Pyramid Collapse Color Interpolation for Undefined Pixels
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Solution Overview
Problem
Existing methods for completing incomplete images require significant computing resources and time to solve systems of linear equations, making them inefficient for quickly determining pixel information for undefined pixels.
Innovation Solution
The approach involves recursively downsampling and upsampling images to fill in undefined pixels by averaging adjacent defined pixel information, reducing computational requirements and achieving a seamless composition with fewer gaps.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of information
If a system of linear equations is used to mathematically derive unknown pixel information, then the completeness of the image is improved, but the computing resources required and time consumption increase significantly
Solution Approach 1:
The patent segments the image into a pyramid structure with multiple resolution levels. Instead of solving a single large system of linear equations for the entire image, the problem is divided into smaller sub-problems at each pyramid level, where only local undefined pixels need to be solved at each stage, significantly reducing computational complexity while maintaining image completeness
Solution Approach 2:
The patent transforms the 2D image problem into a multi-level hierarchical structure by adding the dimension of resolution levels. By working from coarse to fine levels in the pyramid, the method solves fewer equations at each level while collectively filling all undefined pixels, improving processing speed without sacrificing information completeness
2Measurement precision
If a system of linear equations is used to mathematically derive unknown pixel information, then the accuracy of pixel values is improved, but the computational resources required increase significantly
Solution Approach 1:
The patent divides the computational task into segmented stages across pyramid levels. At each level, only local undefined pixels are solved using small systems of equations, rather than solving one large global system. This segmentation maintains pixel value accuracy through iterative refinement while dramatically reducing total computational resource usage
Solution Approach 2:
The patent performs preliminary actions by first solving for undefined pixels at coarser pyramid levels before refining at finer levels. This preliminary computation establishes baseline pixel values that guide subsequent refinement steps, ensuring accuracy while reducing the overall computational burden compared to solving the complete system at full resolution
3Productivity
If recursive downsampling and upsampling is used to fill undefined pixels, then the processing speed is improved, but the complexity of the algorithm increases
Solution Approach 1:
The patent implements a nested pyramid structure where each level contains a downsampled version of the previous level. This nesting allows the algorithm to work systematically from coarse to fine levels, filling undefined pixels at each stage. The recursive nature of the nesting provides a clear framework that manages algorithmic complexity while enabling fast processing through hierarchical decomposition
4Reliability
If the original method is used to complete incomplete images, then the quality of the completed image is improved, but the time required to complete the image increases excessively
Solution Approach 1:
The patent performs preliminary computations at coarser pyramid levels before addressing the full-resolution image. By pre-computing pixel values at lower resolutions and using them to guide refinement at higher levels, the method ensures high-quality image completion while significantly reducing the time required compared to solving the complete system at full resolution from scratch
Data Source
AI summary
One exemplary embodiment involves receiving an image with a set of undefined pixels and a set of defined pixels and recursively modifying the image to generate a seamless composition comprising only defined pixels. Disclosed are embodiments for recursively modifying the image by recursively down sampling the image by a factor to generate a plurality of down sampled images until the down sampled image generated at each recursive down sampling lacks undefined pixels and then recursively up sampling each one of the down sampled images by the factor to generate an up sampled image from the respective down sampled image. Additionally, at each recursive up sampling instance, pasting the next recursively occurring down sampled image on the up sampled image to generate the next recursively occurring image for up sampling.