Edge-avoiding wavelets and their applications

<jats:p> We propose a new family of second-generation wavelets constructed using a robust data-prediction lifting scheme. The support of these new wavelets is constructed based on the edge content of the image and avoids having pixels from both sides of an edge. Multi-resolution analysis, based on these new <jats:italic>edge-avoiding wavelets</jats:italic> , shows a better decorrelation of the data compared to common linear translation-invariant multi-resolution analyses. The reduced inter-scale correlation allows us to avoid halo artifacts in band-independent multi-scale processing without taking any special precautions. We thus achieve nonlinear data-dependent multi-scale edge-preserving image filtering and processing at computation times which are <jats:italic>linear</jats:italic> in the number of image pixels. The new wavelets encode, in their shape, the smoothness information of the image at every scale. We use this to derive a new edge-aware interpolation scheme that achieves results, previously computed by solving an inhomogeneous Laplace equation, through an <jats:italic>explicit</jats:italic> computation. We thus avoid the difficulties in solving large and poorly-conditioned systems of equations. </jats:p> <jats:p>We demonstrate the effectiveness of the new wavelet basis for various computational photography applications such as multi-scale dynamic-range compression, edge-preserving smoothing and detail enhancement, and image colorization.</jats:p>