I'm doing a research on Gabor filter, but when I Googled it, I had very long and complicated articles. Can anyone help me to find a simple explanation about it, or recommend a website or article to read? I want to understand this filter in order to use it in Matlab.
Gabor filters are orientation-sensitive filters, used for texture analysis.
The typically travel in packs, one for each direction. A gabor filter set with a given direction gives a strong response for locations of the target images that have structures in this given direction. For instance, if your target image is made of a periodic grating in a diagonal direction, a gabor filter set will give you a strong response only if its direction matches the one of the grating.
I know it is used a lot in character recognition and fingerprint enhancement. I (try to) use it in bio-medical imaging to characterizes the main orientation in fibril structures.
Here is a very good tutorial by Javier Movellan, pdf
And if you can read french, here is pdf on the creation of filter banks by Adrien Marion
A Gabor filter is some parametrization of the idea of edges. This combines two somewhat contradictory ideas: an abrupt transition AND some fuzzy idea of where it is localized.
It is mathematically a clever idea as it translates well in the Fourier domain: the Fourier transform of a Gabor is a Gaussian in Fourier space, and a Gaussian blob is the most neutral guess of something blurry you can make (think of throwing darts and looking at the patterns of hits).
As a consequence, when you use a Gabor, there is no 'right' formula: it all depends on what you want to detect/filter. In visual neuroscience, a popular choice is to chose a Gabor that corresponds in Fourier space to a blob on the logarithm of frequencies (as from the Weber law, we are sensitive to relative differences of frequencies). These are log-Gabor filters.
To understand Gabor filters, check first what filter parameterization would be best for your particular application.
It is an edge detector. It just applies the Gabor Transform. The Gabor filter is basically a Gaussian (with variances sx and sy along x and y-axes respectively) modulated by a complex sinusoid (with centre frequencies U and V along x and y-axes respectively). See an example here.
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