the watershed segmentation 1 nadine garaisy. general definition 2 a drainage basin or watershed is...
TRANSCRIPT
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THEWATERSHED SEGMENTATION
NADINE GARAISY
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GENERAL DEFINITIONA 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
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INTRODUCTION
The watershed concept was first applied by Beucher and Lantuejoul at 1979, they used it to segment images of bubbles and SEM metallographic pictures
The Watershed transformation is a powerful tool for image segmentation, it uses the region-based approach and searches for pixel and region similarities.
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IMAGE REPRESENTATION
We will represent a gray-tone image by a function:
is the gray value of the image at point
A section of at level is a set defined as:
And in the same way we define as:
=
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REMINDER-IMAGE GRADIENT
An image gradient is a directional change in the intensity or color in an image. Image
gradients may be used to extract information
from images.
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IMAGE GRADIENT
an intensity image a gradient image in the x direction measuring horizontal
change in intensity
a gradient image in the y direction measuring vertical
change in intensity
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IMAGE GRADIENTThe 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 gradient of
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GEODESIC DISTANCEFor two points when 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
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GEODESIC ZONE OF INFLUENCE
The geodesic zone of influence of (when is composed of connected components ) is the set of points inwhose finite distance is closest to (among all components)
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GEODESIC SKELETON BY ZONES OF INFLUENCE
The boundaries between the various zones of influence give the geodesic skeleton by Zones of influence of in
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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
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MINIMA AND MAXIMA An ascending path is a sequence 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
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NON-ASCENDING PATH
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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
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THE WATERSHED
TRANSFORMATION
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http://cmm.ensmp.fr/~beucher/lpe1.gif
THE WATERSHED
TRANSFORMATION
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BUILDING THE WATERSHED
Suppose the flood of the surface has reached the section ,
when it continue and reach the flooding is performed in the
zones of influence .
The components of which are not reached by the flood are
the minima at this level and must be added to the flooded
area
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BUILDING THE WATERSHED
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If we define as the catchment basins of at level and as the minima of at height then:
• The initiation of this iterative algorithm is
• In the end the watershed line is when
BUILDING THE WATERSHED
Visual illustration
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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.
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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
gradient.
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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)
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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
OVER-SEGMENTATION: SOLUTION
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HOMOTOPY MODIFICATION
The first two steps of this algorithm can be done by modifying the gradient
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
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OVER-SEGMENTATION: SOLUTION
Now we look at the final result of the marking as a topographic surface, but in
the flooding process instead of piercing the minima, we only make holes through the
components of the marker set that we produced
The initial image marked with the set
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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
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The algorithm for this solution is as follows:
– section at level of the new catchment basins of
Then:
Initialization:
OVER-SEGMENTATION: SOLUTION
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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.
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OVERLAPING GRAINS
To point out the overlapping regions we first threshold the initial image to a binary image
with only two gray values
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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 matrix-
Then the distance matrix will be-
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OVERLAPING GRAINS
By calculation the maxima of the distance function of the binary image we can provide the markers of
the grains
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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.
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OVERLAPING GRAINS
Finally after marking the background and
calculation the gradient function we run the
homotopy modification and the watershed construction are
preformed
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THE SEGMENTATION PARADIGM
I. Finding the markers and the segmentation.
II. Performing a marker-controlled watershed with these two elements
The segmentation process is divided into two steps:
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FROM - WWW.MATHWORKS.COM 36
WATERSHED TRANSFOTMATION
PROCESS
Source: A gray scale image
Step 1: Use the Gradient Magnitude as the
Segmentation Function - The gradient is high at
the borders of the objects and low (mostly) inside
the objects.
Step 2: Mark the foreground objects
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Step 3: computing the opening-by-
reconstruction of the image
Step 4: Following the opening with a closing can remove the dark spots and stem marks.
Step 5: Calculate the regional maxima to
obtain good foreground markers.
WATERSHED TRANSFOTMATION
PROCESS
FROM - WWW.MATHWORKS.COM
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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
Step 8: Compute Background Markers,
Starting with thresholding operation
WATERSHED TRANSFOTMATION
PROCESS
FROM - WWW.MATHWORKS.COM
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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.
WATERSHED TRANSFOTMATION
PROCESS
FROM - WWW.MATHWORKS.COM
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WATERSHED TRANSFOTMATION
PROCESS – ADVANCE OPTIONS
We can use transparency to superimpose this pseudo-color label matrix on top of the original intensity image.
*Another useful visualization technique is to display the label matrix as a color image
FROM - WWW.MATHWORKS.COM
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ROAD SEGMENTATION
In this study they use the watershed algorithm among others to extract vehicle position on the road and possible obstacles ahead.
The algorithms have been tested on a small database representing different driving situations.
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ROAD SEGMENTATION
The morphological gradient image
The original road image
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ROAD SEGMENTATION
Due to noise and inhomogeneities in the gradient image, the
watershed will produce a lot of minima which leads to over-segmentation of
the image
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ROAD SEGMENTATION
We can enhance the watershed on the gradient image by
modifying the gradient function by defining
new markers which will be imposed as the new
minima.
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ROAD SEGMENTATION
The difference between watershed on simple gradient and watershed on the gradient after modifying using the
regularized gradient
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ROAD SEGMENTATION
Then by selecting the catchment basin located at the front of the vehicle we can extract a coarse marker
of the road.
After smoothing this marker we define it as
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ROAD SEGMENTATION
Then we build an outer marker to mark the region of the image which do not
belong to the road
This marker is defined by
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ROAD SEGMENTATION
Using and we modify the gradient which now contain only two minima and the divide lines are the contours of the
road
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ROAD SEGMENTATION
To obtain the road markers we do a simplification on the image using its gradient, the result is an image made 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.
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ROAD SEGMENTATION
Watershed of the mosaic-image points out only the regions surrounded by higher contrast edges, and we can still extract a
marker for the road
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ROAD SEGMENTATION
The result – Road borders,
corresponding to the watershed of the modified gradient
image
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LANE BY LANE ROAD SEGMENTATION
Original image
Mosaic-image
Watershed of mosaic-image
Lanes markers
enhancement
Final result
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POTENTIAL OBSTACLES DETECTION
The second part of this study was identifying
obstacles on the road, but 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, for instance to a shading. Black marker- the edges of the road
White marker- obstacles-free zone
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POTENTIAL OBSTACLES DETECTION
Difficulties in this segmentation:
false detection due to the shadows, because they are considered as obstacles, this can be solved if given complementary information by telemetry or stereovision
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VISUAL EXAMPLES Illustration of watershed road segmentation: https://www.youtube.com/watch?v=Tibi6a_aeeE
Road Detection Using Region Growing and Segmentation:https://www.youtube.com/watch?v=ADdkfE_J4a0
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REFERENCESTHE WATERSHED TRANSFORMATION APPLIED TO IMAGE SEGMENTATION – S.BeucherROAD SEGMENTATION BY WATERSHEDS ALGORITHEMS – S.Beucher, M.Billodeau and X.YuUSE OF WATERSHEDS IN CONTOUR DETECTION- S.Beucher and C.LantuejoulMATHWORKS.COMWIKIPEDIA
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FOR LISTENING!
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TOPOGRAPHIC MAP