Abstract. The wavelet transform acts to segregate objects in function of their size. We apply this method on images of galaxies to decompose them into coefficients representing only objects of the same size. The total fluxes of the wavelet coefficients describe the cumulative power spectrum of spatial frequencies. Based on this spectrum, we propose a new parameter to quantify the galaxy texture. As expected, it remains small and quite invariant for early-type galaxies, while it covers a large range and takes larger values for late-type galaxies. Combined with a second parameter, our determination of the texture is able to successfully separate galaxy types. By thresholding the wavelet coefficients, we detect luminous lumps. In irregular galaxies, their radial distribution seems to show a double peak. This could be the trace of a privileged radial distance of strong star formation regions.Keywords. galaxies: fundamental parameters (morphology, classification), galaxies: structure, techniques: image processing, methods: data analysis
The wavelet transformThe wavelet transform projects an image onto a basis of finite support functions, whose spatial scales vary. Wavelets are families of functions that integrate to zero and are produced by scaling and translating a single function, called the mother wavelet.As the wavelet's support is finite in space, it is not sufficient to project the image onto a unique function. We must create a set of translating functions by frequency. Consequently, instead of obtaining a scalar as coefficient, we get an image; and this for each spatial frequency. There would be many redundancies if we would compute the coefficient for all spatial units. To avoid that, the projection is performed only onto wavelets whose spatial frequencies l, expressed in pixels, are powers of 2: l = 2 s , where s = 1, 2, 3, ..., n determines the scale.Thus, the wavelet transform yields a set of images, one per scale: the wavelet coefficients. These are composed of objects with characteristic sizes, without losing their locations, and are therefore representations of the structure or texture of the image. The sum of all coefficients recovers the original image.In our case, the mother wavelet is a B-spline function.