MORPHOLOGICAL QUANTIFICATION OF AORTIC CALCIFICATION FROM LOW MAGNIFICATION IMAGES

Image Anal Stereol 2003;22:81-89 Original Research Paper MORPHOLOGICAL QUANTIFICATION OF AORTIC CALCIFICATION FROM LOW MAGNIFICATION IMAGES J ES ÚS A NGULO1, T HAO N GUYEN -K HOA2, Z IAD A. M ASSY2, T ILMAN D R ÜEKE 2 AND J EAN S ERRA1 1 Centre de Morphologie Mathématique, Ecole des Mines de Paris, 35, rue Saint-Honoré, 77305 Fontainebleau, France, 2 Laboratoire INSERM U 507, Hôpital Necker, 161, rue de Sèvres, 75015 Paris, France e-mail: angulo,serra @cmm.ensmp.fr,massy@necker.fr (Accepted May 14, 2003) ✁ ABSTRACT Atherosclerotic and medial vascular calcifications are frequent in chronic renal failure patiens and predict their increased cardiovascular mortality. Experimental models for mice have been recently developed in order to study these disorders. The aim of this paper is to present the morphological image processing algorithms developed for the semi-automated measurement of calcification from sections of aorta stained using von Kossa’s silver nitrate procedure and acquired at low magnification power ( 2 5) on colour images. The approach is separated into two sequential phases. First, the segmentation is aimed to extract the calcification structures and on the other hand to demarcate the region of the atherosclerotic lesion within the tissue. The segmentation yields the image data which is the input to the second phase, the quantification. Calcified structures are measured inside and outside the lesion using a granulometric curve which allows the calculation of statistical parameters of size. The same operator computes the shape of the lesion. The relative proportion of the area of calcification is also calculated respectively for the atherosclerotic lesion area and the area outside such lesions. In conclusion, the here developed method allows quantification of vascular calcified deposits in mouse aorta. This method will be useful for the quantitative assessment of pathological vascular changes in animals and man. ✂ ✄ Keywords: aortic calcification, automation in bioimaging, low magnification histology, mathematical morphology, nephrology, quantitative image analysis. INTRODUCTION widely used for detection of calcifi cation (Lardenoye et al., 2002). Atherosclerotic and medial vascular calcifi cations are frequent in chronic renal failure patients and predict their increased cardiovascular mortality. Experimental models for mice have been proposed in order to study these disorders (Muntzel et al., 2002). The detection of coronary artery calcium, using mainly fluoroscopy, has been shown to be of value in predicting artery disease (Margolis et al., 1980; Reinmuller and Lipton, 1987; Tanenbaum et al., 1989). Recently, electron beam tomography has been introduced for the detection of coronary calcium (Agatston et al., 1990; Morgan-Hughes et al., 2002). In previous studies, mathematical morphology has shown its ability for solving bioimaging problems from low magnifi cation power images in haematological cytology (Angulo and Flandrin, 2003). Such morphological approaches have also been applied successfully to other issues in nephrology (Moreso et al., 1994; Seron et al., 1996). MATERIALS AND METHODS STAINED AORTIC LOW MAGNIFICATION IMAGE The purpose of the present work is to propose an image-based method of quantifi cation for the uremiaenhanced vascular calcifi cation in the aortic root, which allows the evaluation of previously established biological models. The model of apolipoprotein E gene knockout mice has been initially created by homologous recombination in embryonic stem cells. This genetically engineered mouse generates The images were derived from thin sections atherosclerotic lesions within weeks after birth that of aortic tissue. The aim is the extraction and are similar to those found in humans (Zhang et al., quantifi cation of calcifi cation deposits. Confi rmation 1992; Ishibashi