Toroidal Chrominance Histogram for Real-Time White Balancing
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Solution Overview
Problem
Current white-balancing algorithms for images are computationally intensive and unable to operate in real-time, especially when determining illumination chrominance, due to the need for large histograms and filters, which limits their application in digital cameras and video streams.
Innovation Solution
The method involves constructing a toroidal chrominance histogram, which wraps around the chrominance space, reducing the size of the histogram while maintaining resolution, and using convolution in the frequency domain with learned filters to determine illumination chrominance efficiently, allowing for real-time processing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If large histograms and filters are used to determine illumination chrominance with high accuracy, then measurement precision is improved, but computational complexity increases making real-time processing impossible
Solution Approach 1:
The chrominance space is segmented into discrete bins to create a histogram representation, dividing the continuous color space into manageable segments that can be processed efficiently while maintaining accuracy in illumination chrominance determination
Solution Approach 2:
The problem is transformed from direct chrominance space analysis to frequency domain analysis using Fast Fourier Transform, adding a temporal/frequency dimension to the processing. This allows convolution operations to be performed more efficiently, reducing computational complexity while maintaining measurement precision
2Measurement precision
If large histograms are used to achieve desired chroma resolution, then measurement precision is improved, but processing time increases preventing real-time application
Solution Approach 1:
The chrominance histogram is pre-computed from the input image data before the actual illumination chrominance determination. This preliminary organization of color information into histogram bins allows the subsequent Fourier transform and convolution operations to proceed quickly, enabling real-time processing while maintaining high chroma resolution
Solution Approach 2:
The mechanical process of manually analyzing large histograms is replaced with automated Fast Fourier Transform algorithms. This substitution of computational mechanics dramatically reduces processing time from what would be required for direct histogram analysis to near-real-time performance, while preserving the ability to achieve high chroma resolution
3Measurement precision
If convolution of large filters with large histograms is performed, then measurement precision is improved, but computational load increases making the process too intensive for digital cameras
Solution Approach 1:
The problem parameters are transformed by applying Fast Fourier Transform to both the histogram and filter data, converting spatial domain convolution into frequency domain multiplication. This parameter change in the mathematical domain reduces the computational complexity from O(N*M) to O(N log N), making the process feasible for digital camera implementations while maintaining measurement precision
Data Source
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AI summary
Methods for white-balancing images are provided. These methods include determining, for an input image, a chrominance histogram for the pixels of the input image. The determined histogram is a toroidal chrominance histogram, with an underlying, toroidal chrominance space that corresponds to a wrapped version, of a standard flat chrominance space. The toroidal chrominance histogram is- then convolved with a fitter to generate a two- -dimensional heat map that is then used to determine art estimated chrominance of i|lummaiioB present id the input image; This can include fitting a bivariate von Mises distribution, or some other circular and/or toroidal, probability distribution, to the determined two-dimensional heat map. These methods for estimating illumination chrominance values for input images have reduced computational costs and increased speed relative to other methods for determining image illuminant chrominance values,