An image watermarking scheme using new wavelet filter banks
ASID'09 Proceedings of the 3rd international conference on Anti-Counterfeiting, security, and identification in communication
Multiresolution monogenic signal analysis using the Riesz-Laplace wavelet transform
IEEE Transactions on Image Processing
Wavelet steerability and the higher-order Riesz transform
IEEE Transactions on Image Processing
Steerable wavelet frames based on the Riesz transform
IEEE Transactions on Image Processing
Higher-order Riesz transforms and steerable wavelet frames
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
A recursive scheme for computing autocorrelation functions of decimated complex wavelet subbands
IEEE Transactions on Signal Processing
A blind watermarking scheme using new nontensor product wavelet filter banks
IEEE Transactions on Image Processing
Analytical footprints: compact representation of elementary singularities in wavelet bases
IEEE Transactions on Signal Processing
| Hi-index | 0.02 |
Our aim in this paper is to tighten the link between wavelets, some classical image-processing operators, and David Marr's theory of early vision. The cornerstone of our approach is a new complex wavelet basis that behaves like a smoothed version of the Gradient-Laplace operator. Starting from first principles, we show that a single-generator wavelet can be defined analytically and that it yields a semi-orthogonal complex basis of L 2(R2), irrespective of the dilation matrix used. We also provide an efficient FFT-based filterbank implementation. We then propose a slightly redundant version of the transform that is nearly translation-invariant and that is optimized for better steerability (Gaussian-like smoothing kernel). We call it the Marr-like wavelet pyramid because it essentially replicates the processing steps in Marr's theory of early vision. We use it to derive a primal wavelet sketch which is a compact description of the image by a multiscale, subsampled edge map. Finally, we provide an efficient iterative algorithm for the reconstruction of an image from its primal wavelet sketch.