mmareaopen - Area opening.

Synopsis

y = mmareaopen( f, a, Bc )

Input

f: Gray-scale (uint8 or uint16) or binary image (logical uint8).

a: non negative integer.

Bc: Structuring element. ( connectivity). Default: Elementary cross (mmsecross).

Output

y: Gray-scale (uint8 or uint16) or binary image (logical uint8).

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.

Limitation

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

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=1:mmmaxlevel(f)  % 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

See Also

mmareaclose - Area closing

mmfreedom - Control automatic data type conversion.

mmlabel - Label a binary image.

mmsebox - Create a box structuring element.

mmsecross - Cross structuring element.

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