-
MATHEMATICAL MORPHOLOGY IN COLOR SPACES APPLIED TOTHE ANALYSIS
OF CARTOGRAPHIC IMAGES
Jesus Angulo, Jean SerraCentre de Morphologie Mathematique -
Ecole des Mines de Paris
35, rue Saint-Honore, 77305 Fontainebleau, Franceemail:
angulo,serra @cmm.ensmp.fr
ABSTRACTAutomatic analysis of cartographic images is an
importanttask for the development of intelligent geographical
infor-mation systems. Both geometrical features and color
arepowerful cues to extract spatial semantic objects. This
con-tributiondeals with the use of the various color pieces of
in-formation for partitioning color images and for
extractinggeometrical-color features with mathematical
morphologyoperators.
KEY WORDScartographic images, color image processing,
mathematicalmorphology, connections, watershed segmentation,
colortop-hat, color gradient
1 INTRODUCTION
Automatic analysis of cartographic images is an importanttask
for the development of intelligent Geographical Infor-mation
Systems [11].
From an image processing viewpoint, the contents ofa
cartographic color map is typically composed of color re-gions
(each color is associated to a semantic label) and ofsmall
structures, such are text, symbols, lines, etc. There-fore, both
geometrical features and color are powerful cuesto extract spatial
semantic objects.
The extraction of these semantic elements from an im-age can be
made manually or supported by a computer sys-tem. Many efforts are
currently carried out in order to pro-pose satisfactory solutions
for the automated interpretationof cartographic images [10,
12].
We identify two main steps: on the one hand, the seg-mentation
of the image in order to define the color regionsand in order to
extract the text/graphic details, and on theother hand, the
character recognition with OCR, symbolidentification, color
indexation, etc. [21].
In this contribution, we present a method for a full im-age
analysis of cartographic maps based on mathematicalmorphology
operators. The approach deals with the use ofthe various color
pieces of information for hierarchical par-titioning the image into
homogeneous color regions and forextracting a binary layer of the
geometrical-color details.This powerful information can be the
input to the subse-quent pattern recognition algorithms which are
not consid-ered in this study.
The algorithms are illustrated by means of some ex-amples of
color cartographic images, figure 1.
(a) (b) (c)
Figure 1. The color cartographic images used in the
ex-amples.
The rest of the paper is structured as follows. First,the choice
of a suitable color space for morphological im-age processing is
discussed in Section 2. In Section 3 areminder of the problem
arising from the application ofmathematical morphology to color
images is included. Wecontinue in Section 4 with a new extension of
two mor-phological operators to color images. Then, in Section 5are
given the algorithms of our approach for the analysis
ofcartographic images. Finally, conclusions are included inSection
6.
2 COLOR SPACES FOR IMAGE PROCESSING
The choice of a suitable color space representation is stilla
challenging task in the processing and analysis of colorimages. The
RGB color representation has some draw-backs: components are
strongly correlated, lack of humaninterpretation, non uniformity,
etc. A recent study [9] hasshown that many color spaces (HLS,
HSV,...) having beendeveloped for computer graphic applications,
are unsuitedto image processing. A convenient representation
mustyield distances, or norms, and provide independence be-tween
chromatic and achromatic components [19]. In ourworks, we adopt an
improved family of HLS systems thatsatisfy these prerequisites.
This family of spaces is named:Improved HLS (IHLS). There are three
versions of IHLS:using the norm , the norm or the norm .The
equations of transformation between RGB and the newHLS systems are
given in [9] [19] and summarised in [2].
-
For the sake of simplicity, all the examples of the paperwere
obtained according to the equations:
,
! #"$
,
%&
'(*)+)+,-/. 02143
56
143
5+7
8
0
5*9
6
59
7
5
1$0
6
1$0
7
1
6:72;
3= , ?
%
@AB
%&
DC
FE
,
%
%&HG+IJ$KLM
DN
K
.