et al., 1994). We created chronic renal of the presence of calcifi cation is provided by staining failure in these mice by cortical electrocauterization in one kidney and ablation of the contralateral kidney using von Kossa’s silver nitrate method which is 81 A NGULO J ET AL : Morphological quantification of aortic calcium two weeks later. After sacrifi ce, the aortic arch was cut into serial sections in a cryostat. Sections were stained with von Kossa’s silver nitrate method. The animals were treated according to the recommendations of animal care committees, under anesthesia (Protocol: short term anesthesia of a duration of 30-40 min; one IP injection composed of 75 µl Rompun 2% in 25 ml vial, 300 µl Ketamine CLORKETAM 1000 in 10 ml vial, 1.53 ml 0.09% NaCl; the amount of the anesthetic fluid administered 100 120 µl / 20 g body weight). (a) (b) Fig. 1. Images under two magnification powers 10) of a section of the aortic ( 2 5 and sinus showing the elements of interest: tissue, atherosclerotic lesion and calcification structures. ✁ ✁ ✂ In Fig. 1 are depicted two colour images under two magnifi cation powers ( 2 5 and 10) of a section of the aortic sinus showing the elements of interest: tissue, atherosclerotic lesion and calcifi cation structures. In this study, the series of colour images were acquired under very low magnifi cation power at 2 5. The main advantage is that in one image fi eld all the tissue to be examined is included; however there is a considerable drawback since the quality of the structures is mediocre. Therefore the automation of the segmentation and quantifi cation procedures involves the development of specifi c algorithms using advanced techniques of image analysis. This is the rationale behind the use of mathematical morphology operators. As one can see from Fig. 1, other alternatives are possible. For instance, working at the magnifi cation power of 10 and using a motorized microscope is an alternative to acquire several subimages to cover the whole area of interest. This approach has however serious drawbacks including defi nition of lesion at 10, extraction of the whole calcifi cation region and merger of quantifi ed data (overlapping of images). ✁ (c) ✁ ✂ ✁ ✂ (d) ✁ (e) ✁ Fig. 2. Example of microscopic field image from a section of aorta stained using the von Kossa method at low magnification power ( 2 5): (a) RGB colour image fRGB , (b) red component fR , (c) green component fG , (d) blue component f B , (e) saturation component fS . The size of the image is 672 538 pixels on a rectangular raster with 256 grey tone levels for each red, green and blue colour channels. We consider for quantifi cation that at 2 5 magnifi cation and for the resolution used, the size of a pixel is 5 5 µm2 pixel. ✁ ✁ ✂ ✁ ✂ ✄ ✂ 82 Image Anal Stereol 2003;22:81-89 – Fig. 2 is an example of colour image to be processed, fRGB . The red fR , green fG and blue fB colour component images are shown and beside this, the saturation component f S of a 3D-polar coordinate colour representation✁ (Hanbury and Serra, ✁ 2002). ✁ ✁ For✁ a colour ✁ pixel c r✂ g ✂ b ✄ ; i.e. fRGB ✁ c ✄☎ fR c ✄✆✂ fG c ✄✆✂ fB c ✄✝✄ the saturation coordinate f S c ✄ is obtained by the simple expression ✁ ✁ fS c ✄✞ max r✂ g ✂ b ✄ ✁ min r✂ g ✂ b ✄ ✂ – – – In order to detect the tissue in the fi eld image the simplest means is to take f S where the biological structures are clearly defi ned, despite the shading effect (non-uniform illumination). – ✁ f x y✄ ☞ ✁ ✁ opening: γ B f ✄✑ δB ✒ εB f ✄✔✓ ✁ ✁ closing: ϕ B f ✄✞ εB ✒ δB f ✄✔✓ The morphological openings (closings) fi lter out light (dark) structures from the images according to the predefi ned size and shape criterion of the structuring element. Using the spectral properties of the staining procedure on the tissues (calcifi cations appear black and tissues red-pink), we use the colour component images in the following way: The calcifi cation is relatively