On a relaxation-labelling algorithm for quantitative assessment of tumour vasculature in tissue section images

Computers in Biology and Medicine 35 (2005) 157 – 171 http://www.intl.elsevierhealth.com/journals/cobm

On a relaxation-labelling algorithm for quantitative assessment of tumour vasculature in tissue section images Constantinos G. Loukasa; b;∗ , Alf Linneyb a

Gray Cancer Institute, P.O. Box 100, Mount Vernon Hospital, Northwood, Middlesex HA6 2JR, UK b Department of Medical Physics and Bioengineering, University College London, Shropshire House, 11-20 Capper Street, London WC1E 6JA, UK Received 26 June 2003; accepted 18 December 2003

Abstract Although tumour vasculature constitutes a biological factor playing a crucial role in the radiation response of tumours, the current procedures of assessment are semiquantitative, typically employing visual examination of stained histological material. Such techniques are also time consuming, and ine6cient of extracting essential information on the vascular network. Image analysis has yet to contribute signi8cantly in this direction, and most studies to date focus on blood vessel segmentation through empirical, user-selected thresholds. The present paper proposes an alternative segmentation approach, based on a probabilistic relaxation algorithm, applied in microscopic images of stained tissues. After image partitioning various information is obtained, such as vascular domains and geometrical characteristics of vessels. ? 2004 Elsevier Ltd. All rights reserved. Keywords: Medical image analysis; Histology; Segmentation; Vessel counting; Probabilistic relaxation; Clustering; Vasculature

1. Introduction Tumour vasculature is a biological feature that plays a crucial role in the radiation response of solid tumours, and the importance of blood ?ow for the outcome of radiation treatment, was described many years ago [1]. In principle, the growth of a malignant tumour requires the formation of ∗ Corresponding author. Present address: Sobell Department of Motor, Neuroscience and Movement Disorders (Box 146), Institute of Neurology, 8-11 Queen Square, London WC1N 3BG, UK. Tel.: +44-20-7837-3611x4319; fax: +44-20-7278-9836. E-mail address: [email protected] (C.G. Loukas).

0010-4825/$ - see front matter ? 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.compbiomed.2003.12.004

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a new blood vessel network, a process called angiogenesis, which is chaotically organised, leading to a heterogeneous tumour blood supply both spatially and temporarily [2]. Neovascularisation is also believed to be related directly to the metastatic potential of a tumour [3]. Consequently, quantitation and inhibition of angiogenesis might be promising diagnostic and therapeutic approaches. Although recent discoveries have created intense interest in the use of anti-angiogenic drugs for cancer treatment, signi8cant problems surround its clinical application such as the identi8cation of reliable indicators for patients requiring treatment. Non-invasive assessment of tumour vascularity is possible in vivo by means of Doppler sonography, dynamic contrast-enhanced magnetic resonance imaging (MRI), and positron emission tomography (PET). Although these methods may be useful in monitoring the eKect of anti-angiogenic therapy, histology remains the ‘gold standard’. For example, neovascularisation and its in?uence on survival has been studied in various types of carcinomas such as breast [4], head and neck [5], cervix [6], and skin [7]. However, the results of these studies are con?icting, partly because of the diKerences in the existing methodologies of quanti8cation, usually employing manual counting of the number of vessels stained with an antibody (e.g. CD31). Recently, some investigators have attempted to obtain more objective results by performing computer-assisted vessel detection, aiming to circumvent the problems of subjectivity and ill-reproducibility posed during manual counting, and also to decipher more complex information for the tumour examined [5,6,8,9]. However, the number of published papers is still very limited, especially if one considers how much research has focused on the adjacent, but rather more popular, area of cytology automation. Moreover, the degree of success of those image analysis studies was restricted as only rather simple vascular images were analysed, using often arbitrary thresholds, which introduce inevitably a considerable element of subjectivity. There are very few of these studies reporting validation experiments and comparison with manual counting. In this paper a comprehensive image analysis approach is described for automated segmentation, as well as for quantitative analysis, of tumour vasculature in tissue sections. The proposed multistage algorithm is based on a probabilistic grey-level clustering technique, designed to meet the requirements of the vessel detection task. The primary aim of the research was to develop a fast and easily applicable method that could be used in routine clinical practice for detecting microvessels in large-scale histological images acquired by conventional microscopy. The results described below exhibit the potential of such methodology in this least-investigated 8eld of vascular image analysis. 2. Materials 2.1. Immunohistochemical staining of sections The material studied consisted of transitional cell carcinomas of the bladder of patients treated by accelerated radiotherapy carbogen and nicotinamide (ARCON). ARCON is introduced to overcome tumour resistance caused by hypoxia; accelerated radiotherapy enhancing tumour oxygenation by breathing carbon dioxide/oxygen, in conjunction with nicotinamide to improve tumour blood ?ow. The tumour material had been processed through standard procedures, embedded in para6n blocks and 4-m sections cut for immunohistochemistry. Blood vessels were identi8ed with a monoclonal

