Log-Polar Image Encoding with Radial-Angular Correction
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Solution Overview
Problem
Existing image encoding technologies using standard log-polar coordinate systems result in sawtooth patterns for straight image features, leading to inefficient processing and perceivable loss in image quality, particularly in immersive XR environments.
Innovation Solution
Employing a modified log-polar coordinate system that transforms input images into a log-polar format with radial distance as a logarithm of the distance from the origin and angular distance as the arctangent of the slope plus a function of the radial distance, allowing for efficient encoding and decoding without sawtooth patterns.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of substance
If a standard log-polar coordinate system is used for image encoding, then image compression is achieved, but straight image features appear in sawtooth patterns causing processing inefficiency and quality loss
Solution Approach 1:
The patent modifies the standard log-polar coordinate transformation by introducing a correction term to the angular coordinate. Specifically, the angular coordinate θ is adjusted by adding a function of the radial distance ρ (θ' = θ + f(ρ)), which compensates for the sawtooth distortion. This parameter modification eliminates the harmful sawtooth pattern while preserving the compression benefits of the log-polar system.
2Loss of substance
If a standard log-polar coordinate system is used for image encoding, then image compression is achieved, but considerable processing resources are required due to sawtooth patterns
Solution Approach 1:
By modifying the angular coordinate parameter in the log-polar transformation to include a radial distance-dependent correction term, the patent eliminates the sawtooth pattern that causes high-frequency artifacts. This reduces the computational burden during encoding and decoding operations, improving processing efficiency while maintaining compression performance.
3Loss of substance
If a standard log-polar coordinate system is used for image encoding, then image compression is achieved, but user immersion is reduced due to perceivable image quality loss
Solution Approach 1:
The corrected log-polar coordinate system modifies the angular coordinate by adding a function of radial distance, which eliminates the sawtooth pattern that creates visible artifacts in decoded images. This improvement in image quality directly enhances user immersion in XR environments while preserving the compression advantages of the log-polar transformation.
Data Source
AI summary
An encoder for encoding images includes at least one processor configured transform a given input pixel of an input image having (x, y) coordinates in a Cartesian coordinate system into a given transformed pixel of a transformed image having (ρ, θ) coordinates in a log-polar coordinate system, using a log-polar transformation in which a radial distance (ρ) of the given transformed pixel is a logarithm of a distance of the given input pixel from an origin in the Cartesian coordinate system, and an angular distance (θ) of the given transformed pixel is a sum of an arctangent of a slope of a line connecting the given input pixel to the origin and a function of the radial distance, encode the transformed image, by employing a compression algorithm, into an encoded image, and send the encoded image to a display apparatus for subsequent decoding thereat.