Our novel reversible image compression method employs multiscale segmentation within a computationally efficient optimization framework to obtain consistently good performance over a wide variety of images. We present new edge models that deal effectively with two issues that make such models normally unsuitable for compression applications: local applicability and large number of parameters needed for representation. Segmentation information is provided by a recent transform (1993), which we found to possess qualities making it especially suitable for compression. The final residual image is obtained using autocorrelation-based 2-D linear prediction. Different implementations providing lossless compression are presented along with results over a number of common test images. Results show that the proposed approach can be used to yield robust lossless compression, while providing consistently and significantly better results than the best possible JPEG lossless coder.

Results show a consistent 15-20% improvement over the best possible JPEG lossless standard (see the table below). The results are invariant to the amount of detail and noise in the image. It is also found that the typical probability distribution of the residual image values is not Laplacian which do not use explicit edge modelling. It's more Gaussian in shape, thus suggesting that the residual is mostly random noise. In conclusion, we have proposed a theoretically sound lossless compression method, which makes no crude approximations to the structure in the image. We have also proposed ways to represent edge models, which makes coding them compression wise a variable proposition.

The following tables are the results applying the various implementations. All results are in bits per pixel. In (a)-(c), interior (of a region) residual entropy and edge residual entropy are provided in addition to total entropy. Total entropy in all cases includes the overhead storage space.