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antibody against CD31, which is expressed on the surface of endothelial cells. Visualization of the antibody complex was achieved with a chemical reaction using diaminobenzidine resulting in brown staining of the endothelial cell membranes. Mayer’s Haematoxylin was used also for counterstaining all other cell nuclei in blue. 2.2. Image analysis hardware and software The tissue-section images were captured using a Zeiss Axioscop trans-illumination microscope, coupled to a JVC KY55F 1=3

(6:4 × 4:8 mm) 3-CCD colour camera. The image acquisition software was an in-house developed module added to Visilog version 5.02 (Noesis S.A., France). The resolution of the images captured was 768 × 576 pixels and they were saved in a tagged image 8le (TIF) format. The captured images were digitised using a Matrox Meteor TM frame grabber, installed in a PCI bus 600 MHz PentiumTM PC. A × 40 objective (NAobj = 0:75), was used during acquisition, providing a compromise between adequate resolution and maximum 8eld of view of the regions of interest. The pixel size, at the object plane (230 × 173 m2 ) was 0:3 × 0:3 m2 . Prior to processing all images were examined for shade correction. The entire image processing algorithms and software reported here were developed in the C programming language, using the LabWindowsJ =CVITM 5.5 (National Instruments Corporation, USA) libraries. 3. Vessel segmentation using probabilistic relaxation 3.1. Algorithm design Research on image analysis of tissue sections has utilised extensively thresholding techniques, which are probably the most popular in the 8eld of image segmentation. The key-idea behind this methodology is based on the assumption that object and background pixels can be distinguished by their grey-level values. However, when the subpopulations of pixels overlap there will be a standard classi8cation error, as some object pixels will be classi8ed as background and vice versa. Rosenfeld demonstrated that these errors could be greatly reduced by taking into account the spatial relationships among the pixels, rather than simply classifying them on the basis of their grey levels (or other properties) [10]. This study involved a relaxation process aiming to classify image pixels probabilistically into ‘dark’ and ‘light’ clusters (based on their grey intensity values). Each cluster’s probabilities were then adjusted iteratively for each pixel, based on its neighbours’ probabilities, until no further change of pixel population between the two classes occurs. Prompted by this idea, a relaxation process applied for the vessel segmentation task would involve a set of image pixels A = {a1 ; a2 ; : : : ; an } (n is the number of image pixels) and a set of two labels L = {0 ; 1 }, which are the ‘blood vessel’ (BV) and ‘non-BV’ (NBV) classes, respectively. (As will be seen more clearly later, the NBV class essentially encompasses the similar-grey-level cell nuclei and histological background.) From now on we will refer to 0 as the ‘black class’, and 1 as the ‘white class’, imposing a cluster close to 0 and 255, respectively (i.e. the two limits of a grey-level image scale). Label 0 is meant to represent BV pixels, essentially because in the grey-scale version of the original colour image the blood vessels appear dark-grey, indicating that their intensity values range in the vicinity close to zero (i.e. black), whereas the opposite applies to 1 .

