# mmlabelflat
Label the flat zones of gray-scale images.

## Synopsis

y = mmlabelflat( f, Bc = None, _lambda = 0 )

Implemented in Python.

### Input

f | Image Gray-scale (uint8 or uint16) or binary image.
Bc | Structuring Element ( connectivity). Default: `None` (3x3 elementary cross)
_lambda | Double Connectivity given by |f(q)-f(p)|<=_lambda. Default: `0`

### Output

y | Image If number of labels is less than 65535, the data type is uint16, otherwise it is int32.

## Description

mmlabelflat creates the image `y` by labeling the flat zones of `f`, according to the connectivity defined by the structuring element `Bc`. A flat zone is a connected region of the image domain in which all the pixels have the same gray-level ( `lambda=0`). When `lambda` is different than zero, a quasi-flat zone is detected where two neighboring pixels belong to the same region if their difference gray-levels is smaller or equal `lambda`. The minimum label of the output image is 1 and the maximum is the number of flat-zones in the image.

## Examples

Numerical example

    >>> f=uint8([
       [5,5,8,3,0],
       [5,8,8,0,2]])

    >>> g=mmlabelflat(f)

    >>> print g

    [[1 1 2 3 4]
     [1 2 2 5 6]]

    >>> g1=mmlabelflat(f,mmsecross(),2)

    >>> print g1

    [[1 1 2 3 4]
     [1 2 2 4 4]]

Gray-scale image example
A quantized distance transform image is built to be used to compute its flat zones. Note that the background and the hole in the bottom right area are also labeled. The number of the flat zones can be determined by the maximum label value.

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

    >>> d=mmdist(f,mmsebox(),'euclidean')

    >>> g= d /8

    >>> mmshow(g)

    Warning: Converting input image from int32 to uint16.

    >>> fz=mmlabelflat(g,mmsebox());

    Warning: Converting input image from int32 to uint16.

    >>> mmlblshow(fz)

    >>> print mmstats(fz,'max')

    13.0

g | fz |

Quasi-flat zones
In this case two pixels belong to the same quasi-flat zones if they are 8-neighbors ( `mmsebox`) and if their gray-values difference is smaller or equal 3.

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

    >>> g=mmlabelflat(f,mmsebox(),3)

    >>> mmshow(f)

    >>> mmlblshow(g)

f | g |

## Equation

## Source Code

    def mmlabelflat(f, Bc=None, _lambda=0):
        from Numeric import allclose, ravel, nonzero, array
        if Bc is None: Bc = mmsecross()
        zero = mmbinary(mmsubm(f,f))       # zero image
        faux = mmneg(zero)
        r = array(zero)
        label = 1
        y = mmgray( zero,'uint16',0)          # zero image (output)
        while not allclose(faux,0):
            x=nonzero(ravel(faux))[0]        # get first unlabeled pixel
            fmark = array(zero)
            fmark.flat[x] = 1                # get the first unlabeled pixel
            f2aux = mmcmp( f, '==', ravel(f)[x])
            r = mminfrec( fmark, f2aux, Bc)  # detects all pixels connected to it
            faux = mmsubm( faux, r)          # remove them from faux
            r = mmgray( r,'uint16',label)    # label them with the value label
            y = mmunion( y, r)               # merge them with the labeled image
            label = label + 1
        return y

## See also

mmlabel | Label a binary image.
mmsebox | Create a box structuring element.
mmsecross | Diamond structuring element and elementary 3x3 cross.
mmgrain | Gray-scale statistics for each labeled region.
mmblob | Blob measurements from a labeled image.

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