| Re: not-quite meidan filter [message #72727] |
Fri, 01 October 2010 04:42 |
Jeremy Bailin
Messages: 618
Registered: April 2008
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Senior Member |
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On Sep 30, 3:38 pm, JJ <j...@cornell.edu> wrote:
> I would like to do something that is similar to, but not quite the
> same as, a median filter to a 2D array. Instead of choosing the
> median value in a box surrounding each pixel, I would like to chose
> the value in that box that occurs most frequently.
>
> For example, if I had
>
> 1 1 1 1 1
> 1 1 1 1 1
> 2 2 2 2 2
> 2 2 3 3 3
> 3 3 3 3 3
>
> The median would be 2, but I would want the value 1 (it occurs 10
> times, which is more than the 8 instances of the value 3 or the 7
> instances of the value 2).
>
> Can anyone think of a clever way to do this that would be fast in IDL
> (ie, no looping through the pixels)? I need it to work for box sizes
> up to around 21. Ties may be broken arbitrarily.
>
> Is there already a name for this concept?
>
> Thanks.
>
> -Jonathan
Any non-loop solution I've thought of is going to require a lot of
memory, since you're going to end up storing one slice for each
central pixel. For images of size no more than 21, that might be okay,
but it won't work much larger. I'd do something like this:
- create an array with each filter-box-over-an-individual-pixel as a
separate 2D slice in a 3D array
- use VALUE_LOCATE to map your values onto simple integers from 0 to
N-1
- increment the values in slice #i by i*N so that the values in each
slice are unique
- perform the histogram, for which entries i*N through (i+1)*N-1 are
the repeat counts for slice i
- reform the histogram into a 2D array, N by n_slices, and run
SORT_ND on it so that you know where the maximum histogram value for
each slice is
- subtract back out i*N from that value, reform back to the original
dimensions, and do the reverse mapping to go back to your values
-Jeremy.
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| Re: not-quite meidan filter [message #72733 is a reply to message #72727] |
Thu, 30 September 2010 14:22  |
David Fanning
Messages: 11724
Registered: August 2001
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Senior Member |
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JJ writes:
> I would like to do something that is similar to, but not quite the
> same as, a median filter to a 2D array. Instead of choosing the
> median value in a box surrounding each pixel, I would like to chose
> the value in that box that occurs most frequently.
>
> For example, if I had
>
> 1 1 1 1 1
> 1 1 1 1 1
> 2 2 2 2 2
> 2 2 3 3 3
> 3 3 3 3 3
>
> The median would be 2, but I would want the value 1 (it occurs 10
> times, which is more than the 8 instances of the value 3 or the 7
> instances of the value 2).
>
> Can anyone think of a clever way to do this that would be fast in IDL
> (ie, no looping through the pixels)? I need it to work for box sizes
> up to around 21. Ties may be broken arbitrarily.
>
> Is there already a name for this concept?
I don't know. This article might give you some ideas,
though:
http://www.dfanning.com/idl_way/smregval.html
Cheers,
David
--
David Fanning, Ph.D.
Fanning Software Consulting, Inc.
Coyote's Guide to IDL Programming: http://www.dfanning.com/
Sepore ma de ni thui. ("Perhaps thou speakest truth.")
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| Re: not-quite meidan filter [message #72734 is a reply to message #72733] |
Thu, 30 September 2010 14:06 |
JJ
Messages: 36
Registered: January 2007
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Member |
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>
> So you're using a "mode" filter. Try max(histogram(pixels)). You
> should be careful to choose your binsize appropriately if you have non-
> integer data, however; or, alternatively you can use my statistical
> mode which finds the mode of a continuous distribution by maximizing
> the kernel density estimation. If you'd like the code for that, let
> me know.
I think I see what you're suggesting, but unless I'm missing
something, it seems that I would still have to loop over all the
pixels in my image - which is exactly what I don't want to do. It's
good to know the name "mode" though.
I have worked up a solution which will work as long as I have a
limited number of possible values - my test case is only 53 distinct
values, which is OK. I create a 3D array with a slice for each
distinct value, where value of each slice is the coverage (0 or 1) for
that particular value. I then convol each slice with a simple box
kernel filled with 1's, which gives me number of instances of that
value in the box. Then I do a max (dim = 3) on the cube and get the
"max_subscripts", which I can then easily convert to the disticnt
value that I want.