We would like also to compare it with the L*a*b*color space. The
principal advantage of the L*a*b* spaceis its perceptual
uniformity. However, the transformationform the RGB to L*a*b* space
is done by first transform-ing to the XYZ space, and then to the
L*a*b* space [23].The XYZ coordinates are depending on the
device-specificRGB primaries and on the white point of iluminant.
In mostof situations, the illumination conditions are unknown
andtherefore a hypothesis must be made. We propose to choosethe
most common option: the CIE OPQ daylight illuminant.
RS RT RU
RVW RX+W RYZW
R[ RV R\
Figure 2. Color components of an image example (fig-ure 1(b)) in
the RGB, the L*a*b* and the Improved HLScolor spaces.
Let ]^DC0
C
6
C
7
be a color image, its grey-level components in the improved HLS
color spaceare DC_
C`
Ca
and in the L*a*b* color space areDC`$b
Cc+b
Cd*b
. In figure 2 are given the different colorcomponents of an
image example.
3 MATHEMATICAL MORPHOLOGY ANDCOLOR IMAGES
Mathematical morphology is the application of lattice the-ory to
spatial structures [16]. First introduced as a shape-based tool for
binary images, mathematical morphologyhas become a very powerful
non-linear image analysistechnique with operators for the
segmenting, filtering andfeature extraction in grey-scale images.
Formally, the def-
inition of morphological operators needs a totally
orderedcomplete lattice structure: there are no pair of points
forwhich the order is uncertain. Therefore, the application
ofmathematical morphology to color images is difficult dueto the
vectorial nature of the color data.
(a) (b)
Figure 3. Example of morphological color filtering by vec-torial
connected operators ( is the image on figure 1(b)):(a) Opening by
reconstruction, e$fgZhi , and (b) closing byreconstruction jkfgZhi
. The structuring element is a squareof size and the
lexicographical order is lm]4n oqp *r4sts
%uv
p:rw
.
We have proposed a flexible method for the imple-mentation of
morphological vector operators in completetotally ordered lattices
by using lexicographical orderswhich are defined on the RGB color
space and on the im-proved HLS system [3]. In figure 3 are shown a
color open-ing and a color closing of a cartographic image using
oneof the lexicographic orders presented in [3].
The inconvenient of the vector approach is the com-putational
complexity of the algorithms which leads toslow implementations.
Moreover, different choices mustbe made in the lexicographical
orders: priority of compo-nents, degree of influence of the
components, etc.
A second drawback, more specific, deals with the pro-cessing of
the hue component, i.e. with data that are definedon the unit
circle [7].
However, in practice, for many applications (e.g. seg-mentation
and feature extraction) the total orders are notrequired as well as
increment based operators (e.g. gra-dients and top-hats) may be
used for the hue component.Hanbury and Serra [7] have developed the
application ofmorphological operators on the unit circle and more
pre-cisely, they have defined the circular centered gradient andthe
circular centered top-hat.
Another recent study [18] proposes a theory where
thesegmentation of an image is defined as the maximal parti-tion of
its space of definition, according to a given criterion.See also
[20]. The criterion cannot be arbitrary and permitsto maximize the
partition if and only if the obtained classesare connected
components of some connection (connectivecriterion). Therefore, the
choice of a connection inducesspecific segmentation. In this paper,
we adopt this frame-work and we investigate different connections
for segment-ing the cartographic color images.
-
4 COLOR GRADIENTS AND COLOR TOP-HATS
We introduce in this section the extension of the gradientand
the top-hat notions to color images.
4.1 Gradient
The color gradient function of a color image at the point ,
denoted $ , is associated to a measure of color dis-imilarity or
distance between the point and the set of neigh-bours at distance
one from , . For our purposes, threedefinitions of gradient have
been used, Morphological gradient, C : This is the standard
morphological (Beucher algorithm [15]) gradient forgrey level
images ( C s , where is an Eu-clidean or digital space and is an
ordered set ofgrey-levels), C!!DC DC .
Circular centered gradient, h
$
: If $ is a func-tion containing angular values ( s , where is
the unit circle), the circular gradient is calculatedby the
expression [7],
h
$
$
$
+
$
$
+
where & n
&
n iff n & n "! B and & #B n & niff n & n "! B
.
