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.

References

[1] J. Angulo and J. Serra, Morphological color sizedistributions for image classification and retrieval,in Proc. of Advanced Concepts for Intelligent Vi-sion Systems. (ACIVS02), Ghent, Belgium, Septem-ber 2002.

[2] J. Angulo and J. Serra, Segmentacion de imagenescolor utilizando histogramas bi-variables en espacioscolor en coordonedas polares, submitted to Com-putacion y Sistemas, May 2003, 10 p.

[3] J. Angulo and J. Serra, Morphological coding ofcolor images by vector connected filters, in Proc. 7thIEEE Int. Symp. on Signal Processing and Its Appli-cations (ISSPA03), Paris, France, July 2003.

[4] J. Angulo and J. Serra, Color segmentation by or-dered mergings, in Proc. IEEE Conf. on ImageProcessing (ICIP03), Barcelona, Spain, September2003.

[5] S. Beucher and F. Meyer, The Morphological Ap-proach to Segmentation: The Watershed Transforma-tion, in (E. Dougherty Ed.), Mathematical Morphol-ogy in Image Processing, Marcel Dekker, 433481,1992.

[6] S. Beucher, Watershed, hierarchical segmentationand waterfall algorithm, in Mathematical Morphol-ogy and Its Applications to Image Processing, Proc.ISMM94, pp. 6976, Kluwer, 1994.

[7] A. Hanbury and J. Serra, Morphological operatorson the unit circle, IEEE Transactions on Image Pro-cessing, 10(12): 18421850, 2001.

[8] A. Hanbury, Mathematical morphology in the HLScolour space, in Proc. 12th BMVC, British Ma-chine Vision Conference, Manchester, pp. II-451460,2001.

[9] A. Hanbury and J. Serra, A 3D-polar coordinatecolour representation suitable for image analysis,submitted to Computer Vision and Image Under-standing, November 2002, 39 p.

[10] S. Levachkine, A. Velazquez and V. Alexandrov,Color Image Segmentation Using False Colors andIts Applications to Geo-Images Treatment: Alphanu-meric Characters Recognition, in Proc. of the IEEEInternational Geoscience and Remote Sensing Sym-posium, IGARSS01, Sydney, Australia, 9-13 July2001.

[11] S. Levachkine, A. Velazquez, V. Alexandrov andM. Kharinov, Semantic Analysis and Recognitionof Raster-Scanned Color Cartographic Images, in(Blostein and Young-Bin Kwon Eds.), Lecture Notesin Computer Science, Vol. 2390, 178189, Springer-Verlag, 2002.

[12] S. Levachkine, M. Torres and M. Moreno, IntelligentSegmentation of Color Geo-Images, in Proc. of theIEEE International Geoscience and Remote SensingSymposium, (IGARSS03), Toulouse, France, 2003.

[13] F. Meyer, Constrast features extraction, in Quan-titative Analysis of microstructures in Materials Sci-ence, Biology and Medecine, Chermant, J.L. Ed.,Riederer Verlag, 374380, 1977.

[14] F. Ortiz, F. Torres, J. Angulo and S. Puente, Compar-ative study of vectorial morphological operations indifferent color spaces, in Proc. of Intelligent Robotsand Computer Vision XX: Algorithms, Techniques,and Active Vision, SPIE Vol. 4572, 259268, Boston,November 2001.

[15] J.F. Rivest, P. Soille and S. Beucher, Morphologicalgradients, Journal of Electronic Imaging, 2(4):326336, 1993.

[16] J. Serra, Image Analysis and Mathematical Morphol-ogy. Vol I, and Image Analysis and MathematicalMorphology. Vol II: Theoretical Advances, AcademicPress, London, 1982 and 1988.

[17] J. Serra, Connectivity for sets and functions, Fun-damenta Informaticae, 41, 147186, 2002.

[18] J. Serra, Connection, Image Segmentation and Fil-tering, in Proc. XI International Computing Confer-ence (CIC02), Mexico DF, November 2002.

[19] J. Serra, Espaces couleur et traitement dimages,CMM-Ecole des Mines de Paris, Internal Note N-34/02/MM, October 2002, 13 p.

[20] J. Serra, Image Segmentation, in Proc. IEEE Conf.on Image Processing (ICIP03), Barcelona, Spain,September 2003.

[21] A. Velazquez and S. Levachkine, Text/Graphics sep-aration and recognition in raster-scanned color carto-graphic maps, in Proc. of the 5th IAPR InternationalWorkshop on Graphics Recognition, GREC03), 92103, Barcelona, Spain, 2003.

[22] L. Vincent, Grayscale area openings and closings,their efficient implementation and applications, in(Serra and Salembier Eds.), Mathematical Morphol-ogy and its Applications to Signal Processing, Proc.ISMM93, UPC Publications, 2227, 1993.

[23] G. Wysecki and W.S. Stiles, Color Science : Conceptsand Methods, Quantitative Data and Formulae, 2ndedition. John Wiley & Sons, New-York, 1982.