more contrasted against the rest of tissues in f R , therefore this component is used for extracting the calcifi cations. ✎ ✠ y B The two elementary operations of erosion and dilation can be composed together to yield a new set of operators having desirable feature extractor properties which are given by: (1) – ✁ ✁ erosion: ε B f x ✄☛✄✞ inf ✏ The top-hat transformation is a powerful operator which permits the detection of contrasted objects on non-uniform backgrounds (Meyer, 1977). There are two versions: – – For segmenting the region of the atherosclerotic lesion a combined method of thresholding and manual interaction is achieved from f G . white top-hat: The ✁ residue✁ of the initial ✁ image f and an opening γ f ✄ ; i.e. ρ f ✄✕ f γ f ✄ , extracts bright structures, ✁ black top-hat: The residue of ✁ a closing ϕ f ✄ and ✁ the initial image f ; ρ ✖ f ✄✗ ϕ f ✄ f , extracts dark structures. Usually, the top-hat is accompanied by a thesholding operation, in order to binarise the extracted structures. Through this choice of the colour components, the color shading effect is negligible. Anyway, a method for shading correction of color images (Tomaževič et al., 2002; Derganc et al., 2003) can be used in applications with important multispectral inhomogeneities. A granulometry is the study of the size distributions of the objects of an image. Formally, a granulometry can be defi ned as a family of openings ✁ γn ✄ n ✘ 0 such that ✙ n ✚ 0 ✂✛✙ m ✚ 0 ✂ γn γm γm γn Γ γmax ✜ n ✢ m✣ . Moreover, granulometries by closings (or anti-granulometry) can also ✁ be defi ned as families ϕ ✄ n ✘ 0 . Performing the of increasing closings Φ MORPHOLOGICAL IMAGE PROCESSING granulometric analysis of an nimage f with Γ is AND QUANTIFICATION equivalent to mapping each opening of size n✁ with ✁ ✁ ✤ ☛ ✄ ✄ γ f of the opened image. ✤ f ✄ is a measure n First introduced as a shape-based tool for binary the area of f in the binary case (number of pixels) images, mathematical morphology has become a very and the volume in the grey scale case (sum of pixel powerful nonlinear image analysis technique with values). The size distribution or ✁pattern spectrum of operators capable of handling sophisticated image f with respect to Γ, denoted PSΓ f ✄ is defi ned as the processing tasks in binary, grey-scale, colour and following (normalised) mapping multiresolution imaging modalities. A tutorial in the technique can be found in (Serra, 1982, 1988; Coster ✁ ✁ PSΓ f ✂ n ✄✑ PS f ✂ n ✄✞ and Chermant, 1989). In this section we briefly review ✁ ✁ ✁ ✁ the basic morphological operators used in this work. ✤ γn f ✄✝✄ ✥✤✁ γn✦ 1 f ✄✝✄ ✂ n ✚ 0 (2) m f✄ In the framework of digital grids, a grey-tone ✁ image can be represented by a function f : D f ✟ T , f ✄ maps each size n to The pattern spectrum PS 2 Γ where D f is a subset of Z and T ✡✠ tmin ✂ ☛✂ tmax ☞ is an some measure of the bright image structures with ordered set of grey-levels. Let B be a subset of Z2 and this size (loss of bright image structures between✁ two s ✌ N a scaling factor. sB is called structuring element successive openings). The pattern spectrum PSΓ f ✂ n ✄ (shape probe) B of size s. The basic morphological is a probability density function (a histogram): a large operators are: impulse in the pattern spectrum at a given scale ✁ ✁ ✁ indicates the presence of many image structures at that – dilation: δ B f x ✄☛✄✍ supy ✎ B ✠ f x y ✄ ☞ ✂ ✂ ✂ ✂ 83 A NGULO J ET AL : Morphological quantification of aortic calcium the convergence to the u’s. An alternative to make the choice of ✒ u1 ✂ u2 ✓ easier is a method which relies on a double thresholding combined with a geodesic reconstruction; the technique is known as thresholding by hysteresis (Soille, 1999). For instance, in order to extract light structures we have to take u 2 tmax and let uTlow be a low threshold value and uThigh be a high threshold value. Using this double threshold, two ✁ binary images are obtained: Iwide T✡ uTlow ✢ tmax ☛ f ✄ and ✁ Inarrow T✡ uThigh ✢ tmax ☛ f ✄ . The fi nal binary image is given by the reconstruction of Iwide using Inarrow as a marker; i.e. scale. It is also possible to use standard probabilistic defi nitions to compute the moments of PS.