Euclidean gradient, %$ C : Very interesting forvectorial
functions ( $ DC +### C& * ), itis based on computing the
Euclidean distance '($ ,)$ $
'*$H
+
)+
'*$H
+
)
.
We define a series of gradients for a color image :
1. Luminance gradient: ` $ C` ;
2. Hue circular gradient: _ $ h
C_
;
3. Saturation weighing-based color gradient: a $ Ca
-,
h
C_
Ch
a
-,
C`
(where Cha
is thenegative of the saturation component);
4. Supremum-based color gradient: /.1032 $ Ca:
+
C`2
+
h
C_
;
5. Chromatic gradient: 54 $ )$4DCc Cd ;
6. Perceptual gradient: %6 $ )$HDC` Cc Cd .
In figure 4 is depicted a comparative of the gradientsof a color
image. As we can see, the quality of the gra-dients is different.
We show in Section 5 that the colorgradient is a scalar function
which can be used with thewatershed transformation for segmenting
the color imagesand we discuss how the different gradients perform
on thesegmentation results.
(a) (b) (c)
(d) (e) (f)
Figure 4. Examples of color gradients ( is the image onfigure
1(b)): (a) ` , (b) _ , (c) a , (d)
.1032
, (e)74 and (f) )6 .
4.2 Top-hat
The top-hat transformation is a powerful operator whichpermits
the detection of contrasted objects on non-uniformbackgrounds. In
the sense of Meyer [13], there are twoversions of the top-hat (the
residue between a numericalfunction and an opening or a closing).
It involves incre-ments and hence can be defined to circular
functions likethe hue component. The three definitions of top-hat
used inthis work are :
White top-hat, 89
7
DC
: The residue of the initial imageC and an opening e
7
DC
, i.e. 89
7
DC
C e
7
DC
,
extracts bright structures. Black top-hat, 8
1
7
DC
: The residue of a closing j7
DC
and the initial image C , i.e. 81
7
DC
j
7
DC
C ,
extracts dark structures. Circular centered top-hat, 8 w
7
: Fast variations ofan angular function (defined in the unit
circle) [7], i.e.8
w
7
-:9
-
2. Black-achromatic top-hat : 8(@1
7
8
1
7
DC`
8
1
7
DCa
. Dually, it catches the fast variations of darkregions (i.e.
negative peaks of luminance) and the fastvariations of achromatic
regions on saturated back-ground (i.e. unsaturated peaks: black,
white and greyon color regions).
3. Chromatic top-hat: 8 47
Ca
,
8
7
DC_
8
9
7
DCa
.
This operator extracts the fast variations of color re-gions on
saturated color background (i.e. saturatedcolor peaks on uniform
color regions) and the fastvariations of saturated color regions on
achromatic(unsaturated) background (i.e. saturated color peakson
achromatic regions).
(a) (b)
Figure 5. Examples of color top-hats ( are the images onfigure
1(a)-(b)): (a) Black-achromatic top-hat, 8 @
1
7
and(b) chromatic top-hat, 8 4
7
. The structuring element isa square of size @ .
Figure 5 shows the top-hat of two color images
(thewhite-achromatic top-hat is not meaningful for these
ex-amples). We observe that the extracted objets can be dif-ferent
and on the other hand, a certain kind of structuresare better
defined on one top-hat than on the other. Theircontributions are
consequently complementary.
Usually, the top-hat is accompanied by a thesholdingoperation,
in order to binarise the extracted structures. Wepresent in Section
5 an interesting method for making thethresholding operation
easier.
Figure 6. Overview to the proposed approach.
5 MORPHOLOGICAL ANALYSIS OF COLORCARTOGRAPHIC IMAGES
The morphological approach for analysing the color carto-graphic
images is summarised in the overview of figure 6.The further
details of these steps are discussed below.
