Computer Vision Foundations · free preview
Gabor Filters
A complex exponential windowed by a Gaussian makes an oriented band-pass filter whose transform is a Gaussian shifted off the origin, the joint localization optimum and a model of cortical simple cells.
1. A wave inside a window
A wave inside a window
2. The spectrum is a Gaussian that moved house
The spectrum is a Gaussian that moved house
3. Sigma trades space for frequency
Sigma trades space for frequency
4. The cortex got there first
The cortex got there first
5. Where the spectrum lands
A Gabor filter is built from a Gaussian times a complex exponential at frequency (u0, v0). Where does its Fourier transform put its energy?
6. Choosing sigma for a task
A texture inspection system must detect small defects that break a fine stripe pattern, and the defects span only a few pixels. What sigma should its Gabor filters use?
7. Frequency spread under doubling
A Gabor's spatial sigma is doubled while its carrier frequency is unchanged. Write the factor by which its frequency spread changes, as a number.
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