✁ The fi rst µ 1 ∑n nPS f ✂ n ✄ , the moment µ is given by µ k-th pattern ✁ spectrum moment, k ✚ 2, is computed ✁ k n µ f n . In particular, the fi rst PS as µ k ✄ ✂ ✄ ∑n four moments: mean µ , variance µ 2 , skewness µ 3 and kurtosis µ 4 are often used. Using a pair of an opening γ and a closing ϕ as primitives, an operator of contrast enhancement can be obtained (Serra, 1989). This toggle mapping or two states contrast κ is generated by the following criterion applied to each point x, ✁✂✂✂ ✁ ✁ ✂✂✂ γ f ✁ x ✄✝✁✄ ✂✂✂ ✁ ✁ κ f x ✄✝✄ ϕ f x ✄✝✄ if ✁ f x ✄✝✆ ✁ ✁ ✁ f x✄ γ f x ✄✝✄ ✄ ϕ ✁ f ✁ x ✄✝✄ if ✂✂✂ ✁ ✁ ✁ ✁ ϕ f x ✄✝✄ f x ✄✝✞ f x ✄ ✂✂✂ ✂✂✂☎ ✁ γ f x ✄✝✄ f x ✄ ✁ ✁ if ϕ f x ✄✝✄ ✁ f x ✄✕ ✁ f x✄ ✁ ✁ ✁ ✁ I low γ f x ✄✝✄ such that f ✄✑ δgi ✦ 1 ✁ ✁ ✁ (6) We start by binarising the saturation component f S for detecting the tissue presented in the fi eld image by using a simple thresholding operation at uT1 (a low value; e.g. uT1 10, has shown to be suitable for this kind of images), see Fig. 3(a), f ✄ (idempotence). I x ✄✑ T✡ u1 ✢ u2 ☛ f x ✄☛✄✍✌☞ ✂ (4) The thresholding transformation of the image f between the grey levels u1 and u2 (typically u1 tmin ✁ or u2 tmax ), T✡ u1 ✢ u2 ☛ f ✄ , yields the binary image I such that for each pixel x the binary value is given by ✁ ✁ ✁ rec ☛ f ✄✞ γ Inarrow ✂ Iwide ✄ Detection of tissue in the field image ✁ γ rec g ✂ f ✄✑ δgi f ✄ ✁ uThigh ✢ tmax The approach is separated into two sequential phases. First, the segmentation is aimed on the one hand to extract the calcium structures and on the other hand to demarcate the region of the lesion on the tissue. The segmentation yields the image data which are the input to the second phase, the quantifi cation. The calcifi cation structures are measured inside and outside the lesion using a granulometric curve which allows to calculate some statistical parameters of size. The same operator is used to compute the shape of the lesion. The relative proportion of area of calcifi cation is also calculated. A morphological tool that complements the opening and closing operators for feature extraction (extract the marked particles) is the morphological reconstruction, implemented using the geodesic dilation operator based on restricting the iterative dilation of ✁ a function marker f by B✁ to a function ✁ ✏ ✁ mask g, δgn f ✄✍ δg1 δgn 1 f ✄ , where δg1 f ✄✍ δB f ✄✠✟ g. The reconstruction by dilation is defi ned by δgi ✎✑✏ ALGORITHMS (3) The closing and the opening may be replaced by a dilation and an erosion of f . ✁ T✡ hyst uT Is ✁ 1 u1 ✍ f x ✄ ✍ u2 0 otherwise . (5) ✁ T✡ uT1 ✢ tmax ☛ fS ✄ ✂ (7) In order to remove the noise and mistakes due to the small pieces of tissue (histology artefact), the image is then fi ltered by applying a reconstruction using an opening as the marker, The choice of ✒ u1 ✂ u2 ✓ determines the set of grey levels associated with the object of interest. The histogram summarises the grey-level contents of an image and typically, the optimal threshold values can be obtained from an analysis of the histogram, see in (Angulo and Flandrin, 2003) the method of automated thresholding which combines the classical selection of the threshold value by minimising the sum of within class variances with a morphological technique for selecting the central mode values which speeds up Itissue ✁ ✁ γ rec γs1 B Is ✄✆✂ Is ✄ ✂ (8) with s1 such that s1 B is larger than the size of the noise and the small artefact pieces of tissue (good results were obtained with s1 5); the structuring element B is a circle. See the result in Fig. 3(b). 