5.1 Hierarchical partition into homogeneousregions
The aim of the first step is the partitioning of the imageinto
disjoint regions whose contents are homogeneous incolor, texture,
etc. In order to have a more flexible andrich approach, we propose
to use a multiscale segmenta-tion, that is, the partitioning is
composed of a hierarchi-cal pyramid with successive levels more and
more simpli-fied. In [4] we have introduced two algorithms for
hierar-chical color image segmentation. The first one is based ona
non-parametric pyramid of watersheds, comparing dif-ferent color
gradients. The second segmentation algorithmrelies on the merging
of chromatic-achromatic partitionsordered by the saturation
component. Several connections(jump connection, flat zones and
quasi-flat zones) are usedas connective criteria for the
partitions. Both approachesinvolve a color space representation of
type HLS, wherethe saturation component plays an important role in
orderto merge the chromatic and the achromatic information dur-ing
the segmentation procedure. The presented methodsare both good and
fast. We would like now to evaluate theapplication of these
algorithms to the cartographic images.We describe here the
fundamentals of the algorithms andwe comment on the preliminary
results.
5.1.1 Waterfall algorithm for color images
The watershed transformation, a pathwise connection, isone of
the most powerful tools for segmenting images. Thewatershed lines
associate a catchment basin to each mini-mum of the function [5].
Typically, the function to flood isa gradient function which
catches the transitions betweenthe regions. The watershed method is
meaningful only forgrey tone images (is based on the existence of a
total order-ing relation in a complete lattice). However, it can be
eas-
-
ily used for segmenting color images by defining a
scalargradient function corresponding to the color image. Us-ing
the watershed on a grey tone image without any prepa-ration leads
to a strong over-segmentation (large numberof minima). A well-known
method for avoid the over-segmentation involves a non-parametric
approach which isbased on merging the catchment basins of the
watershedimage belonging to almost homogenous regions; this
tech-nique is known as waterfall algorithm [6].
Level 1 Level 2 Level 3 Level 4
Figure 7. Pyramid of segmentation by waterfall algorithm( is the
image on figure 1(b)). First row, mosaic imagesand second row,
watershed lines.
Let be a positive and bounded function ( ) and let F be its
watershed. An efficient algorithmfor implementing the waterfalls is
based on building a newfunction J : J iff F and J
iff h ( J is obviously greater than ) and then, is reconstructed
by geodesic erosions from J [5], i.e.
b
J$
. The minima of the resulting function
cor-
respond to the significant markers of the original , more-over,
the watershed transform of
produces the catchmentbasins associated with these significant
markers. In prac-tice, the initial image is the gradient of the
mosaic image (after a watershed transformation, is obtained by
cal-culating the average value of the function in each
catchmentbasin). By iterating the procedure described above, a
hier-archy of segmentations is obtained. Dealing with color im-ages
has the drawback of the method for obtaining the mo-saic color
image of the level . We propose to calculatethe average values
(associated to the catchment basins) inthe RGB components, i.e.
]
0
6
7
. The gra-dient of level is obtained from , i.e. 9 .In practice,
all the presented gradient functions can be ap-plied on . It is
possible to consider a contradiction thefact that, for the mosaic
image, the values are averaged inthe RGB color components and then,
the gradients (andconsequently the watersheds) are computed using
othercolor components. However, this procedure of data merg-ing
allows to obtain good results and on the other hand, thecalculation
of the mean of angular values (H, a*, b* com-ponents) is not
trivial.
The example of figure 7 illustrates the color water-fall
technique (using a ), with the different levels of the
(a) (b) (c)
(d) (e) (e)
Figure 8. Examples of level 4 of waterfall pyramid
usingdifferent color gradients ( is the image on figure 1(b)):
(a)
`
, (b) _ , (c) a , (d) .1032
, (e) 74 and (f) )6 .
pyramid. The segmentation results corresponding to thedifferent
gradients are given in figure 8. Other tests havebeen performed on
a representative selection of color im-ages and the results have
been similar [4]. The use of onlythe brightness ( ` ) or only the
color ( _ and 74 ) infor-mation produces very poor results. We can
observe in fig-ure 4 that the supremum-based color gradient is the
mostcontrasted and obviously achieves to good results of
seg-mentation. The perceptual gradient, which has very inter-esting
properties for colorimetric measures in perceptuallyrelevant units,
leads to better results for the dark regions.However, the best
partitions have been obtained with theproposed saturation
weighing-based color gradient. Therationale behind this operator is
the fact that the chromaticimage regions correspond to high values
of saturation andthe achromatic regions (grey, black or white) have
low val-ues in Ca (or high values in C h
a
). According to the expres-sion of a , for the chromatic regions
the priority is givento the transitions of _ and for the achromatic
regions thecontours of ` are taken.