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For each pixel ai , a set of local measurements is used as a basis to estimate the following probabilities: pi (0 ) : Pixel i belongs to 0 if it initially belonged to 0 : qi (0 ) : Pixel i belongs to 1 if it initially belonged to 0 : qi (1 ) : Pixel i belongs to 1 if it initially belonged to 1 : pi (1 ) : Pixel i belongs to 0 if it initially belonged to 1 : The probabilities satisfy also the condition: pi (S ) + qi (S ) = 1

∀ai ∈ A; s = {0; 1}

and

0 6 pi (S ); qi (S ) 6 1:

(1)

The relaxation process is speci8ed by choosing a mode of interaction between pixels. The algorithmic steps followed by the algorithm are given below: Step 1: A critical condition is the initialisation scheme for the probabilities, as it aKects the convergence speed and the 8nal results. In contrast to the original method proposed by Rosenfeld, here we use logistic, instead of linear, functions: pi0 (0 ) =

1 ; 1 + e−((k−gi )=(k−min))

qi0 (0 ) = 1 − pi0 (0 ); qi0 (1 ) =

1 1+

e−(gi −k)=(max−k))

pi0 (1 ) = 1 − pi0 (1 );

(2) ; (3)

where , max and min are the mean, largest and smallest image grey-intensities, respectively, gi is the grey-level of the pixel i, and k is a regulatory factor, which from now on we will call mean shift. The superscript refers to the iteration which is currently zero. Also, k ∈ [0; 1] and it determines the point where pi0 (0 ) and qi0 (1 ) are equal. For example, when k = 0:8, ai has a higher probability of being included in the BV class (i.e. black class) if gi 6 0:8. Accordingly, ai has a higher probability of being included in the NBV class (i.e. white class) if gi ¿ 0:8. Thus, the mean shift is helpful if one wants, for example, to shift this equal probability ‘benchmark’ and give initially some preference exclusively to those pixels having very small grey-values, particularly close to 0, for being included in the BV class (k ¡ 1). The term  is called the decay rate, is always positive, and controls how non-deterministic the initial classi8cation is, regulating the slope of the exponential term. As will be shown more clearly in the Results, in contrast to the linear functions implemented in the original paper [10] the logistic functions used here aKect favourably the 8nal output and computational cost, whereas their parameters k and  give the algorithm a kind of ‘self-adaptation’ quality.

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Step 2: After the pixel probabilities are calculated, the statistical coe6cient C(i; S ; j; T ), denoting the compatibility between labelling ai by S and labelling aj by T , can be estimated by  1   if S = T;  − (2(g − g i j )=(max−min )+1) 1+e C(i; S ; j; T ) = (4)  −1   if S =  T; 1 + e−(2(gi −gj )=(max−min)+1) where S; T = {0; 1}, representing the two available classes 0 and 1 . C(i; S ; j; T ) is a function that returns a measure between the extreme limits of −1 and 1; that is, pixels are compatible if their grey-values agree. We used the concept of logistic probabilities also within the compatibility coe6cient in order to provide the algorithm with additional assets of ‘fuzziness’ during clustering, as opposed to the original relaxation method that had simply CA = 1 when S = T , and CA = −1 otherwise. Step 3: The 8nal updating formula for the probability of labelling ai at the (k + 1)st iteration step is pik+1 =

pik (1

pik (1 + Qi (0 )) : + Qi (0 )) + qik (1 + Qi (1 ))

(5)

A similar expression holds for the q values: qik+1 =

qik (1 + Qi (1 )) ; pik (1 + Qi (0 )) + qik (1 + Qi (1 ))

(6)

where Qi is the compatibility of a region around the pixel ai , and is de8ned as the weighted average compatibility of all eight neighbours u (u = 8) centred at ai : u

1 Qi (S ) = (CA (i; S ; j; 0 )pj + CA (i; S ; j; 1 )qj ): u j=1

(7)

