Hybrid Lossless Coder of Medical Images with Statistical Data Modelling
CAIP '01 Proceedings of the 9th International Conference on Computer Analysis of Images and Patterns
Lossless image compression using pixel reordering
ACSC '04 Proceedings of the 27th Australasian conference on Computer science - Volume 26
An N-Dimensional Pseudo-Hilbert Scan for Arbitrarily-Sized Hypercuboids
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
A generalized 3-D Hilbert scan using look-up tables
Journal of Visual Communication and Image Representation
Lossless asymmetric single instruction multiple data codec
Software—Practice & Experience
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Though most image coding techniques use a raster scan to order pixels prior to coding, Hilbert and other scans have been proposed as having better performance due to their superior locality preserving properties. However, a general understanding of the merits of various scans has been lacking. This paper develops an approach for quantitatively analyzing the effect of pixel scan order for context-based, predictive lossless image compression and uses it to compare raster, Hilbert, random and hierarchical scans. Specifically, for a quantized-Gaussian image model and a given scan order, it shows how the encoding rate can be estimated from the frequencies with which various pixel configurations are available as previously scanned contexts, and from the corresponding conditional differential entropies. Formulas are derived for such context frequencies and entropies. Assuming an isotropic image model and contexts consisting of previously scanned adjacent pixels, it is found that the raster scan is better than the Hilbert scan which is often used in compression applications due to its locality preserving properties. The hierarchical scan is better still, though it is based on nonadjacent contexts. The random scan is the worst of the four considered. Extensions and implications of the results to lossy coding are also discussed