84 Image Anal Stereol 2003;22:81-89 (a) (a) (b) (b) Fig. 3. Detection of tissue in the field image: (a) Binary image after thresholding saturation component, Is ; (b) cleaned binary mask of tissue, Itissue . (c) Interactive segmentation of the region of atherosclerotic lesion In the tissue, the atherosclerotic lesion zone squares with a texture of tissue less thick than the rest, recognising visually, but its precise morphological defi nition is almost impossible. Therefore due to the fact that the automated segmentation of the lesion on the tissue can not be achieved without some mistakes and in order to avoid the propagation of these errors to the quantifi cation step, we preferred to developed an interactive approach. (d) In a fi rst step the human expert must perform a manual dot-marking of the region of interest (ROI) using the computer mouse on the colour image. This zone associated to the lesion has to be closed, see Fig. 4(d), but it is possible for the human user to demarcate several closed partial ROI’s: the defi nitive ROI is the union of the partial ones and is represented by the binary image Imrk . (e) Fig. 4. Interactiv segmentatio of the region of lesion: (a) Simplified green component using an opening by reconstruction, f G ; (b) followed by closing by reconstruction, fG ; (c) negative of the binary mask without empty image zones, I g ; (d) manual dotmarking region of interest, Imrk ; (e) binary mask of lesion inside the region of interest, Ilesion . The automated step works on the green component fG . This image is simplifi ed by means of an opening by reconstruction (which simplifi es the light structures), fG ✁ ✁ γ rec γs2 B fG ✄✆✂ fG ✄✆✂ (9) 85 A NGULO J ET AL : Morphological quantification of aortic calcium followed by a closing by reconstruction (which simplifi es the dark structures), ✁ ✁ ϕ rec ϕs3 B fG ✄✆✂ fG ✄✆✂ fG (10) where the sizes of the opening and the closing 15 and s3 have been empirically fi xed to s2 10 respectively (B is a circle). The corresponding example of tissue image after simplifi cation is shown in Fig. 4a - b. The image f G must be binarised for extracting the empty zones (zones of the fi eld without tissue); the optimal threshold value uT2 for each image is obtained by the algorithm presented in Angulo (02). The result of this thresholding process at uT2 , ✁ T✡ tmin ✢ uT2 ☛ fG ✄✆✂ Ig (a) (11) is a fi rst binary mask which is then restricted to the manual defi ned Imrk to obtain the binary mask of the region of lesion, Imrk ✟ Ig Ilesion (b) (12) ✂ See the result in Fig. 4e. Extraction of calcification In the red component of the aortic section colour image fR the calcium appears as dark structures upon a bright background. In order to enhance the contrast of the calcifi cations against the background a toggle mapping is taken, ✁ κ fR ✄✆✂ fR (c) (13) Fig. 5. Extraction of calcification: (a) Contrast enhancement of calcification on red component, fR ; (b) extracted calcification by means of a dual top-hat, f c ; (c) binary mask of calcification after thresholding by hysteresis, Icalci f . where the two primitives of κ are an erosion and a dilation of size 3, see Fig. 5(a). From this image, a black top-hat of size s4 extracts the calcifi cation (s4 corresponds to the size of the biggest calcium structures which can be found); experimentally we have fi xed s4 25 with a circular structuring element, fc ✁ ρ ✖ fR ✄ Quantification of atherosclerotic lesion ✁ (14) ✂ ✁ I ✄ be the surface area; i.e., number of pixel Let to ones, of the binary image I. We start by calculating the size of the tissue and the lesion regions, ✁ Atissue On the image fc , Fig. 5(b), a thresholding by hysteresis is performed to provided the binary mask of calcifi cations (see Fig. 5(c)), Icalci f T✡ uhyst T low ✎✑✏ uThigh ✢ tmax ☛ ✁ f✄ ; ✁ Itissue ✄ ✂ ✁ Alesion ✁ Ilesion ✄ ✂ (16) We propose to characterise the shape of the lesion region by means of a pattern spectrum curve, ✁ PSlesion . The structuring elements are PS Ilesion ✂ n ✄ circles of increasing size n 2 (in fact, the practical shape is an octagon: isotropic approach to a circle 4 to n 70. The in the square grid), from n granulometric curves describe in a compact way the different thickness of the wall of the aortic valves: each (15) ✂ the choice of the threshold values is not so critical (the top-hat facilitates just the thresholding); e.g. u Tlow 50 and uThigh 70. 