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Colour Mathematical Morphology For Neural Image Analysis

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IntroductionColour Morphology and Lattice TheoryFigure 1Figure 2Colour Spaces and Vectorial ProcessingFigure 3Figure 4Immunostaining Technique in Wholemount RetinasFigure 5Application for Retinas of MonkeysFigure 6Figure 7Figure 8Figure 9Figure 10Figure 11ResultsFigure 12Figure 13Figure 14Figure 15Figure 16Figure 17Figure 18ConclusionsFigure 19Figure 20AcknowledgementsReferencesColour Mathematical MorphologyFor Neural Image AnalysisThis paper presents an algorithm for automatic neural image analysis in immunostainedvertebrate retinas. We present a useful tool for cell quantification avoiding the losst ofinformation of traditional binary techniques in automatic recognition of images. Theapplication is based on the extension of the mathematical morphology to colour images. In qthepaper, we define the basics and more complex morphological operations to vectorial imageprocessing. We propose and demonstrate a colour image reconstruction by geodesic transforma-tions. In addition, we adapt the morphological segmentation of greyscale image to thesegmentation of multispectral images of retinas of monkeys.# 2002 Elsevier Science Ltd. All rights reserved.F. Ortiz1, F. Torres1, E. De Juan2and N. Cuenca31Department of Physics, Systems Engineering and Signal TheoryUniversity of Alicante, P.O. Box 99, 03080 Alicante, SpainE-mail: [email protected] of Physiology, Genetics and MicrobiologyUniversity of Alicante, P.O. Box 99, 03080 Alicante, SpainE-mail: [email protected] of Biotechnology, University of AlicanteP.O. Box 99, 03080 Alicante, SpainIntroductionFor years, analysis of biomedical images has beenincreasingly important in medical research and diag-nosis generation. The use of image processing tools isvery essential when images to analyse are very numerousor these do not have good quality. The medicalresearcher only interprets the results and offers his finaldiagnosis with the automatically processed image. Inthis paper, we present a new algorithm for segmentationand classification of neural images of monkeys.Number and diameter quantification of cells isimportant in cell biology, but it is a hard and tediouswork. The commercial and available software forautomatic image analysis is very useful in this sense,but all the images need to be binarized in this software.The binary process transforms a greyscale or colourimage to a binary image with a consequent loss ofinformation: the programs confuse two cells that areconnected like a single particle and cells with back-ground.In the present study, we use images from normalretinas of monkeys to identify the number of dopami-nergic and calretinin cells. Both cell types are importantin the retinal visual information processing and areinvolved in retinal disease. In Parkinson’s disease,retinal dopaminergic and calretinin cells are alteredand produce visual abnormalities. The quantification ofthese cell types allows us to determine the degree ofdamage in this disease. In this paper, we present an1077-2014/02/$35.00 r 2002Elsevier Science Ltd. Alll rights reserved.Real-Time Imaging 8, 455–465 (2002)doi:10.1006/rtim.2002.0288, available online at http://www.idealibrary.com onalgorithm for neural image analysis based on geodesictransformations for the reconstruction of colour images.We will extend the classical morphological operations tocolour images.Morphological image processing is a nonlinear imageprocessing developed by Matheron and Serra [1,2]. Thisprocessing technique has proved to be a powerful toolfor many computer-vision tasks in binary and greyscaleimages, such as edge detection, noise suppression, imageenhancement, skeletonization, segmentation, patternrecognition, etc.The extension of mathematical morphology to colourimage is not straightforward [3]. Mathematical mor-phology is based on the set theory (complete lattice)where the notion of order is very important. In binaryand greyscale images, the pixels are ordered by theirvalue but, in colour images, each pixel is vector-valued(RGB, HSI, HSV, etc.). There is, therefore, no naturalorder for vectors, and as such, the extension ofmorphological operations to colour images requires aspecific study of the order in multivariate data.In the following section, we comment the state of theart in colour morphology. Later, the method chosen forcolour image processing will be shown. Next, we willexplain the application of colour morphology in theprocessing of images from retinas of monkeys. Later on,we develop the algorithm used here and we show theresults obtained.Colour Morphology and Lattice TheoryIn colour images, the pixels are represented by vectorialvalues in which vector element is a greyscale imageP(x, y)=[P1(x, y), P2(x, y), P3(x, y)]T[4]. Trahanias andVenetsanopoulos [5] summarized several techniques forordering multivariate data. The two main approaches toprocessing are marginal ordering and vectorial ordering.In [3] Comer and Delp commented on the differencesbetween marginal and vectorial processing. With mar-ginal ordering, each component P1, P2or P3is orderedindependently and the operations are applied in eachcolour channel of the image (Figure 1).The use of marginal ordering in colour imageprocessing is the most straightforward approach. Never-theless, this method may introduce visual changes incolour and may be unacceptable in applications that usecolour for object recognition (as in our case). A vectorialmethod for morphological processing is more advisablefor avoiding the above-mentioned disadvantages. Invectorial ordering only one processing is done on three-dimensional (3D) data (Figure 2). In vectorial data,there are several ways of establishing the order:K Ordering by one component.K Canonical ordering.K Ordering by distance.K Lexicographical orderIn ordering by one component, the ordering is decided byjust one element. In canonical ordering, all threecomponents of a colour space must have either higheror lower values than another vectorial colour. Inordering by distance, a distance function is used as anorder measure, etc In [6,7] these methods are discussedin greater detail.The lattice description of morphology allows mor-phological theorems and techniques to be applied toimages other than binary or greyscale [8–10]. A lattice isa partially ordered set in which any two elements possessa least upper bound (called supremum) and a greatestlower bound (infimum). The supremum and the infimumare represented by the symbols _ and ^,


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