I want to know the difference between the 2D continuous and discrete gabor filter when it comes to matlab implementation. I found many files related to 2D gabor filter on mathworks file exchange but I am unable to find any file related to 2D continuous gabor wavelet. I want to use continuous gabor filter to enhance blood vessels in retinal images.
Unlike the discrete wavelet transform, the continuous wavelet transform CWT can operate at every scale, from that of the original signal up to some maximum scale that you determine by trading off your need for detailed analysis with available computational horsepower.
The CWT is also continuous in terms of shifting: during computation, the analyzing wavelet is shifted smoothly over the full domain of the analyzed function.
That being said, the numerical implementation in Matlab can only be discrete, but you can refine the way it is done to enhance analysis where you need it, and it will be closer to continuous.
There are answers to requests for gabor wavelet function in Matlab:
http://www.mathworks.in/matlabcentral/fileexchange/13776-improved-2d-gabor-filter/content/gaborfilter.m
http://www.mathworks.com/matlabcentral/fileexchange/28751-gabor-filtering-on-an-image/content/gab/gabor_fn.m
first of all, you can't execute continuous functions in computer systems, such as Matlab.
search "gabor wavelet" instead of " 2D continuous gabor wavelet".
well thanks @siana & @sina but I still wonder what's the difference between the two I am trying to implement the following two articles their mathematical interpretation is some what different than the available definition of CWT Gabor available. The articles are attached.
Article Using the 2-D Morlet wavelet with supervised classification ...
Second article is this
Article Multilayered thresholding-based blood vessel segmentation fo...
SIMPLEGABOR is a good toolbox for Gabor filtering in Matlab:
http://www.it.lut.fi/project/simplegabor/
Pointwise multiplication of functions of frequencies corresponds in the Fourier dual time-domain to the operation of convolution (or of Cauchy product if the time-scale is discrete.) The process of modifying a signal with a fixed convolution is called a linear filter in signal processing. The corresponding Fourier dual frequency function is then referred to as “frequency response” or the “frequency response function.”
More generally, in the continuous case, since convolution tends to improve smoothness of functions, physicists call it “smearing.”
Calculating the Fourier coefficients is “analysis,” and adding up the pure frequencies (i.e., summing the Fourier series) is called "synthesis". But this view carries over more generally to engineering where there are more operations involved on the two sides, e.g., breaking up a signal into its frequency bands, transforming further, and then adding up the “banded” functions in the end. If the signal out is the same as the signal in, we say that the analysis/synthesis yields perfect reconstruction.
After reading these abstracts, it seems that would be best to not employ continuous wavelet analysis (with any wavelet… by the way, which wavelet you choose may also changes the way they enhance the classification of what is "important") because it would be too cumbersome. I would combine the wavelet analysis with a clustering or optimization method if the pattern you want to recognize is known. This way the algorithm becomes adaptive to the newly discovered area and decides if it's worth pursuing a more in depth (higher resolution) analysis or not. The way the thresholding is set up is another freedom degree and that can be made adaptive too. Maybe there are people who have already made their own algorithms, but the best bet would be to program the ones you need, to suit your task.
I came to know that technically there's no difference between the 2D discrete and Continuous Gabor filter when it comes to MATLAB every thing is discrete
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