top- hat transform for signal processing

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Annu Sheoran
Annu Sheoran on 26 Nov 2021
Commented: DGM on 26 Nov 2021
Hello, I want to know how to write matlab code for top-hat and bottom-hat (morphological operation) for signal processing??

Answers (2)

Image Analyst
Image Analyst on 26 Nov 2021
I know imtophat() and imbothat() should work for 1-D signals. They're in the Image Processing Toolbox. Observe:
v = randi(20, 1, 15)
v = 1×15
14 18 16 5 9 7 5 20 18 17 14 2 1 19 1
windowWidth = 3;
v2 = imtophat(v, true(1, windowWidth))
v2 = 1×15
0 4 2 0 4 2 0 3 1 0 0 0 0 18 0

DGM on 26 Nov 2021
Edited: DGM on 26 Nov 2021
The tophat and bottomhat operations are the difference of the source image and the opening/closing of said image with the selected strel. They represent the changes made -- i.e. the objects removed by opening or the holes filled by closing.
If you're trying to write your own, then:
For binary data, they should be equivalent to
outpict = inpict & ~imopen(inpict,se); % tophat
outpict = ~inpict & imclose(inpict,se); % bothat
For numeric data, they are
outpict = inpict - imopen(inpict,se); % tophat
outpict = imclose(inpict,se) - inpict; % bothat
The same should apply for 1D cases. Ultimately, opening and closing operations can be further reduced to a set of routines based on a simple moving-window maximum filter.
DGM on 26 Nov 2021
movmax could be used in the 1D case, but I intentionally was trying to speak generally. To that end, it's worth noting that movmax() is something that I still consider relatively new (though I guess it's in OP's version).
Yes, it's reasonable to assume the availability of included tools once IPT is being used, but I had to consider two things. I don't know if this is just another "how do I reinvent the wheel for my homework problem" question. Additionally, I didn't want to pseudocode something using generic function names like "open()" or "close()" knowing that someone would actually copy and paste them and run them blind.

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