### Lecture03_Watershed

```THE
WATERSHED
SEGMENTATION
1
GENERAL DEFINITION
A drainage basin or watershed
is an extent or an area of land
where surface
water from rain melting snow
or ice converges to a single
point at a lower elevation,
usually the exit of the basin,
where the waters join another
waterbody, such as
a river, lake, wetland, sea,
or ocean
2
INTRODUCTION
The Watershed transformation is
a powerful tool for image
segmentation, it uses the regionbased approach and searches for
pixel and region similarities.
The watershed concept was first
applied by Beucher and Lantuejoul
at 1979, they used it to segment
images of bubbles and SEM
metallographic pictures
3
IMAGE REPRESENTATION
We will represent a gray-tone image by a function:
: ℤ2 → ℤ
() is the gray value of the image at point
 A section of  at level  is a set  () defined as:
=  ∈ ℤ2 :   ≥
And in the same way we define  () as:
=  ∈ ℤ2 :   ≤
⟺   =  +1
4
directional change in
the intensity or color
in an image. Image
to extract information
from images.
5
an intensity image
a gradient image in the x
a gradient image in the y
direction measuring
direction measuring vertical
horizontal change in intensity
change in intensity
6
The morphological gradient of a picture is
defined as
= ⨁ −  ⊝
Where ⨁ is the dilation of  and  ⊝  is
its erosion.
But because  is continuously differentiable,
is nothing more than the modulus of the
=
=

2

+

2 1/2
7
GEODESIC DISTANCE
For two points ,   when  ⊂ ℤ2
we define the geodesic distance
(, ) as the length of the shortest
path (if any) included in  and linking
and .
Let  be any set included in , then:
= { ∈ : ∃ ∈ ,  ,  }
is the set of all points of  that are at a
finite geodesic distance from .
8
GEODESIC ZONE OF
INFLUENCE
The geodesic zone of influence of  (when  is composed
of  connected components  ) is the set of points
in  whose finite distance is closest to  (among all
components)
= { ∈ :  ,  finite
and ∀  ≠ ,  ,  <  ,  }
9
GEODESIC SKELETON BY ZONES
OF INFLUENCE
 The boundaries between
the various zones of
influence give the geodesic
skeleton by Zones of
influence of  in .
=
( )

= / ()
10
MINIMA AND MAXIMA
The set of points in the
function  can be seen as
topographic surface , The
lighter the gray value of the
function at the point  the
higher the altitude of the
corresponding point on the
surface
11
MINIMA AND MAXIMA
 An ascending path is a sequence {1 , 2 , . . } On the surface
such that:
∀  ,   ,   ,
≥  ⟺   ≥ ( )
 A point  belongs to a minimum if there is a no ascending
path starting from . It can be considered as a sink of the
topographic surface (see next slide). The set  of all the
minima of  is made of various connected components
()
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ASCENDING PATH
13
NON-ASCENDING PATH
14
THE WATERSHED
TRANSFORMATION
If we look at the image  as a topographic surface, imagine
that we pierce each  () of the topographic surface
and then we plunge this surface into a lake, the water
entering through the holes floods the surface and if two or
more floods coming from different minima attempt to
merge, we avoid this event by building a dam on the
points of the surface where the floods would merge.
At the end of the process only these dams will emerge
and this is what define the watershed of the function
15
THE WATERSHED
TRANSFORMATION
16
THE WATERSHED
TRANSFORMATION
http://cmm.ensmp.fr/~beucher/lpe1.gif
17
BUILDING THE WATERSHED
Suppose the flood of the surface has reached the section
(), when it continue and reach +1  the flooding is
performed in the zones of influence +1

.
The components of +1  which are not reached by the
flood are the minima at this level and must be added to the
flooded area
18
BUILDING THE WATERSHED
19
BUILDING THE WATERSHED
If we define   as the catchment basins of  at level
and  () as the minima of  at height  + 1 then:
+1  = +1

+1 = +1 ()/+1
∪ +1

(  )
• The initiation of this iterative algorithm is −1  =⊘
• In the end the watershed line is   =     when
= max()
 Visual illustration
20
OVER-SEGMENTATION
PROBLEM
Unfortunately, most times the real watershed transform of the
gradient present many catchment basins, Each one corresponds
to a minimum of the gradient that is produced by small
variations, mainly due to noise.
21
OVER-SEGMENTATION:
SOLUTION
The over-segmentation
could be reduced by
appropriate filtering, but
the best results is obtained
by marking the patterns to
be segmented before
preforming the watershed
transformation of the
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OVER-SEGMENTATION:
SOLUTION
FIRST: we mark each blob
of protein of the original
image (by extracting the
minima of the image
function)
23
OVER-SEGMENTATION:
SOLUTION
SECOND: by applying the
watershed on the initial
image we can mark the
background with
connected marker
surrounding the blobs
 We define these two
steps as marker set
24
HOMOTOPY MODIFICATION
The first two steps of this
algorithm can be done by
function to a new wery similar
function ′ , the difference
between the two is that in ′
the initial minima are replaced
by the set , this modification
is called homotopy
modification
25
OVER-SEGMENTATION:
SOLUTION
Now we look at the final
result of the marking as a
topographic surface, but in
the flooding process
minima, we only make
holes through the
components of the marker
set that we produced
The initial image marked with the
set
26
OVER-SEGMENTATION:
SOLUTION
This way the flooding will
produce as many
catchment basins as there
are markers in , this way
the watershed lines of the
contours of the objects
will be on the crest lines
of this topographic
surface
27
OVER-SEGMENTATION:
SOLUTION
The algorithm for this solution is as follows:
() – section at level  of the new catchment basins of
Then:
+1 () = +1 ∪ (  )
Initialization:
−1  =
28
OVERLAPING GRAINS
 In some cases we have an
image with overlapping
figures, that we need to
segment, in order to do that
we need to point out the
overlapping regions.