86 Image Anal Stereol 2003;22:81-89 peak corresponds to the thickness of a sector of the wall. These histograms of shape can be parametrised by using their statistical moments. The surface area in pixels of an octagon of size n is given by the formula 7n2 4n 1. In order to (Serra, 1982), Noctagon 2 obtain the sizes in µm we have to multiply the area in pixels by 5 5 µm2 pixel for all the measurements. ✂ ✂ ✄ ✂ (a) Quantification of calcification In order to quantify the calcium, we compute fi rst the absolute and the relative surface of calcifi cations inside and outside the lesion, ✁ ✁ Acalci f i Acalci f o ✁ ✁ Icalci f Icalci f Acalci f Acalci f o Ilesion ✄ ✂ ✁ Itissue Ilesion ✄✝✄✆✂ ✟ ✟ i ✁ ✁ ✁ Acalci f i ✁ ✂ Ilesion ✄ Acalci f Itissue Fig. 6. Two examples of aortic section images: (a) with low calcification content (mouse 35); (b) riches in calcification (mouse 40). On the left, the initial images and on the right, summary of segmented structures: the background in black, the tissue in gray, the lesion in white and the calcification in red. (18) o Ilesion ✄ (b) (17) ✂ (19) Besides these parameters, the calcifi cation structures inside the lesion✁ are quantifi ed by using a size Ilesion ✂ n ✄ PScalci f i (the distribution, PS Icalci f structuring elements of openings are again circles of increasing size n 2, from n 3 to n 23) and its moments. Pattern spectrum of lesion 0.16 Mouse 35 Mouse 40 0.14 ✟ Normalised size (area) 0.12 ✂ RESULTS AND DISCUSSION 0.1 0.08 0.06 0.04 0.02 In Fig. 6 two examples of segmented aortic section images are depicted: one corresponding to a mouse with low calcifi cation content (control mouse) and another to high calcifi cation (uremic mouse). In Fig. 7 their associated pattern spectra are shown. 0 0 10 20 30 40 n (size of opening) 50 60 70 (a) 22 (b) Size distribution of calcification 0.8 Mouse 35 Mouse 40 0.7 In Table 1 the obtained parameters of the lesion are included. For mouse 35 the area of lesion is larger than for mouse 40, but above all, the thickness of the walls is considerably greater. Besides being used for determining the relative amount of calcium located inside, the size of the atherosclerotic lesion may be signifi cant a priori. However, due to the fact that during the tissue preparation procedure the shape of the atherosclerotic lesion may be modifi ed involuntarily, the practical usefulness of the parameters from PSlesion remains doubtful. Other techniques of tissue preparation could be envisaged in order to achieve more reproducible sections in such a way that the parameters associated to PSlesion will be very important. Normalised size (area) 0.6 0.5 0.4 0.3 0.2 0.1 0 2 4 6 8 10 12 14 n (size of opening) 16 18 20 Fig. 7. Quantification of size and shape using morphological granulometries (curves associated to the examples of Fig. 6): (a) Pattern spectrum of the region of lesion; (b) Size distribution of calcification structures inside the lesion. 87 A NGULO J ET AL : Morphological quantification of aortic calcium Table 1. Size (Atissue and Alesion ) and shape (first four moments of PSlesion ) parameters of lesion zone for the examples of Fig. 6. Mouse 35 Mouse 40 Atissue 120859 160483 Alesion 59079 78696 µ 38.55 51.17 Acalci f o 170 37137 Acalci f i 0.0139 0.5476 The approach has however several limitations. On the one hand, in order to minimise the errors of segmentation, an interactive algorithm was developed which involves a necessary human action for each image. Obviously, the task is simple (some “clicks” of mouse) but time consuming. The balance between automation and precision leads sometimes to this