Eqs. (5) and (6) are repeated until some termination criterion is satis8ed. That is, if the probability of labelling a pixel is greater than 0.9 or smaller 0.1, this pixel is no longer computed in the process. 3.2. Image segmentation The algorithm was tested on a number of histological images with various qualities of staining, and all of them containing variable vascular con8gurations. The latter was also the main reason for not considering any shape characteristics of the vascular structures during the clustering process. Blood vessels may appear circular, elongated, and generally without having speci8c geometrical properties, as a result of diKerent cutting angles of the biopsy and of their tortuous shape in the tumour region. Hence their shape is random, as only a small section (or sections) of an entire vessel may be contained in the histological image. Since the aforementioned relaxation method does not deal with colour image data, the original image was 8rst split to its red (R), green (G), and blue (B) spectral bands. The blue component, which was found to have the best contrast between blood vessels and background/cells, was then

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Fig. 1. The blue components of two originally colour histological images with high (a), and low (b), staining quality, respectively. Blood vessel sections are shown in dark-grey. In the original images vessels and cell nuclei (here in light-grey), were stained in brown and light-blue, respectively. Bar, approximately 30 m.

used as the input to the grey-level clustering algorithm. 1 Fig. 1(a)–(b) are the blue components of two large-scale histological images of high and low staining quality, respectively, containing blood vessels (in dark-grey) and tumour cells (in light-grey). The variable geometry of the vascular structures is also evident in both images, partly due to the chaotic organisation of the vascular network in the tumour, containing several vascular structures with random shapes. The corresponding image histograms are shown in Fig. 2(a)–(b), from which it can be seen that both are characterised by a broad peak towards the right side of the scale that corresponds to the 1

All grey-scale images shown here represent essentially the blue spectral components of the corresponding colour histological images.

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Fig. 2. The grey-level histograms of the images shown in Fig. 1(a) and (b).

NBV class. Although the blood vessels exhibit some good contrast, the grey-level frequencies of their pixels are not enough to form a distinct peak in the histogram. Fig. 3(a)–(b) shows the output images using the relaxation process based on the proposed logistic probabilities concept. Pixels labelled as vessels are shown in white. Fig. 3(c)–(d) show the outcome after applying the original version [10], in which the initial classi8cation scheme assumes that pixels have equal probabilities of being included in either class (i.e. ‘black’ and ‘white’), when their grey-values are equal to . The output images lead to the conclusion though that this is not the case here, as there are many pixels with values gi ¡ , which are labelled mistakenly at the beginning with a signi8cant probability of being included in the BV class, making thus impossible the alteration of the initial labelling at a later stage. Thus, many cell nuclei with low grey-values were eventually labelled as vessel-pixels. The large number of misclassi8ed cell nuclei pixels denotes also that the two classes concerned (i.e. BV and NBV), are equally distant from a grey-level lower than . The precise position of this level was very di6cult to determine though, since there is no sharp valley in the image histograms which would allow the estimation of where this level in-between the pixel distributions might be. Our relaxation version based on logistic probabilities generated accurate segmentation results, characterised by a very low number of false positive responses. From Fig. 3(a)–(b) it can be seen that most of the pixels belonging to the BV class were labelled correctly. The accuracy in the edge localisation is also satisfactory, even in cases where the contours of the blood vessels are stained very weakly. For example, the vessel section at the bottom left corner of Fig. 1(a) that has essentially a width of very few pixels. The algorithm identi8es it without gaps. For the image with low staining quality (Fig. 1(b)) the results are also robust. Almost all the blood vessels were stained inhomogeneously, and weakly, resulting in a grey-level image with lower contrast compared to Fig. 1(a). Furthermore, the image includes several sections of the same or diKerent vessels, indicated by the presence of very small dark-grey regions, some of which are hardly visible to eye. However, the algorithm seems capable of identifying even those small vessel sections that are stained weakly in the original histological image. Other noticeable features of the method include its great computational speed, (convergence speed equal to 14 iterations, whereas in the original relaxation was 33 iterations), and the presence of very few insigni8cant misclassi8cations; which may be eliminated using a binary 8lter.

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Fig. 3. The output segmented images corresponding to those shown in Fig. 1(a)–(b), after applying the proposed algorithm based on logistic probabilities (a)–(b), and using the original version of the relaxation algorithm (c)–(d).

