Optimizing depth-of-field based on a range map and a wavelet transform

The imaging properties of small cameras in mobile devices exclude restricted depth-of-field and range-dependent blur that may provide a sensation of depth. Algorithmic solutions to this problem usually fail because high- quality, dense range maps are hard to obtain, especially with a mobile device. However, methods like stereo, shape from focus stacks, and the use of ashlights may yield coarse and sparse range maps. A standard procedure is to regularize such range maps to make them dense and more accurate. In most cases, regularization leads to insuficient localization, and sharp edges in depth cannot be handled well. In a wavelet basis, an image is defined by its significant wavelet coeficients, only these need to be encoded. If we wish to perform range-dependent image processing, we only need to know the range for the significant wavelet coeficients. We therefore propose a method that determines a sparse range map only for significant wavelet coeficients, then weights the wavelet coeficients depending on the associate range information. The image reconstructed from the resulting wavelet representation exhibits space-variant, range-dependent blur. We present results based on images and range maps obtained with a consumer stereo camera and a stereo mobile phone.