Wavelet applied to Computer Vision in Astrophysics

摘要

Multiscale analyses can be provided by application of discrete wavelet transforms. For image processing purposes, we applied algorithms which imply a quasi isotropic vision. For a uniform noisy image, a wavelet coefficient W has a probability density function (PDF) p(W) which depends on the noise statistic. The PDF was determined for many statistical noises: Gauss, Poisson, Rayleigh, exponential. For CCD observations, the Anscombe transform was generalized to a mixed Gauss+Poisson noise. From the discrete wavelet transform a set of significant wavelet coefficients (SSWC) is obtained. Many applications have been derived like denoising and deconvolution. Our main application is the decomposition of the image into objects, i.e. the vision. At each scale an image labelling is performed in the SSWC. An interscale graph linking the fields of significant pixels is then obtained. The objects are identified using this graph. The wavelet coefficients of the tree related to a given object allow one to reconstruct its image by a classical inverse method. This vision model has been applied to astronomical images, improving the analysis of complex structures.