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mmregmin
Regional Minimum (with generalized dynamics).

Synopsis

y = mmregmin ( f , Bc = NullStrel, option = "binary" )

Input

f Image Gray-scale (uint8 or uint16) image

Bc Structuring Element

(connectivity).

Default: NullStrel (3x3 elementary cross)
option String

Choose one of: BINARY: output a binary image; VALUE: output a grayscale image with points at the regional minimum with the pixel values of the input image; DYNAMICS: output a grayscale image with points at the regional minimum with its dynamics; AREA-DYN: int32 image with the area-dynamics; VOLUME-DYN: int32 image with the volume-dynamics.

Default: "binary" ('binary')

Output

y Image Gray-scale (uint8 or uint16) or binary image

Description

mmregmin creates a binary image f by computing the regional minima of f, according to the connectivity defined by the structuring element Bc. A regional minimum is a flat zone not surrounded by flat zones of lower gray values. A flat zone is a maximal connected component of a gray-scale image with same pixel values. There are three output options: binary image; valued image; and generalized dynamics. The dynamics of a regional minima is the minimum height a pixel has to climb in a walk to reach another regional minima with a higher dynamics. The area-dyn is the minimum area a catchment basin has to raise to reach another regional minima with higher area-dynamics. The volume-dyn is the minimum volume a catchment basin has to raise to reach another regional minima with a higher volume dynamics.

The dynamics concept was first introduced in [GR92] and it is the basic notion for the hierarchical or multiscale watershed transform.

Examples

Numerical example:
a = uint8([
    [10,  10,  10,  10,  10,  10,  10],
    [10,   9,   6,  18,   6,   5,  10],
    [10,   9,   6,  18,   6,   5,  10],
    [10,   9,   9,  15,   4,   9,  10],
    [10,   9,   9,  15,  12,  10,  10],
    [10,  10,  10,  10,  10,  10,  10]])
print mmregmin(a)
[[False False False False False False False]
 [False False  True False False  True False]
 [False False  True False False  True False]
 [False False False False  True False False]
 [False False False False False False False]
 [False False False False False False False]]
print mmregmin(a,mmsecross(),'value')
[[0 0 0 0 0 0 0]
 [0 0 6 0 0 5 0]
 [0 0 6 0 0 5 0]
 [0 0 0 0 4 0 0]
 [0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0]]
print mmregmin(a,mmsecross(),'dynamics')
[[ 0  0  0  0  0  0  0]
 [ 0  0  4  0  0  1  0]
 [ 0  0  4  0  0  1  0]
 [ 0  0  0  0 14  0  0]
 [ 0  0  0  0  0  0  0]
 [ 0  0  0  0  0  0  0]]
Image example, filtering the regional minima:

Typically, the regional minima is very numerous in a real image. To filter the regional minima, one can use the mmhmin , mmclose , mmareaclose , or other functions that simplifies basins. 

f1=mmreadgray('bloodcells.tif')
m1=mmregmin(f1,mmsebox())
mmshow(f1,m1)
f2=mmhmin(f1,70)
mmshow(f2)
m2=mmregmin(f2,mmsebox())
mmshow(f2,m2)
f1,m1 f2
f2,m2
Multiscale watershed

To build a pyramid of nested segmentations, use the marker for the watershed only the minima above a given dynamic. Two levels of this pyramid are build below, one with dynamic above 20 and the other, above 40. 

f=mmreadgray('cameraman.tif')
g=mmgradm(f)
mh=mmregmin(g,mmsecross(),'dynamics')
ws1=mmcwatershed(g, mmbinary(mh, 20))
ws2=mmcwatershed(g, mmbinary(mh, 40))
mmshow(ws1)
mmshow(ws2)
ws1 ws2

Equation

See also

mmfreedom Control automatic data type conversion.
mmregmax Regional Maximum.
mmsebox Create a box structuring element.
mmsecross Diamond structuring element and elementary 3x3 cross.
mmhmin Remove basins with contrast less than h.
mmareaclose Area closing
mmvmin Remove basins with volume less than v.
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