A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Spherical wavelets: efficiently representing functions on the sphere
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Multiresolution analysis for surfaces of arbitrary topological type
ACM Transactions on Graphics (TOG)
The lifting scheme: a construction of second generation wavelets
SIAM Journal on Mathematical Analysis
Optimal triangular Haar bases for spherical data
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Distinctive Image Features from Scale-Invariant Keypoints
International Journal of Computer Vision
Wavelet families of increasing order in arbitrary dimensions
IEEE Transactions on Image Processing
Hi-index | 0.00 |
This paper introduces triangular wavelets, which are two-dimensional nonseparable biorthogonal wavelets defined on the regular triangular lattice. The construction that we propose is a simple nonseparable extension of one-dimensional interpolating wavelets followed by a straightforward generalization. The resulting three oriented high-pass filters are symmetrically arranged on the lattice, while low-pass filters have hexagonal symmetry, thereby allowing an isotropic image processing in the sense that three detail components are distributed uniformly. Applying the triangular filter to images, we explore applications that truly benefit from the triangular wavelets in comparison with the conventional tensor product transforms.