[mmsecross] [Up] [mmseline] Structuring Elements

mmsedisk
Create a disk or a semi-sphere structuring element.

Synopsis

B = mmsedisk( r = 3, DIM = "2D", METRIC = "EUCLIDEAN", FLAT = "FLAT", h = 0 )

Implemented in Python.

Input

r Double Non-negative integer.

Disk radius.

Default: 3

DIM String

'1D', '2D, or '3D'.

Default: "2D"

METRIC String

'EUCLIDEAN', ' CITY-BLOCK', 'OCTAGON', or ' CHESSBOARD'.

Default: "EUCLIDEAN"

FLAT String

'FLAT' or 'NON-FLAT'.

Default: "FLAT"

h Double

Elevation of the center of the semi-sphere.

Default: 0

Output

B Structuring Element

Description

mmsedisk creates a flat structuring element B that is disk under the metric METRIC , centered at the origin and with radius r or a non-flat structuring element that is a semi-sphere under the metric METRIC, centered at (0, h) and with radius r. This structuring element can be created on the 1D, 2D or 3D space.

Examples

Examples of flat structuring elements.

>>> a=mmseshow(mmsedisk(10,'2D','CITY-BLOCK'))

              
>>> b=mmseshow(mmsedisk(10,'2D','EUCLIDEAN'))

              

              
>>> c=mmseshow(mmsedisk(10,'2D','OCTAGON'))

              

              
>>> mmshow(a)

              

              
>>> mmshow(b)

              

              
>>> mmshow(c)
        

              

            

            

              
                

                  
                  
                  
                  
                

                

                  a
                  b
                  c
                  
                

              
            

          

          

          
Examples of non flat structuring elements.

          

          

            

              
>>> d=mmseshow(mmsedisk(10,'2D','CITY-BLOCK','NON-FLAT'))

              

              
>>> e=mmseshow(mmsedisk(10,'2D','EUCLIDEAN','NON-FLAT'))

              

              
>>> f=mmseshow(mmsedisk(10,'2D','OCTAGON','NON-FLAT'))

              

              
>>> mmshow(d)

              
Warning: Converting input image from int32 to uint16.

              
>>> mmshow(e)

              
Warning: Converting input image from int32 to uint16.

              
>>> mmshow(f)
        

              
Warning: Converting input image from int32 to uint16.

            

            

              
                

                  
                  
                  
                  
                

                

                  d
                  e
                  f
                  
                

              
            

          

          

            

              
>>> g=mmsedisk(3,'2D','EUCLIDEAN','NON-FLAT')

              

              
>>> mmseshow(g)

              
array([[-2147483647, -2147483647,           1,           1,           1, -2147483647,
             -2147483647],
       [-2147483647,           2,           2,           2,           2,           2,
             -2147483647],
       [          1,           2,           3,           3,           3,           2,
                       1],
       [          1,           2,           3,           3,           3,           2,
                       1],
       [          1,           2,           3,           3,           3,           2,
                       1],
       [-2147483647,           2,           2,           2,           2,           2,
             -2147483647],
       [-2147483647, -2147483647,           1,           1,           1, -2147483647,
             -2147483647]],'i')

              
>>> h=mmsedisk(3,'2D','EUCLIDEAN','NON-FLAT',5)

              

              
>>> mmseshow(h)
        

              
array([[-2147483647, -2147483647,           6,           6,           6, -2147483647,
             -2147483647],
       [-2147483647,           7,           7,           7,           7,           7,
             -2147483647],
       [          6,           7,           8,           8,           8,           7,
                       6],
       [          6,           7,           8,           8,           8,           7,
                       6],
       [          6,           7,           8,           8,           8,           7,
                       6],
       [-2147483647,           7,           7,           7,           7,           7,
             -2147483647],
       [-2147483647, -2147483647,           6,           6,           6, -2147483647,
             -2147483647]],'i')

            

          

        

      

    

    

      
Equation

      

        

          
Flat structuring element:

          
Euclidean distance:

          

            
          

          
City block distance (4-connectivity):

          

            
          

          
Chess board distance (8-connectivity):

          

            
          

          
Octagon distance:

          

            
          

          
Non-flat structuring element:

          
Euclidean distance:

          

            
          

          
city block distance:

          

            
          

          
chess board distance:

          

            
          

        

      

    

    

      
Source Code

      

        
def mmsedisk(r=3, DIM="2D", METRIC="EUCLIDEAN", FLAT="FLAT", h=0):
    from string import upper
    from Numeric import resize, transpose, arange
    from Numeric import sqrt, arange, transpose, maximum
    METRIC = upper(METRIC)
    FLAT   = upper(FLAT)            
    assert DIM=='2D','Supports only 2D structuring elements'
    if FLAT=='FLAT': y = mmbinary([1])
    else:            y = int32([h])
    if r==0: return y
    if METRIC == 'CITY-BLOCK':
        if FLAT == 'FLAT':
            b = mmsecross(1)
        else:
            b = int32([[-2147483647, 0,-2147483647],
                       [          0, 1,          0],
                       [-2147483647, 0,-2147483647]])
        return mmsedil(y,mmsesum(b,r))
    elif METRIC == 'CHESSBOARD':
        if FLAT == 'FLAT':
            b = mmsebox(1)
        else:
            b = int32([[1,1,1],
                       [1,1,1],
                       [1,1,1]])
        return mmsedil(y,mmsesum(b,r))
    elif METRIC == 'OCTAGON':
        if FLAT == 'FLAT':
            b1,b2 = mmsebox(1),mmsecross(1)
        else:
            b1 = int32([[1,1,1],[1,1,1],[1,1,1]])
            b2 = int32([[-2147483647, 0,-2147483647],
                        [          0, 1,          0],
                        [-2147483647, 0,-2147483647]])
        if r==1: return b1
        else:    return mmsedil( mmsedil(y,mmsesum(b1,r/2)) ,mmsesum(b2,(r+1)/2))
    elif METRIC == 'EUCLIDEAN':
        v = arange(-r,r+1)
        x = resize(v, (len(v), len(v)))
        y = transpose(x)
        Be = mmbinary(sqrt(x*x + y*y) <= (r+0.5))
        if FLAT=='FLAT':
            return Be
        be = h + int32( sqrt( maximum((r+0.5)*(r+0.5) - (x*x) - (y*y),0)))
        be = mmintersec(mmgray(Be,'int32'),be)
        return be
    else:
        assert 0,'Non valid metric'
    return B
    

      

    

    

      
See also

      

        

          
            

              mmfreedom
              Control automatic data type conversion.
            

            

              mmsebox
              Create a box structuring element.
            

            

              mmsecross
              Diamond structuring element and elementary 3x3 cross.
            

            

              mmseline
              Create a line structuring element.
            

            

              mmimg2se
              Create a structuring element from a pair of images.
            

            

              mmseshow
              Display a structuring element as an image.
            

            

              mmdil
              Dilate an image by a structuring element.
            

          
        

      

    

    

      

        

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