-resolution image that is both sharp and smooth, employing iteratively re-weighted least squares and configurable fidelity terms for optimal results.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If interpolation methods are used for upsampling, then the image resolution is increased, but the edges become blurred
Solution Approach 1:
The patent changes the mathematical parameters of the upsampling process by using higher-order derivatives (second, third, and fourth derivatives) instead of standard interpolation. This allows the system to model edge behavior more accurately and produce sharp edges while maintaining increased resolution.
Solution Approach 2:
The patent performs preliminary computation of multiple derivative orders before the actual upsampling process. By pre-calculating first, second, third, and fourth derivatives of the input image, the system prepares edge information in advance that guides the upsampling process to preserve edge sharpness rather than blurring them.
2Ease of manufacture
If nearest neighbor duplication is used for upsampling, then the implementation is simple, but the output image appears blocky
Solution Approach 1:
The patent transforms the simple duplication approach into a sophisticated derivative-based method. By changing from zero-order (pixel value duplication) to higher-order derivative operations, the system achieves smooth transitions and natural-looking images while maintaining computational efficiency through optimized algorithms.
3Manufacturing precision
If complex data-driven approaches are used for upsampling, then new detail can be added, but visible artifacts appear when matches are imprecise
Solution Approach 1:
The patent replaces complex data-driven matching mechanisms with a continuous mathematical field approach using derivatives. Instead of discrete patch matching that creates artifacts when imprecise, the derivative-based method operates continuously across the image, producing natural transitions without visible artifacts while still enhancing detail.
Data Source
AI summary
Systems and methods for upsampling input images may evaluate potential upsampling solutions with respect to an objective function that is dependent on a sparse derivative prior on second derivative(s) of the potential upsampling solutions to identify an acceptable higher-resolution output image. The objective function may also be dependent on fidelity term(s) and/or sparse derivative prior(s) on first derivative(s) of potential upsampling solutions. The methods may include applying the iteratively re-weighted least squares procedure in minimizing the objective function and generating improved candidate solutions from an initial solution. The identified solution may be stored as a higher-resolution version of the input image in memory, and made available to subsequent operations in an image editing application or other graphics application. The methods may produce sharp results that are also smooth along edges. The methods may be implemented as program instructions stored on computer-readable storage media, executable by a CPU and/or GPU.