How to find local maxima in an image
Question about the concept of object detection. I am stuck after finding the corner of an image and I want to know how to find a point within the calculated angles.
Suppose I have a grayscale image that has data like this
A = [ 1 1 1 1 1 1 1 1;
1 3 3 3 1 1 4 1;
1 3 5 3 1 4 4 4;
1 3 3 3 1 4 4 4;
1 1 1 1 1 4 6 4;
1 1 1 1 1 4 4 4]
if i use
B = imregionalmax(A);
the result will be like this:
B = [ 0 0 0 0 0 0 0 0;
0 1 1 1 0 0 1 0;
0 1 1 1 0 1 1 1;
0 1 1 1 0 1 1 1;
0 0 0 0 0 1 1 1;
0 0 0 0 0 1 1 1]
The question is, how do I select the highest peak within the maximum local area (in the example, how I chose 5 out of 3 and 6 out of 4)?
My idea was to use B to detect each region and use it again imregionalmax()
, but I am not good at coding and need advice or other ideas.
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There are several other simple ways to implement a 2D peak finder: ordfilt2
or imdilate
.
ordfilt2
The most direct method is to use ordfilt2
that sorts the values in local neighborhoods and picks the nth value. (The MathWorks example demonstrates how to implement a maximum filter.) You can also implement a 3x3 peak finder with ordfilt2
by, (1) using a 3x3 domain that does not include the center pixel, (2) selecting the largest (8th) value, and (3) compared to the central value:
>> mask = ones(3); mask(5) = 0 % 3x3 max
mask =
1 1 1
1 0 1
1 1 1
There are 8 values taken into account in this mask, so the 8th value is max. Filter output:
>> B = ordfilt2(A,8,mask)
B =
3 3 3 3 3 4 4 4
3 5 5 5 4 4 4 4
3 5 3 5 4 4 4 4
3 5 5 5 4 6 6 6
3 3 3 3 4 6 4 6
1 1 1 1 4 6 6 6
The trick is compared to A
, the center value of each neighborhood:
>> peaks = A > B
peaks =
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0
imdilate
Image dilation is usually done on binary images, but grayscale decorating is just a max filter (see the Definitions section of the imdilate
docs) The same trick used with ordfilt2
applies here: define a neighborhood that does not include a central neighborhood pixel, apply filter and compare with unfiltered image:
B = imdilate(A, mask);
peaks = A > B;
NOTE . These methods only detect one pixel peak. If any neighbors have the same value, this will not be a peak.
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The imregionalmax function gives you an 8-connected area containing at most and its 8 neighbors (i.e. the 3x3 areas you are seeing). Then you could use morphological operations with the same 3x3 building block to trim those regions at their centers. For example.
B = imregionalmax(A);
C = imerode(B, ones(3));
or equivalent
B = imregionalmax(A);
D = bwmorph(B, 'erode');
Alternatively, you can write your own maximum search function using block processing :
fun = @(block) % your code working on 'block' goes here ...
B = blockproc(A, ones(3), fun)
But it will most likely be slower than the built-in functions. (I don't have the toolkit right now, so I can't try this.)
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