# mmdist
Distance transform.

## Synopsis

y = mmdist( f, Bc = None, METRIC = None )

Implemented in Python.

### Input

f | Image Binary image.
Bc | Structuring Element (connectivity) Default: `None` (3x3 elementary cross)
METRIC | String 'EUCLIDEAN', or 'EUC2' for squared Euclidean. Default: `None`

### Output

y | Image distance image in uint16, or in int32 datatype with EUC2 option.

## Description

mmdist creates the distance image `y` of the binary image `f`. The value of `y` at the pixel `x` is the distance of `x` to the complement of `f`, that is, the distance of `x` to nearest point in the complement of `f`. The distances available are based on the Euclidean metrics and on metrics generated by a a regular graph, that is characterized by a connectivity rule defined by the structuring element `Bc`. The implementation of the Euclidean algorithm is based on LotuZamp:01.

## Examples

Simple numeric example

    >>> a = mmframe(mmbinary(ones((5,9))),2,4)

    >>> f4=mmdist(a)

    >>> f8=mmdist(a,mmsebox())

    >>> fe=mmdist(a,mmsebox(),'EUCLIDEAN')

Image example

    >>> f = mmreadgray('gear.tif')

    >>> f = mmneg(mmgradm(f))

    >>> d4=mmdist(f)

    >>> d8=mmdist(f,mmsebox())

    >>> de=mmdist(f,mmsebox(),'EUCLIDEAN')

    >>> mmshow(f)

    >>> mmshow(d4%8)

    Warning: Converting input image from int32 to uint16.

    >>> mmshow(d8%8)

    Warning: Converting input image from int32 to uint16.

    >>> mmshow(de%8)

    Warning: Converting input image from int32 to uint16.

f | d4%8 | d8%8 | de%8 |

## Equation

distance of a point x to a set X:
distance function:
distance function using structuring element:
Relationship between erosion and distance transform:

## Limitations

To generate useful Distance transforms, the structuring elements must be symmetric and have the origin included. The Euclidean distance transform is rounded to the nearest integer, since it is represented as an unsigned integer image. Use the option EUC2 to compute exact squared Euclidean distance transform.

## Source Code

    def mmdist(f, Bc=None, METRIC=None):
        from string import upper
        from Numeric import zeros, sqrt
        if Bc is None: Bc = mmsecross()
        if METRIC is not None:
           METRIC = upper(METRIC)
        f = mmgray(f,'uint16')
        y = mmintersec(f,0)
        if (METRIC == 'EUCLIDEAN') or (METRIC == 'EUC2'):
            b = int32(zeros((3,3)))
            i=1
            while not mmisequal(f,y):
                a4,a2 = -4*i+2, -2*i+1
                b = int32([[a4,a2,a4],
                           [a2, 0,a2],
                           [a4,a2,a4]])
                y=f
                i=i+1
                f = mmero(f,b)
            if METRIC == 'EUCLIDEAN':
                f = uint16(sqrt(f)+0.5)
        else:
            if mmisequal(Bc, mmsecross()):
                b = int32([[-2147483647,  -1, -2147483647],
                           [         -1,   0,          -1],
                           [-2147483647,  -1, -2147483647]])
            elif mmisequal(Bc, mmsebox()):
                b = int32([[-1,-1,-1],
                           [-1, 0,-1],
                           [-1,-1,-1]])
            else: b = Bc
            while not mmisequal(f,y):
                y=f
                f = mmero(f,b)
        return y

## See also

mmfreedom | Control automatic data type conversion.
mmdtshow | Display a distance transform image with an iso-line color table.
mmero | Erode an image by a structuring element.
mmgdist | Geodesic Distance Transform.
mmsebox | Create a box structuring element.
mmsecross | Diamond structuring element and elementary 3x3 cross.

[`mmopen`] [Up] [`mmgdist`] |
Copyright (c) 2003, Roberto A. Lotufo, UNICAMP-University of Campinas; Rubens C. Machado, CenPRA-Renato Archer Research Center.