[mmregmax] [Up] [mmsuprec] Connected Operators

mmregmin
Regional Minimum (with generalized dynamics).

Synopsis

y = mmregmin( f, Bc = None, option = "binary" )

Implemented in Python.

Input

f Image Gray-scale (uint8 or uint16) image.
Bc Structuring Element

(connectivity).

Default: None (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"

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 Grimaud:92 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)

              
[[0 0 0 0 0 0 0]
 [0 0 1 0 0 1 0]
 [0 0 1 0 0 1 0]
 [0 0 0 0 1 0 0]
 [0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0]]

              
>>> 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

      

        

          

            
          

        

      

    

    

      
Source Code

      

        
def mmregmin(f, Bc=None, option="binary"):
    if Bc is None: Bc = mmsecross()
    fplus = mmaddm(f,1)
    g = mmsubm(mmsuprec(fplus,f,Bc),f)
    y = mmunion(mmthreshad(g,1),mmthreshad(f,0,0))
    return y
    

      

    

    

      
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
            

          
        

      

    

    

      

        

          
                    [mmregmax]
                
                    [Up]
                    
                    [mmsuprec]
                
          Python
        

        

          Copyright (c) 2003, Roberto A. Lotufo, UNICAMP-University of Campinas; Rubens C. Machado, CenPRA-Renato Archer Research Center.