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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B-YF. Istanbul 2004

morphology is the watershed segmentation. It gives a partition
of image into catchment basins where every local minimum of
the image belongs to one basin and the basins' boundaries are
located on the “crest” values of the image (Geraud, et.al.,2001).
However, the watershed algorithm usually leads to
over-segmentation due to the presence of non significant local
minima in the image, and therefore it cannot be applied directly
except for a few simple cases where the target object is brighter
than the background or vice versa (Pesaresi &
Benediktsson, 1999). Many solutions to the over-segmentation
problem were proposed, eg, the selection of markers before
flooding to reduce the infection of non significant local
minima(Serra & Salembier,1993), or the merging of different
basins after flooding to reduce regions obtained by watershed
segmentation (Beucher,1994; Meyer,1994; Demarty &
S.Beucher, 1998;). All the said approaches assume that the
region of interest for detection is large and homogenous relative
to the spatial and spectral resolution of the sensor. Consequently,
these approaches are very difficult to be applied in segmentation
of very complex scenes.
In this paper, a multi-scale segmentation method for remotely
sensed image based on mathematical morphology is proposed.
The idea is to characterize image structures by their
morphological ^ features obtained by ^ morphological
transformation. The pixels with the same characteristics in the
image could be a connected component. This method avoids
over-segmentation occurred in the watershed segmentation.
2. METHODOLOGY
2.1 Definition of Basic Concept and Operators
Infimum (:) and Supremum (1): The greatest lower bound
is defined as infimum and the smallest upper bound as
supremum for a particular set.
Structure Element (N(p) ): It is the set of neighbors of a
pixel p denoted as N(p)
Erosion (e x) : Grey image /(p) eroded by structure
element N, is defined by the infimum of the values of the grey
level function as follows:
47
enf(p)=h fe |» eN(p)ur(p) 0
Dilation (Oy ) : Grey image f(p) dilated by structure
element is defined by the supremum of the values of the grey
level function.
à. f(p)- V f T e N(P)u f») Q)
Opening (yy): Erosion followed by dilation with the same
structure element is denoted as opening:
FN f(p) = ÔNEN f(p) (3)
Closing (py ): It is defined as the result of dilation followed
by erosion with the same structure element as follows:
à, f(p) =&N Sy fp) (4)
One of the characteristics of opening and closing operations is
to erase objects smaller than the structure element. If the grey
image can be considered as a topographical relief, then opening
can cut the peaks (objects lighter than neighborhood), and
closing can fill valleys (objects darker than neighborhood ).
Top-Hat transform and inverse Top-Hat transform: The
opening operation is anti-extensive, ie grey scale of every pixel
in the opening processed image is not greater than that in the
original image, and lighter objects smaller than structure
element will be erased by opening operation. So the residual
between original image and opening image can be defined as
Top-Hat transform (r7(p)) ;
Uf(p)» f(p)- yu f(p)o f(p)- vex f(p) (9
This operation can extract the lighter objects smaller than the
structure element.
The closing is extensive, ie grey scale of every pixel in the
closing image is not smaller than that in the original image, and
the valleys will be filled. So the residual between closing image
and original denoted as inverse
image is Top-Hat
transform (rr p)}: