Multidimensional Gabor-Like Filters Derived from Gaussian Functions on Logarithmic Frequency Axes (2402.09419v1)
Abstract: A novel wavelet-like function is presented that makes it convenient to create filter banks given mainly two parameters that influence the focus area and the filter count. This is accomplished by computing the inverse Fourier transform of Gaussian functions on logarithmic frequency axes in the frequency domain. The resulting filters are similar to Gabor filters and represent oriented brief signal oscillations of different sizes. The wavelet-like function can be thought of as a generalized Log-Gabor filter that is multidimensional, always uses Gaussian functions on logarithmic frequency axes, and innately includes low-pass filters from Gaussian functions located at the frequency domain origin.
- David J. Field. Relations between the statistics of natural images and the response properties of cortical cells. J. Opt. Soc. Am. A, 4(12):2379–2394, Dec 1987. doi: 10.1364/JOSAA.4.002379. URL https://opg.optica.org/josaa/abstract.cfm?URI=josaa-4-12-2379.
- Self-invertible 2d log-gabor wavelets. International Journal of Computer Vision, 75:231–246, 2007. doi: 10.1007/s11263-006-0026-8. URL https://link.springer.com/article/10.1007/s11263-006-0026-8.
- Dennis Gabor. Theory of communication. Journal of the Institution of Electrical Engineers, 93, 1946.
- Yunlong Sheng. Wavelet transform. In Transforms and Applications Handbook, chapter 10. CRC press, third edition, 2010. doi: 10.1201/9781315218915.
- Clemens Valens. A really friendly guide to wavelets. 1999. URL http://iar.cs.unm.edu/~williams/cs530/arfgtw.pdf.
Sponsor
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.