3.3. Vessel contour extraction During segmentation, along with the process of grouping an image into homogeneous units, a segment must be composed of a continuous collection of adjacent and touching pixels. This is a very important condition that is hardly ever met during analysis of real images, such as those encountered in histology, in which robust staining quality is not the general rule, making the absolute extraction of biological structures with tortuous shape, such as tumour blood vessels, a di6cult task. Segments of the same vessel must be enclosed by a continuous border, which some times cannot be achieved by merely performing grey-level clustering, given that stain uniformity is not consistent across the displayed vascular sections. Thus, even a small ‘gap’ across the vessel border would yield a fragmented vessel, which is a signi8cant error if certain geometrical parameters are required for further analysis. Considering the previous comments, pixel discontinuity is a di6cult issue to deal with, especially if one uses a segmentation algorithm that is based purely on a characteristic feature clustering

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technique. A remedy for such problems could be found by post-processing information relevant to the spatial properties of the objects after segmentation. Edge detection constitutes such an approach, capable of separating regions by detecting edges among perceptually diKerent objects. In [11,12], we presented an edge detection algorithm (named as OLGA), able to identify a thick pattern of edges around cell nuclei boundaries, which can essentially yield solid objects with continuous boundaries. This cell nuclei edge detector was also exploited with success in identifying the contours of other biological structures in tissue sections, such as the blood vessels studied here. Speci8cally, in order to connect two or more vessel-parts, which may have been identi8ed by either of the previous clustering methods, the OLGA principle was used initially to 8nd edges of all objects in the image, including those of blood vessels. Similar to the relaxation process, edge detection was performed on the colour band that exhibited the best contrast for the blood vessels. Then, following a series of morphological processes (region 8lling and low-pass 8ltering), the contours of all structures in the image were extracted. Fig. 4(a) illustrates another example of an image containing blood vessels with non-uniform staining, and many regions in their interior which have not absorbed the vessel stain, indicating the presence of erythrocytes. As a result of this phenomenon the logistic relaxation technique failed to delineate the entire vessel contours in several cases (some of these are indicated by the arrows in Fig. 4(b)). Fig. 4(c) illustrates the result after applying the OLGA principle. It is clear that in addition to the cell nuclei, which are not the primary objects of investigation at this stage, the complete blood-vessel contours are detected robustly, as a result of identifying patterns of thick edges around their borders. Fig. 4(d) shows the 8nal segmentation outcome after combining the image of the vascular segments detected with relaxation (Fig. 4(b)), and edge detection (Fig. 4(c)). In particular, using a region growing principle the process started with a set of seed points that consists of the correctly classi8ed regions after relaxation, and appending to each seed point those neighbouring pixels enclosed by the vessel borders detected after performing edge detection. Thus, this process grows the initially incomplete vascular segments, found by relaxation, until they reach their borders. Fig. 4(d) illustrates the 8nal segmentation of the image shown in Fig. 4(a), whereas Fig. 4(e)–(f) show the 8nal segmentation of another two histological images with a greater number of vessels. Vessel borders are marked in white. It can be seen, that almost every blood vessel or vessel section is well identi8ed and its boundary well localised. 4. Results In order to provide a statistical analysis of the algorithm’s performance the overall speci8city (SPE) and sensitivity (SEN) was measured after calculating the true positive scores (TPS) and false positive scores (FPS), using the vessel counts generated by the logistic relaxation algorithm. Furthermore, we asked for expert assistance in determining the actual vascular segments. Thus, the overall method’s performance (i.e. vessels versus non-vessels) against an ‘actual’ state, was based on clinical evaluations performed by two experts who marked the blood vessels contained in the images. The individual counts obtained were used for the comparison. The algorithm was applied separately, followed by some standard morphological procedures, such as hole-8lling to obtain solid objects, low-pass 8ltering to reject some small-size particles, and the contour extraction process described previously. The parameters mean shift and decay rate were set to: k = 0:8 and a = 5, respectively.

