Image coding from the wavelet transform extrema

Summary form only given, as follows. A multiresolution edge detection can be performed with a wavelet transform. Indeed, for some particular wavelets, the wavelet transform of an image provides the local gradient of the image at different resolutions. A multiresolution edge detection is therefore equivalent to a detection of local extrema in the image wavelet transform (local extrema of the image gradient). It is shown that one can build a complete image representation by recording the value and the position of these local extrema on a dyadic sequence of resolutions: 1/2, 1/4, 1/8 etc. An iterative procedure that reconstructs the image from these local extrema is described. The algorithm is based on the reproducing kernal of a wavelet transform; it is numerically stable. This reconstruction shows that an image can be coded from the edges which appear on a dyadic sequence of resolutions, without losing any information. Such an adaptive coding is useful for pattern recognition but also for data compression. Indeed, the edges of an image can be efficiently coded into chains with predictive techniques.