kind of approach. On the other hand, working on low magnifi cation microscopic images entails that the image structures can be very small, limiting the resolution of the methods. For instance in Fig. 7 (right), notice that the size distribution of calcium for the control mouse (small calcifi cation structures) is limited to the openings of size n 3 and 5. The classical problem of reproducibility of histologic preparations (sectioning, staining, etc.) must be also taken into account in order to prevent artefacts, like dust or others. Acalci f o 0.0014 0.2314 (a) Mouse 35 Mouse 40 µ 2.19 5.59 µ2 µ3 0.39 74.21 0.48 12.92 µ4 208019.51 720299.94 ✂ Table 2. Surface area parameters and first four moments of PScalci f i of lesion zone for the examples of Fig. 6. Acalci f i 821 43094 µ3 -1176.89 -206.51 has been used. The results of the interactive human segmentation of the atherosclerotic lesion and the extraction of calcifi cation have been subjected to evaluation by another human grader in order to fi nd out serious mistakes: only 3 cases among the set of 173 have been rejected and manually corrected (1 7%). In view of these results we can state that the behaviour of the image analysis algorithms is quite satisfactory. Regarding the parameters of calcifi cation, summarised in Table 2, the use of this set of parameters yields an easy way to identify the different levels of calcifi cation. Obviously, the most interesting parameters are the relative surfaces of calcifi cation and the two fi rst moments of size distribution: the mean size of calcium structures and the variance of size (which gives an idea of size dispersion and is helpful for distinguishing large compact calcifi cations from large disintegrated calcifi cations). Mouse 35 Mouse 40 µ2 293.03 647.21 µ4 0.32 729.99 (b) The robustness of an algorithm can be defi ned with respect to changes in the parameters or to image quality. The present algorithms have seven confi gurable parameters: uT1 (threshold value for the tissue determination on f S ), s1 (size of the tissue fi ltering on fS ), s2 and s3 (size of the tissue simplifi cation on fG ), s4 (size of the calcium enhancement on fR ), uTlow and uThigh (threshold values for the calcium extraction on f R ). The threshold value uT2 is obtained automatically for each image. The values proposed for the other parameters have been set after empirical tests on a random selection of 10 images which covers the different levels of pathology and image quality. Someone who would like to use these methods with a different magnifi cation or a different camera has to start by using a training set of images (representative of its problem) in order to adjust the values of parameters. In any case, some tests of images at 10 have shown that the approach is quite robust. CONCLUSION The robustness and accuracy of segmentation results allowed us to consider the subsequent quantifi cation as a correct procedure. The morphological parameters obtained have been analysed and correlated to several biomedical parameters (Massy et al., 2003). We also envisage to apply this quantifi cation approach to the study of calcifi cation using non-invasive techniques, for instance by obtaining the morphological information by means of electron beam tomography or other imaging technique. In the previous studies based on computed tomography (Agatston et al., 1990, Morgan-Hughes et al., 2002), the quantifi cation of calcifi cation has not been attempted using morphological techniques. ✁ Once these parameters were fi xed, a deep study has been performed on the basis of the present methods. A database of 173 images corresponding to 45 mice To summarise the algorithmic discussion above, we conclude that quantitative measurements of 88 Image Anal Stereol 2003;22:81-89 histologic sections by morphological image analysis software are very useful. They provide a powerful tool for improving and automating experimental