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Fig. 4. (a) Another example of a histological image containing several non-uniformly stained blood vessels. (b) The output image after applying the logistic relaxation algorithm. Arrows indicate some fragmented regions where the algorithm failed to extract the complete vessel boundaries. (c) The output image after applying edge detection [11,12]. (d)–(f) The 8nal vessel segmentation result after employing the ‘vessel contour extraction’ process, described in the text, for the image shown in (a). (e)–(f) Another two examples of vascular images containing several vessels segmented by the proposed method. Vessel contours are marked in white for better visualisation. Bar, approximately 30 m.

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Table 1 Vessel segmentation results on 15 large-scale histological images, obtained by the proposed algorithm Images

TP

FP

True vessel-count

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

17 28 21 28 123 64 38 30 22 18 88 13 19 41 14

1 2 1 0 4 1 2 4 1 1 2 0 1 0 0

17 28 21 28 125 64 38 30 22 18 90 13 19 43 14

Sensitivity: 0.99 Speci8city: 0.96

Total: 570 vessels

TP and FP are the true positive and false positive responses of the algorithm. The true vessel counts for each image are also shown (see text for details).

Any object labelled as vessel both by the experts and the computer, was counted as true positive. Any object that was detected by an algorithm positively, but it was not hand-labelled as a vessel, was counted as false positive. The TPS was established by dividing the number of true positives (TP), by the total count of objects hand-labelled as vessels. The FPS was established by dividing the number of false positives (FP), again by the total number of vessels labelled correctly (handlabelled), since the number of objects hand-labelled as not vessel was uncertain and very di6cult to estimate because the images contained hundreds of objects other than vessels (usually cell nuclei and cellular debris). Sensitivity and Speci8city were calculated as SEN = TPS and SPE = 1 − FPS. The algorithm was tested using a set of 15 images, with both good and high staining quality, encountered in routine clinical practice. These images re?ected test cases without any prior information on the status and extent of vasculature. Table 1 shows the TPS and FPS of the segmentation method and for each image studied. For comparison, the true vessel-counts are also provided, where it can be seen that the histological images consisted of various numbers of vessels ranging from 13, to as many as 125. The two experts generated almost identical results, apart from three images (5, 11, 14) in which the diKerence was less than 3% and thus an average value was used (results not shown here). Our algorithm presents a high performance with SEN=99:4% and SPE=96:1%, whereas there were only three images in which the algorithm failed to detect all the vessels, that is the images 5, 11 and 14. Note that these are the same to the images that the experts did not reach complete agreement, mainly due to the high number of vascular structures, and the staining quality. The algorithm appears also to have better sensitivity than speci8city, which means it tends to be better at detecting more real vessels than not detecting false vessels. In overall, 6 out of 570 vessels were not detected,

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whereas 20 objects were detected mistakenly as vessels by the system. This tendency might be due to the region growing process involved during the extraction of the vessel contours, typically when no-vessel objects are mistakenly identi8ed as vessels during relaxation. However, this phenomenon was observed rarely, as demonstrated by the algorithm’s performance (6 out of 570 false negative alarms), and a possible remedy might be through size-8ltering, or user-interaction. In such extreme cases, the proposed methodology would provide an aid for examining the extracted vessels by the clinician, who would in any case be responsible for analysing the histological material. 5. Vascular domains After detecting the vessel boundaries the processing comes to the 8nal stage where quantitative information for the vascular structures and the cell nuclei contained in each vascular domain is extracted. Fig. 5(a)–(d) illustrates some typical examples of images containing the cell nuclei (detected using OLGA edge detection [11,12], and vascular domains around each vessel (using the morphological operation SKIZ—skeleton by in?uence zone [13]). The inner contours inside the outer cell borders serve the purpose of obtaining the correct number of cells, when more than one touch/overlap with one another [14]. A vessel domain represents essentially a region around a vessel, where each pixel point has the closest distance to the vessel located in the same domain, compared to all other vessels contained in the image. To put it in a diKerent way, the boundaries around each domain de8ne those median lines that are equidistant to adjacent vessels [13]. The segmentation of an image into vascular domains aims to provide information regarding the maximum number of cell nuclei, or in general the tissue area, that a particular vessel may supply with oxygen in a tumour region. Such information provides a better understanding of the relationship between tumour cells and vascularity. Similar routines have been also developed by others [5], but for tissue-section images acquired by means of ?uorescence microscopy. The methodology described here provides additional information, regarded as crucial by the clinicians, such as the particular number of cells and tissue area enclosed in each vascular domain, as well as parameters associated with the shape of the vessels (e.g. the longest vessel axis, the angle of this axis with respect to the horizontal axis, etc.). 6. Summary and conclusions This paper describes a blood vessel segmentation algorithm suitable for images stained for neovascularisation. Although, most investigators have made considerable eKorts to develop image analysis algorithms for detecting, or classifying, cellular structures in tissue sections, tumour vasculature has attracted very little attention. The quanti8cation of histology sections stained for endothelial cells is one of the few practical approaches to measuring angiogenesis in human tumours. However, the scoring of angiogenesis is usually made manually by counting intratumoural microvessels, which is tedious, time consuming, and suKers from de8ciency in providing more quantitative information that may be proved clinically vital in the future. The vessel detection task was investigated using a grey-level clustering technique based on probabilistic relaxation. The proposed method included some modi8cations of the original process reported

