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4 Conclusion

The MathMorph method reproduces the image pixels up to a given threshold. The quality of the image depends on the estimate of the noise standard deviation before the application of MathMorph transformations. The method has good performance on uncrowded astronomical fields. When a crowded field or an extended object is present in the image, the compression rate becomes much lower than the one obtained with the pyramidal median transform and, with traditional estimation of noise standard deviation, the faint extensions of objects and faint objects are lost in the compression.

The PMT method provides impressive compression rates, coupled with acceptable visual quality. This is due to the progressive noise suppression at successive scales. Nevertheless, on some crowded regions the PMT cannot compress more than 50:1, because a lot of objects' information is to be coded, in a small amount of image scales.

It is robust and can allow for certain image imperfections. On a Sun Ultra-Enterprise (250 MHz, 1 processor), compressing a $1024 \times 1024$ image takes about 8 seconds (CPU time), with subsequent very fast decompression.

The decomposition of the image into a set of resolution scales, and furthermore the fact they are in a pyramidal data structure, can be used for effective transmission of image data (Percival & White 1996). Current work on Web progressive image transmission capability has used bit-plane decomposition (Lalich-Petrich et al. 1995). Using resolution-based and pyramidal transfer and display with Web-based information transfer is a further step in this direction. Java code implementing this functionality for PMT compressed images, is also available.

In the scope of the ALADIN project (Genova et al. 1999), we finally implemented the distribution of JPEG compressed images as a first step, due to the portability of JPEG among the different Web browsers. We are preparing to distribute PMT compressed images using the progressive resolution property in the near future.

Acknowledgements

We wish to thank J. Guibert, MAMA, for providing the test images, D. Dubaj and A. Schmidtbuhl for extensive tests on images, L. Huang and A. Bijaoui for helping in the tuning of the MathMorph approach, O. Bienaymé for providing the calibrated object catalogue, and J. Bartlett for helpful discussions. S. Mei acknowledges support from CNR, Italy. We are grateful to the referee, M. Albrecht, for his comments.


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