Abstract
We extend the wavelet transform to handle multidimensional signals that are smooth save for singularities along lower-dimensional manifolds. We first generalize the complex wavelet transform to higher dimensions using a multidimensional Hilbert transform. Then, using the resulting hypercomplex wavelet transform (HWT) as a building block, we construct new classes of nearly shift-invariant wavelet frames that are oriented along lower-dimensional subspaces. The HWT can be computed efficiently using a 1-D dual-tree complex wavelet transform along each signal axis. We demonstrate how the HWT can be used for fast line detection in 3-D.
| Original language | English (US) |
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| Title of host publication | ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings |
| Volume | 3 |
| State | Published - 2004 |
| Event | Proceedings - IEEE International Conference on Acoustics, Speech, and Signal Processing - Montreal, Que, Canada Duration: May 17 2004 → May 21 2004 |
Other
| Other | Proceedings - IEEE International Conference on Acoustics, Speech, and Signal Processing |
|---|---|
| Country/Territory | Canada |
| City | Montreal, Que |
| Period | 5/17/04 → 5/21/04 |
ASJC Scopus subject areas
- Electrical and Electronic Engineering
- Signal Processing
- Acoustics and Ultrasonics