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Fig. 5. (a)–(d) Example images showing detection of cell nuclei and vascular domains, after obtaining the vessel contours (see text for details). Fig. 5(c) and (d) correspond to those shown in Figs. 1(a) and 4(a), respectively. Bar, approximately 30 m.

in [10], incorporating: (a) a factor giving priority to pixels with intermediate grey-values for being included into a speci8c class, (b) logistic probabilities for faster and smoother classi8cation and label-updating, a feature similar to the sigmoid activation functions used in the neural networks methodology, and (c) a consistency measure between the pixel’s probability and its original grey-level each time the results are re8ned. Application on images with diKerent levels of staining showed that this approach was able to provide fast and accurate segmentation, as demonstrated by vessel detection experiments comparing computer-generated and manual scores provided by experienced observers (SEN = 99:4% and SPE = 96:1%). However, in some cases the relaxation algorithm did not generate closed vessel contours, as its main purpose was to group the image into homogeneous regions, and not necessarily to create vessels consisting of spatially adjacent regions that belong to the same structure. This is an important condition that is never ful8lled in the literature, and yet a very di6cult issue to deal with considering

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that vessels are essentially 3D objects, segments of which are mapped in a 2D tissue section, as the biopsy is cut at a particular angle. Thus, there is a profound lack of knowledge regarding the size and shape of the displayed vessels, having essentially random spatial characteristics in the 2D section. Combining the output images after relaxation and edge detection oKered the advantage of adding indispensable information for the spatial properties of the vessel borders, something that essentially 8lled the ‘gap’ required for resolving the problem of pixel discontinuity. The generated binary images, after relaxation and edge detection, could then be combined, using region growing, for obtaining the complete vessel contours. Finally, after the vessels are segmented many quantitative measurements, such as vascular density and blood vessel shape analysis, can easily be performed. These measures are exceptionally useful as they can be tested in clinical specimens to establish whether they provide potential prognostic information or can be used to assess changes after radio- or chemo-therapy [6]. These and several other image analysis techniques have also been integrated into a speci8c problem-designed image analysis software (BloVes, 2 see [15]) providing a useful tool for facilitating the quantitative analysis of histological sections in a fast and automated manner. Acknowledgements The 8nancial support of the Cancer Research UK is gratefully acknowledged (CRUK Grants SP219510202 & SP2195/003). C. Loukas was funded by a postgraduate scholarship from the Cancer Research Campaign (Grant STU 045/001). The authors would like to thank Mrs. Locke for development of the image acquisition software, Mr. Newman for assistance with hardware, Dr. A. Sibtain for assistance with manual counting, and Prof. Wilson for assistance with biology-related issues. References [1] G. Schwartz, Uber desensibiliserung gegen rontgen und radiumstrahlen, Munchener Medizinischen Wochenschrift 24 (1909) 1–2. [2] G.G. Steel, Basic Clinical Radiobiology, 2nd Edition, Arnold, London, 1997. [3] N. Weidner, P.R. Carroll, J. Flax, W. Blumenfeld, J. Folkman, Tumour angiogenesis correlates with metastasis in invasive prostate carcinoma, Am. J. Pathol. 143 (1993) 401–409. [4] S.B. Fox, R.D. Leek, M.P. Weekes, R.M. Whitehouse, K.C. Gatter, A.L. Harris, Quantitation and prognostic value of breast cancer angiogenesis: comparison of microvessel density, Chalkley count, and computer image analysis, J. Pathol. 177 (1995) 275–283. [5] J. Bussink, J.H. Kaanders, P.F. Rijken, C.A. Martindale, A.J. van der Kogel, Multiparameter analysis of vasculature, perfusion and proliferation in human xenografts, Br. J. Cancer 77 (1998) 57–64. [6] W. Tjalma, E. Van Marck, J. Weyler, L. Dirix, A. Van Daele, G. Goovaerts, G. Albertyn, P. Van Dam, Quanti8cation and prognostic relevance of angiogenic parameters in invasive cervical cancer, Br. J. Cancer 78 (1998) 170–174. [7] S. Strieth, W. Hartschuh, L. Pilz, N.E. Fusenig, Angiogenic switch occurs late in squamous cell carcinomas of human skin, Br. J. Cancer 82 (2000) 591–600. 2

