An Efficient Re-indexing Algorithm for Colour-Mapped Images

The efficiency of lossless compression algorithms for fixed-palette images (indexed images) may change if a different indexing scheme is adopted. Many lossless compression algorithms adopt a differential-predictive approach. Hence, if the spatial distribution of the indexes over the image is smooth, greater compression ratios may be obtained. Because of this, finding an indexing scheme that realizes such a smooth distribution is a relevant issue. Obtaining an optimal re-indexing scheme is suspected to be a hard problem and only approximate solutions have been provided in literature. In this paper, we restate the re-indexing problem as a graph optimization problem: an optimal re-indexing corresponds to the heaviest Hamiltonian path in a weighted graph. It follows that any algorithm which finds a good approximate solution to this graph-theoretical problem also provides a good re-indexing. We propose a simple and easy-to-implement approximation algorithm to find such a path. The proposed technique compares favorably with most of the algorithms proposed in literature, both in terms of computational complexity and of compression ratio.