5.1.2 Ordered partition merging for colorimages
This segmentation approach is based on the applicationof other
morphological connections to color images. Forthe sake of
simplicity, we just use here the jump connec-tion [17].
Let *4 be the jump connection of module whichsegments the
function C obtaining a partition , i.e.
DC
. The jump connection is defined for functionsC(Fs where is a
totally ordered lattice. As for thewatershed, the application to
color images involves specialconsiderations. In the HLS color
systems, the *4 could beapplied to each grey level component,
obtaining a partitionfor each component, i.e.
DC`
,
DCa
,
DC_
.
Remark that we must fix a color origin for the hue compo-
-
nent in order to have a totally ordered set which involvessome
disadvantages [7]. Typically, non-significant smallregions appear
in the partitions (over-segmentation). Thesegmentation may be
refined by the classical region grow-ing algorithm, based on
merging initial regions accordingto a similarity measure between
them. For the region merg-ing process, each region is defined by
the mean of grey lev-els and the merging criterion is the area of
the region(regions with area smaller than are merged to the
mostsimilar adjacent regions).
(a) (b) (c)
(d) (e) (f)
Figure 9. Examples of segmentation by jump connection
+ region merging , , ( is the image onfigure 1(b)): (a)
Chromatic partition, DC_ , (b) achro-matic partition, DC` , (c)
saturation partition, DCa ,(d) saturation-based weighted contours
of chromatic andachromatic partitions, a , (e) segmentation of
weightedpartition by watershed transformation, , (f) contoursof
watershed lines on initial color image.
In figure 9(a)-(c) are shown the partitions by jumpconnection
improved by region merging. Now, the ques-tion is how the obtained
partitions can be combined. Aswe can see in the example, the
partition DC_ repre-sents well the chromatic regions (very
interesting for thecartographic images), as well as DC` the
achromaticones. We propose the following strategy. Starting fromthe
mosaic image associated to DCa , denoted !a wecan use this function
in order to weight the contours ofthe chromatic and achromatic
partitions, in a similar waythan for the saturation weighing-based
color gradient, i.e.
a
!a
,
DC_
$
h
a
,
DC_
,
see figure 9(d). The segmentation of the weighted partition
a is obtained again by using the watershed transformation,
F
a
, figure 9(e)(f).The increasing values of parameters and lead
to
a new pyramid of segmentation. The performance of
thissegmentation is relatively good. The main problem is
theadequate choice of values for this parameters.
Therefore, we can conclude that for the aim of parti-tioning the
cartographic image the most indicated methodis the waterfall
algorithm.
5.2 Feature extraction
The feature extraction involves basically obtaining thecolor
top-hats which extract all the text/graphic details, aswe have
shown in the precedent discussion, followed by athreshold.
Now, the great difficulty arises from the binarisationof the
top-hats in order to generate the semantic layer of thecolor
image.
Besides the problem for finding the optimal thresholdvalue, if
we try the thresholding transformation directly onthe top-hat
image, it is probably that the result will be verynoisy, figure
10(a).
We propose to use an area opening operator. The areaopening
[22], e c , is a connected filter that removes brightstructures
whose area is less that a give threshold but pre-serves the
contours of the remaining objects.
Taking a size of ! , it is possible to remove manynoisy details.
Moreover, the residue between this filteredimage and an area
opening of large size ( e c
Qr
e
c
)allows us to remove the background contribution, makingthe
threshold easier, see the examples of figure 10(b)(c).
