Geometrical Image Representation for Curve Singularity Compression
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Solution Overview
Problem
Current image compression techniques using first generation linear representations are suboptimal for two-dimensional images with singularities along curves, as they result in excessive coefficients and fail to achieve near-optimal approximation rates, while second generation representations are not effectively adapted for digital images defined on discrete grids.
Innovation Solution
A geometrical image representation is introduced, utilizing a computed image-adaptive geometrical flow field to characterize the inherent singularity structure of images, allowing for a compact representation of image pixels and reducing the number of parameters required, which is applicable in various image processing applications such as compression and denoising.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If first generation linear representations (e.g., 2-D wavelet transforms) are used for image compression, then the representation is computationally simple and can be implemented efficiently, but the approximation rate is suboptimal for images with singularities along curves, resulting in excessive coefficients
Solution Approach 1:
The patent segments the image representation by separating smooth regions from singularities along curves. It uses curvelet transforms to specifically target and represent curve singularities, while other coefficients represent smooth regions. This segmentation allows optimal representation of different image features with appropriate basis functions for each type.
Solution Approach 2:
The patent transitions from first generation 2-D wavelet transforms to second generation representations that incorporate curvelet transforms. This dimensional change in the transform domain allows capturing singularities along curves by introducing directional sensitivity at multiple scales, achieving near-optimal approximation rates for curve singularities while maintaining computational feasibility.
2Manufacturing precision
If second generation representations (e.g., curvelet transforms) are used to improve approximation rate for curve singularities, then the representation becomes more accurate, but the computational complexity increases and adaptation to discrete digital images is challenging
Solution Approach 1:
The patent applies local quality by using different transform representations for different regions of the image. Curvelet transforms are applied specifically where curve singularities are detected, while standard transforms suffice for smooth regions. This localized application of complex transforms reduces overall computational complexity while maintaining high approximation accuracy where needed.
Solution Approach 2:
The patent performs preliminary detection of singularity structures and curve orientations before applying the full curvelet transform. By pre-identifying regions with curve singularities and their dominant orientations, the system can selectively apply computationally intensive transforms only where necessary, reducing overall computational complexity while achieving near-optimal approximation rates.
Data Source
AI summary
A method and apparatus is disclosed herein for geometrical image representation and/or compression. In one embodiment, the method comprises creating a representation for image data that includes determining a geometric flow for image data and performing an image processing operation on data in the representation using the geometric flow.