studies on structural-functional correlations in tissues with histopathologic changes. Meyer F (1977). Constrast features extraction. In: Chermant JL, ed. Quantitative Analysis of microstructures in Materials Science, Biology and Medecine. Stuttgart: Riederer Verlag, 374-80. Moreso F, Ser´on D, Vitri´a J, Griny´o JM, Colom´e-Serra FM, Par´es N, Serra J (1994). Quantification of interstitial chronic renal damage by means of texture analysis. Kidney 46:1721-7. ACKNOWLEDGMENTS The authors thanks the comments and suggestions of the anonymous reviewers. Morgan-Hughes GJ, Roobottom CA, Marshall AJ (2002). Aortic valve imaging with computed tomography: A review. J Heart Valve Disease 11(5):604-11. REFERENCES Agatston AS, Janowitz WR, Hildner FJ, Zusmer NR, Viamonte M, Detrano R (1990). Quantification of Coronary Artery Calcium Using Ultrafast Computed Tomography. J Am Coll Cardiol 15:827-32. Muntzel M, Massy ZA, Ruellan N, Descamps-Latscha B, Lacour B, Drueke TB (2002). Chronic renal failure increases oxidative stress and accelerates atherosclerosis in apolipoprotein-E knock-out (EKO) mice (Abstract). Nephrol Dial Transplant 17:46. Angulo J, Flandrin G (2003). Automated detection of working area of peripheral blood smears using mathematical morphology. Anal Cell Pathol 25:37-49. Reinmuller R, Lipton MJ (1987). Detection of coronary artery calcification by computed tomography. Dynam Cardiovasc Imag 1:139-45. Coster M, Chermant JL (1989). Pr´ecis d’analyse d’images, 2nd. ed. Paris: Les Presses du CNRS. Derganc J, Likar B, Bernard R, Tomaževič D, Pernuš F (2003). Real-time automated visual inspection of color tablets in pharmaceutical blisters. Real-Time Imaging 9:113-24. Ser´on D, Moreso F, Gratin C, Vitri´a J, Colom E, Griny´o JM, Alsina J (1996). Automated Classification of Renal Interstitium and Tubules by Local Texture Analysis and a Neural Network. Anal Quant Cytol Histol 18:410-9. Hanbury A, Serra J (2002). A 3D-polar Coordinate Colour Representation Suitable for Image Analysis. Submitted to Comput Vis Image Und. Serra J (1982). Image Analysis and Mathematical Morphology. Vol I. London: Academic Press. Serra J (1988). Image Analysis and Mathematical Morphology. Vol II: Theoretical Advances. London: Academic Press. Ishibashi S, Herz J, Maeda N, Goldstein JL, Brown MS (1994). The two-receptor model of lipoprotein clearence: Tests of the hypothesis in ”knockout” mice lacking the low density lipoprotein receptor, apolipoprotein E, or both proteins. Proc Natl Acad Sci USA 91:4431-5. Serra J (1989). Toggle mappings. In: Simon JC, ed. From Pixels to Features. Amsterdam: North Holland, 61–72. Soille P (1999). Morphological image analysis. Berlin, Heidelberg: Springer-Verlag. Lardenoye J, de Vreis M, lowik C, Xu C,Dhore C, Cleutjens, J van Hinsberg V, van Bockel J, Quax P (2002). Accelerated atherosclerosis and calcification in vein grafts. Circ Res 91:577-84. Tanenbaum SR, Dondos GT, Veselik KE, Prendergast MR, Brundage BH, Chomka EV (1989). Detection of calcific deposits in coronary arteries by ultrafast computed tomography and correlation with angiography. Am J Cardiol 63:870-2. Margolis JR, Chen JTT, Kong Y, Peter H, Behar VS, Kisslo JA (1980). The diagnostic and prognostic significance of coronary artery calcification. Radiology 137:609-16. Tomaževič D, Likar B, Pernuš F (2002). Comparative evaluation of retrospective shading correction methods. J Microsc-Oxford 208:212-23. Massy Z, Nguyen-Khoa T, Angulo J, Munzel M, Ivanovski O, Szumilak D, Ruellan N, Descamps-Latscha B, Lacour B, Drüeke T (2003) Uremia accelerates calcification in apolipoprotein E knock-out (EKO) mice. To be presented in 17th Congress of the International Society of Nephrology – 40th Congress of the European Renal Association, Berlin, June 8-12. Zhang SH, Reddick RL, Piedrahita JA, Maeda N (1992). Spontaneous hypercholesterolemia and arterial lesions in mice lacking apolipoprotein E. Science Oct 16;258(5081):468-71. 89