I have read materials on gabor filters recently and get confused about this.
A Gabor filter g(x,y,sigma,theta,omega) is the product of a gaussian window and a sinusoid function. When apply this filter to an image f(x,y), they do convolution operation g * f and yeilds an output image. With selected parameters the output can be an edge image of f(x,y). This is what I learned.
But it confuses me when I look at the convolution equation from another perspective. it can be interpreted in this way: the original image f is first multiplied by the gaussian window, which accomplishes low pass filter, and then the preliminary result does the fourier transform. This is almost contray to what we want to do in edge detection,which is closely connected with high pass filter.
Can anyone tell me where the problem lies? I would appreciate it!
Hi Jenkins Yu,
Gabor filter's impulse response is the multiplication of a harmonic function with a Gaussian function.
As per convolution theorem, the convolution of Fourier Transformation (FT) of harmonic function and FT of Gaussian function is nothing but FT of a Gabor filter's impulse response [ FT(Gabor) = FT(Harmonic) FT(Gaussian) ].
Gabor filters with different frequencies and with orientations in different directions (similar to those of the human visual system) have been used to localize and extract edges from images.since edges are rich in high frequency components, whereas other regions of an image are relatively smooth in nature.
Hope it would be useful.
Regards,
Sumaiya.
Thanks Sumaiya Shahul! But I still wonder what if I look at this in space domain? Like I described in the question:
the original image f is first multiplied by the gaussian window, which accomplishes low pass filter, and then the preliminary result does the fourier transform.
It still confuses me.
Dear Jenkins Yu,
First of all, the original image f is not first multiplied by the Gaussian window. But by the resultant multiplication of a harmonic function with a Gaussian function.
Definitely we would get edges by applying Gabor filter(multiplication of a harmonic function with a Gaussian function), since Gabor filter has impulses according to the corresponding harmonic function. While applying Gabor filter to an image, it would produce high value if an image has edges (high frequency). For other non edge regions, it would produce low value, indicates the multiplication of impulses with smooth region.
Regards,
Sumaiya.
Gabor filter enhances the textural evidence of the object, and in further steps, edges can be detected using any established edge detector.
Please read this paper
https://arxiv.org/ftp/arxiv/papers/1405/1405.0921.pdf
hello dear
this is Gabor filter use this code
http://www.mathworks.com/matlabcentral/fileexchange/23253-gabor-filter
Since they uses several scales, in teory allow to detect smal variations
Helllo Jenkins yu . Please refer to this papers for more details: Preprint A Simplified Approximation of Gabor Function like Simple Cel...
Conference Paper Efficient Approximation of Gaussian Function for Signal and ...
We can use many filters such as Gaussian function in the spatial domain
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