Modified Hilbert Curve for Rectangles and Cuboids and Its Application in Entropy Coding for Image and Video...

Area of Science:

• * Digital signal processing
• * Data compression algorithms
• * Computational geometry

Background:

• * Previous work combined Hilbert scan and symbol grouping for efficient run-length entropy coding.
• * Existing 2-D Hilbert curves are limited to square dimensions (2^n x 2^n), posing challenges for arbitrary rectangular subbands in image compression.
• * Extending these methods to 3-D for video compression requires adaptable Hilbert curve constructions.

Purpose of the Study:

• * To detail the construction of modified 2-D Hilbert curves for arbitrary rectangular sizes.
• * To extend the modified Hilbert curve construction to 3-D cuboids.
• * To apply these modified curves in a novel 3-D video compression algorithm using run-length entropy coding.

Main Methods:

• * Development of a modified 2-D Hilbert curve algorithm adaptable to rectangular dimensions.
• * Extension of the modified Hilbert curve construction from 2-D rectangles to 3-D cuboids.
• * Integration of the modified 2-D and 3-D Hilbert curves into run-length-based entropy coding for compression algorithms.

Main Results:

• * Successful construction and demonstration of modified 2-D Hilbert curves for arbitrary rectangular inputs.
• * Extension of the modified Hilbert curve concept to 3-D cuboids.
• * Implementation of a novel 3-D video compression algorithm utilizing the modified 3-D Hilbert curves and run-length entropy coding.

Conclusions:

• * The modified Hilbert curves effectively address the limitations of fixed-size square definitions for practical image and video data.
• * The developed 2-D and 3-D modified Hilbert curves offer a flexible foundation for advanced entropy coding techniques.
• * These modified Hilbert curves have potential applications in future data compression and other unknown areas.