A detailed description and further information regarding availability of this software tool can be obtained by contacting the author: [email protected].

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[8] M. Barbareschi, N. Weidner, G. Gasparini, L. Morelli, S.T. Forti, C. Eccher, Microvessel density quanti8cation in breast carcinomas, Appl. Immunohistochem. 3 (1995) 75–84. [9] P.F. Rijken, H.J. Bernsen, A.J. van der Kogel, Application of an image analysis system to the quantitation of tumour perfusion and vascularity in human glioma xenografts, Microvasc. Res. 50 (1995) 141–153. [10] A. Rosenfeld, R.C. Smith, Thresholding using relaxation, IEEE Trans. Pattern Anal. Mach. Intell. 3 (1981) 598–606. [11] C.G. Loukas, G.D. Wilson, B. Vojnovic, A. Linney, An image analysis based approach for automated counting of cancer cell nuclei in tissue sections, Cytometry 55A (2003) 30–42. [12] C.G. Loukas, P.R. Barber, G.D. Wilson, B. Vojnovic, A. Linney, An edge detection based approach for automated counting of cancer cell nuclei in large-scale histological images, Proc. Med. Image Understand. Anal. (2000) 149–152. [13] R.C. Gonzalez, R.E. Woods, Digital Image Processing, Addison-Wesley, Reading, MA, USA, 1992. [14] C.G. Loukas, G.D. Wilson, B. Vojnovic, A. Linney, Automated segmentation of cancer cell nuclei in complex tissue sections, SPIE: Biomonitor. Endosc. Technol. 4158 (2000) 188–198. [15] C.G. Loukas, Quantitative image analysis of biological factors in?uencing radiotherapy, Ph.D. Thesis, University College London, University of London, UK, 2002. Constantinos G. Loukas graduated from University of Athens, Greece, in 1996 with a B.Sc. in Physics. He received his M.Sc. in Medical Physics in 1998 from University of Surrey, UK, and his Ph.D. in Medical Image Processing in 2002 from University College London. He is currently employed by GlaxoSmithKline (GSK) as a research scientist, working in the Institute of Neurology (London) on brain signal analysis. His research interests include medical image and signal processing, computational neuroscience, pattern recognition, and neural networks. Alf Linney was awarded a Ph.D. in Physics from Imperial College in 1965 and is now Professor of Medical Physics at University College London. He heads a Medical Imaging group which specialises in image processing and analysis for diagnostic purposes, and has over more than 20 years developed systems based on computer graphics for the simulation and planning of surgery and the design and manufacture of customised implants. He has been awarded the Royal College of Surgeon’s Tomes Medal in recognition of this work.