 For example the figure here is
a TEM (transmission electron
microscopy) image of grains
of silver nitrate scattered on a
photographic plate.
29
OVERLAPING GRAINS
To point out the
overlapping regions we
first threshold the initial
image to a binary image
with only two gray
values
30
REMINDER: DISTANCE
FUNCTION
the distance function of an image assigns for each pixel a
number that is the Euclidean distance between that pixel
and the nearest nonzero pixel.
For example: suppose we have this image matrix0 0 0
0 1 0
0 0 1
Then the distance matrix will be1.4142 1 1.4142
1
0
1
1.4142 1
0
31
OVERLAPING GRAINS
By calculation the maxima
of the distance function of
the binary image we can
provide the markers of
the grains
32
OVERLAPING GRAINS
The markers of the
overlapping regions are
obtained by executing the
watershed transformation
of the inverted distance
function −  , it will
produce divide lines which
will cut the overlapping
grains, that way we can
mark them.
33
OVERLAPING GRAINS
Finally after marking the
background and
function we run the
homotopy modification
and the watershed
construction are
preformed
34
THE SEGMENTATION
The segmentation process is divided into two steps:
I. Finding the markers and
the segmentation.
II. Performing a markercontrolled watershed
with these two
elements
35
WATERSHED TRANSFOTMATION
PROCESS
Source: A gray scale
image
Magnitude as the
Segmentation Function The gradient is high at
the borders of the objects
and low (mostly) inside
the objects.
FROM - WWW.MATHWORKS.COM
Step 2: Mark the
foreground objects
36
WATERSHED TRANSFOTMATION
PROCESS
Step 3: computing the
opening-byreconstruction of the
image
Step 4: Following the
opening with a closing
can remove the dark
spots and stem marks.
FROM - WWW.MATHWORKS.COM
Step 5: Calculate the
regional maxima to
obtain good
foreground markers.
37
WATERSHED TRANSFOTMATION
PROCESS
Step 6: Superimpose the
foreground marker
image on the original
image, Notice that the
foreground markers in
some objects go right up
to the objects' edge
Step 7: cleaning the
edges of the marker
blobs and then
shrinking them a bit
FROM - WWW.MATHWORKS.COM
Step 8: Compute
Background Markers,
Starting with
thresholding operation
38
WATERSHED TRANSFOTMATION
PROCESS
Step 9: Compute Background
Markers, using the watershed
transform of the distance
transform and then looking
for the watershed ridge lines
of the result
Step 10: Visualize the Result,
one of the techniques is to
superimpose the foreground
markers, background markers,
and segmented object
boundaries.
FROM - WWW.MATHWORKS.COM
39
WATERSHED TRANSFOTMATION
*Another useful visualization
technique is to display the
label matrix as a color image
We can use transparency to
superimpose this pseudocolor label matrix on top of
the original intensity image.
FROM - WWW.MATHWORKS.COM
40
In this study they use the
watershed algorithm among
others to extract vehicle
The algorithms have been
tested on a small database
representing different
driving situations.
41
The morphological
42
Due to noise and
inhomogeneities in the
watershed will produce a
to over-segmentation of
the image
43
We can enhance the
watershed on the
function by defining
new markers which will
be imposed as the new
minima.
44
The difference between watershed on simple gradient and
watershed on the gradient after modifying using the
45
Then by selecting the
catchment basin located at
the front of the vehicle we
can extract a coarse marker
After smoothing this marker
we define it as 1
46
Then we build an outer
marker to mark the region
of the image which do not
This marker is defined by
2
47
Using 1 and 2 we
which now contain
only two minima and
the divide lines are
the contours of the
48
To obtain the road markers we do a
simplification on the image using its
of catchment basins tiles of constant
gray values- this image is called the
mosaic-image.
The gradient of this image will be
null everywhere except on the divide
lines where it will be equal to the
absolute difference of the gray-tone
values of the to catchment basins.
49
Watershed of the mosaic-image points out only the regions
surrounded by higher contrast edges, and we can still extract a
50
borders,
corresponding to the
watershed of the
image
51
SEGMENTATION
Original
image
Mosaicimage
Watershed
of mosaicimage
Lanes
Final result
markers
enhancement
52
POTENTIAL OBSTACLES
DETECTION
The second part of this
study was identifying
this detection is useless
without a good definition of
the nature of the obstacles,
the problem in this part was
distinguishing a dangerous
obstacle from a light
variation in intensity due,
Black marker- the edges of the road
White marker- obstacles-free zone
53
POTENTIAL OBSTACLES
DETECTION
Difficulties in this segmentation:
false detection due to the
considered as obstacles, this
can be solved if given
complementary information by
telemetry or stereovision
54
VISUAL EXAMPLES
 Illustration of watershed road segmentation:
 Road Detection Using Region Growing and
Segmentation:
55
REFERENCES
THE WATERSHED TRANSFORMATION APPLIED TO IMAGE
SEGMENTATION – S.Beucher
ROAD SEGMENTATION BY WATERSHEDS ALGORITHEMS –
S.Beucher, M.Billodeau and X.Yu
USE OF WATERSHEDS IN CONTOUR DETECTION- S.Beucher
and C.Lantuejoul
MATHWORKS.COM
WIKIPEDIA
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57
TOPOGRAPHIC MAP
58
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