Gram Matrix Image Encoding via Singular Value Decomposition
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Solution Overview
Problem
Existing image encoding methods either lose context information due to quantization distortion or fail to reduce the amount of information effectively, as they require encoding basis vectors that are similar in size to the image pixels, and methods like PCA struggle to generalize across images with different features.
Innovation Solution
An image encoding method that generates and encodes a gram matrix representing image features through feature map generation, gram matrix calculation, singular value decomposition, and encoding of representative coefficients and vectors, allowing for reduced code amounts while maintaining image context.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If DCT/DST transform and quantization is used for image encoding, then coding efficiency is improved, but image quality deteriorates due to loss of context information
Solution Approach 1:
The patent changes the parameter being encoded from traditional DCT/DST coefficients to gram matrix elements derived from feature maps. This parameter transformation allows preserving contextual relationships while enabling more efficient compression through the specific structure and properties of gram matrices.
Solution Approach 2:
The patent introduces feature maps as an intermediary between the original image and the encoded representation. These feature maps capture contextual information, and their gram matrices serve as a compressed intermediary representation that preserves essential context while reducing data volume.
2Loss of information
If PCA is used to maintain image context, then context information is preserved, but the amount of information is not reduced because basis vectors are similar in size to image pixels
Solution Approach 1:
The patent extracts only the essential contextual information by computing gram matrices from feature maps and then performing eigenvalue decomposition to retain only the top k eigenvectors with largest eigenvalues. This extraction process separates the essential context-preserving components from the redundant information.
Solution Approach 2:
The patent transforms the representation from pixel-space basis vectors (which are as large as the image) to gram matrix eigenvectors (which are much smaller). This parameter change in the mathematical domain enables dimensionality reduction while preserving contextual relationships.
3Quantity of substance
If block-based transform encoding is used, then compression ratio is increased, but block distortion occurs at block boundaries affecting image quality
Solution Approach 1:
The patent applies gram matrix encoding universally across the entire image rather than dividing it into blocks. This unified approach eliminates block boundaries and associated distortion while maintaining compression efficiency through the global contextual information captured in the gram matrices.
Data Source
AI summary
An image encoding method that generates and encodes a gram matrix representing an image feature when encoding an image to be encoded includes a feature map generation step of generating a plurality of feature maps from the image to be encoded; a gram matrix generation step of generating a gram matrix through calculations between/among the feature maps; a representative vector determination step of generating a representative vector and a representative coefficient value by singular value decomposition of the gram matrix; and a vector encoding step of encoding the representative coefficient value and the representative vector.