In fact, this is also a step of segmentation (the thresh-old
method is another connective criterion [18, 20]). Weconsider that
the segmentation of the cartographic image iscomposed of the
partitioning using the waterfall algorithmand the text/graphics
detail extraction using the thresholdedtop-hats.
5.3 Color indexing and post-processing
Color is an important attribute for image retrieval: coloris an
intuitive feature for which it is possible to use an ef-fective and
compact representation. Color information inan image can be
represented by a single 3-D histogram orthree separate 1-D
histograms. These color representationsare invariant under rotation
and translation of the image. Asuitable normalisation also provides
scale/size invariance.The histograms are feature vectors which are
used as im-age indices. A distance measure is used in the
histogramspace to measure the similarity of two images [1].
In [2], we defined two bivariate histograms: J_Ha
(putting together the hue component and the saturationcomponent)
and J `$a (luminance and saturation compo-nents) associated to the
HLS color representation. We pre-sented an algorithm for the
partitioning of these histogramsusing morphological tools which
yields another interestingmethod for segmentation color images. In
view of the com-pact representation of the chromatic-achromatic
image in-formation, the bivariate histograms are also very useful
forthe color distribution indexing of an image.
In the case of cartographic color images, one of themosaic color
images of the segmentation pyramid (wheremany non significant color
details have been removed) canbe used for computing the bivariate
histograms, see fig-ure 11. Then, the histograms could be
considered the indexfor a retrieval system based on the color
content.
-
(a)
(b) (c)
Figure 10. Examples of thresholding simplification by
areaopening e c . (a) Initial black-achromatic top-hat and
binaryimage after thresholding at t . (b) and (c) First row:area
opening of size and q , secondrow: residues between the area
opening of size and thecorresponding large area opening, third row:
binary imagesafter thresholding residues images at .
(a) (b) (c)
Figure 11. Examples of normalised bivariate color his-togram
images: (a) Initial image (mosaic of level 4 of thesegmentation
pyramid), (b) chromatic histogram C _Ha , (c)achromatic histogram C
`$a .
Finally, there are other morphological operatorswhich can be
applied to the binary semantic layer in or-der to simplify the
subsequent steps of pattern recognition:for the separation between
text and graphics and for thereading of the text (mainly using an
OCR systems). Forinstance, it is possible to build the skeleton of
the binarystructures for better outlining the objets (characters,
lines,symbols, etc). The most interesting transformation is
themorphological thinning [16] which preserves the homotopyand
yields robust skeletons, see examples in figure 12.
The color of the text/graphics is also meaningful andtherefore,
the simple masked binary layer with the origi-nal color image
constitutes an interesting information, seefigure 12.
(a) (b) (c) (d)
Figure 12. Examples of post-processing of semantic lay-ers
(first row, from the black-achromatic top-hat and sec-ond row, from
the chromatic top-hat; of the image on fig-ure 1(b)): (a) Initial
color image, (b) extracted text/graphiclayer, (c) morphological
thinning, (d) text/graphic layermasked with original color.
6 CONCLUSION
In this paper, we have proposed a new method for anal-ysis of
cartographic color images based on mathematicalmorphology
operators. We have discussed the extensionof the gradient and the
top-hat notions to color images inthe hue/luminance/saturation
spaces. These morphologicalcolor operators can be used for
hierarchical partitioning of
-
images into homogeneous regions and for details extrac-tion. We
also have described a technique for indexing thecolor distribution
and for thresholding easily the extracteddetails.
We demonstrated on the preliminary image examplesthat the
proposed approach is able to achieve to good seg-mentation results,
providing robust and reproducible algo-rithms (very few parameters
to set). We would like to eval-uate deeply the performance of these
techniques, compar-ing with other kinds of non-morphological
techniques.
In summary, we believe that this approach can be usedas a first
step in an automated system for the managementof cartographic maps
in the framework of geographical in-formation systems.
Acknowledgements
The authors would like to thank Miguel Torres and Ser-guei
Levachkine of the Centre for Computing Research-IPN, Mexico City,
for providing the images used in thisstudy.
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