This method is reasonably fast (especially compared to how long a loop
would take), but seems a little clunky and might cause trouble with a
lot more values. Come to think of it though, I don't need the whole
cube - I could just process one value at a time and just keep the
maximum so far.
Any better solutions appreciated.
Thanks.
-Jonathan
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| Re: not-quite meidan filter [message #72735 is a reply to message #72734] |
Thu, 30 September 2010 13:51 |
jeanh
Messages: 79
Registered: November 2009
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Member |
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On 30/09/2010 3:38 PM, JJ wrote:
> I would like to do something that is similar to, but not quite the
> same as, a median filter to a 2D array. Instead of choosing the
> median value in a box surrounding each pixel, I would like to chose
> the value in that box that occurs most frequently.
>
> For example, if I had
>
> 1 1 1 1 1
> 1 1 1 1 1
> 2 2 2 2 2
> 2 2 3 3 3
> 3 3 3 3 3
>
> The median would be 2, but I would want the value 1 (it occurs 10
> times, which is more than the 8 instances of the value 3 or the 7
> instances of the value 2).
>
> Can anyone think of a clever way to do this that would be fast in IDL
> (ie, no looping through the pixels)? I need it to work for box sizes
> up to around 21. Ties may be broken arbitrarily.
>
> Is there already a name for this concept?
>
> Thanks.
>
> -Jonathan
Hi,
this is what I use (similar to Gray's suggestion)
function getMajority,data, central=central
;This function returns the majority value of the input array.
;If there is a tie, a random mode is returned.
;If the central keyword is specified, if there is a tie and the value of
the central cell of the array is in one of
;the mode, then this value is returned.
;
;
;Written by Jean-Gabriel Hasbani (firstname@lastname.ca)
;December 2007
majority = -1
;Use histogram to find the mode
histo = histogram(data, min=0, r=ri)
;Get the number of time the mode(s) value is repeated
MaxVal = max(histo)
;Find every entry in the histogram that have this frequency
maxValInd = where(histo eq maxVal, count)
;If there is only 1 mode, return its value
if count eq 1 then return, data[ri[ri[maxValInd]]]
;else, look at all the possible values (modes) and return a random one
;If the keyword is specified, if the central cell is of the type of one
of the majority, return this value
if keyword_set(central) then begin
;get the central cell value
centralValue = data[n_elements(data)/2 - 1]
;For each mode, get the value and compare is with the central value
for i = 0, count-1 do begin
histoData = data[ri[ri[maxValInd[i]]]]
if histoData eq centralValue then return, centralValue
endfor
endif
;Create a random index
randomID = randomu(seed,count)
randomID = (sort(randomID))[0]
;return the random mode value
return, data[ri[ri[maxValInd[randomID]]]]
end
Jean
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| Re: not-quite meidan filter [message #72736 is a reply to message #72735] |
Thu, 30 September 2010 13:29 |
Gray
Messages: 253
Registered: February 2010
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Senior Member |
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On Sep 30, 3:38 pm, JJ <j...@cornell.edu> wrote:
> I would like to do something that is similar to, but not quite the
> same as, a median filter to a 2D array. Instead of choosing the
> median value in a box surrounding each pixel, I would like to chose
> the value in that box that occurs most frequently.
>
> For example, if I had
>
> 1 1 1 1 1
> 1 1 1 1 1
> 2 2 2 2 2
> 2 2 3 3 3
> 3 3 3 3 3
>
> The median would be 2, but I would want the value 1 (it occurs 10
> times, which is more than the 8 instances of the value 3 or the 7
> instances of the value 2).
>
> Can anyone think of a clever way to do this that would be fast in IDL
> (ie, no looping through the pixels)? I need it to work for box sizes
> up to around 21. Ties may be broken arbitrarily.
>
> Is there already a name for this concept?
>
> Thanks.
>
> -Jonathan
So you're using a "mode" filter. Try max(histogram(pixels)). You
should be careful to choose your binsize appropriately if you have non-
integer data, however; or, alternatively you can use my statistical
mode which finds the mode of a continuous distribution by maximizing
the kernel density estimation. If you'd like the code for that, let
me know.
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