Image analysis using space-filling curves and 1D wavelet bases

摘要

Images are transformed into signals using a Peano-Hilbert space-filling curve: this continuous mapping captures local informations when Hilbert's curve is wandering inside the image. Then the obtained signal is analysed using 1 D (one-dimensional) wavelet orthogonal bases. The spaces of details of smaller and smaller scales are considered. They are built from a scaling function. An image can be computed by selecting wavelet coefficients corresponding to one or several scales and using the inverse Peano-Hilbert procedure. Due to the good localization of wavelet analysis local and global patterns can be detected and global ones can be reinforced. So the edge detection of global edges is prepared and easier with mathematical morphology.