[mmareaclose] [Up] [mmvmin] Connected Operators

mmareaopen
Area opening

Synopsis

function y = mmareaopen ( f , a , Bc )

Input

f Image Gray-scale (uint8 or uint16) or binary image
a Double

non negative integer.
Bc Structuring Element

Default: 3x3 elementary cross

( connectivity).

Output

y Image

Same type of f

Description

mmareaopen removes any grain (i.e., connected component) with area less than a of a binary image f. The connectivity is given by the structuring element Bc. This operator is generalized to gray-scale images by applying the binary operator successively on slices of f taken from higher threshold levels to lower threshold levels.

Examples

Numerical examples:
f=mmbinary(uint8([...

 1, 1, 0, 0, 0, 0, 1;...

 1, 0, 1, 1, 1, 0, 1;...

 0, 0, 0, 0, 1, 0, 0]));

y=mmareaopen(f,4,mmsecross)

y =
     0     0     0     0     0     0     0
     0     0     1     1     1     0     0
     0     0     0     0     1     0     0

f=uint8([...

   10,   11,   0,    0,   0,   0,  20;...

   10,    0,   5,    8,   9,   0,  15;...

   10,    0,   0,    0,  10,   0,   0]);

y=mmareaopen(f,4,mmsecross)

y =
   10   10    0    0    0    0    0
   10    0    5    5    5    0    0
   10    0    0    0    5    0    0
Binary image
a=mmreadgray('form-1.tif');

b=mmareaopen(a,500);

mmshow(a);

mmshow(b);
a b
Gray-scale image
a=mmreadgray('bloodcells.tif');

b=mmareaopen(a,500);

mmshow(a);

mmshow(b);
a b

Equation

Algorithm

function y = mmareaopen_equ(f, a, Bc)
if nargin == 2
  Bc = mmsecross;
end
if mmis(f,'binary')
  fr = mmlabel(f,Bc);      % binary area open, use area measurement
  g = mmblob(fr,'area');
  y = mmthreshad(g,a);
else
  y=zeros(size(f));
  for k in range(1,mmmaxlevel(f)+1)  % gray-scale area open, use thresholding decomposition
    fk = mmthreshad(f,k);
    fo = mmareaopen(fk,a,Bc);
    if mmcmp(fo,'==',0)
      break;
    end
    y = y + double(fo);
  end
end

Limitations

The structuring elements allowed are the elementary cross (4-connected) and the elementary box (8-connected).

See also

mmfreedom Control automatic data type conversion.
mmlabel Label a binary image.
mmsebox Create a box structuring element.
mmsecross Diamond structuring element and elementary 3x3 cross.
mmareaclose Area closing
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