D iscussion on Colour Pixel Classification

The results show n in the previous tables confirm the very good perform ance of the K ohonen netw ork especially in the RGB space, w here correct classification exceeds 80% for the pixels belonging to the BV class, and for both staining qualities. How ever, as the num ber of colour features increases, the overall perform ance along w ith the classification score for the BV class decreases (see also Fig. 5.9), although it could be expected that m ore colour features w ould generate less misclassifications. In reality, this is due to the fact that adding too m any features as inp u ts in a p attern classification system can, paradoxically, lead to deterioration of the recognition perform ance after a certain point, as addition of features decreases the nu m b er of points per un it volum e in the corresponding feature space. This phenom enon has been

term ed the curse of dimensionality and it applies in m ost classification system s

w hich are restricted to w ork w ith a lim ited quantity of data, as w as the case in this study. Thus, increasing the dim ensionality of the space leads to the point w here the data is very sparse, in w hich case it provides a very poor

presentation of the m apping [Bishop, 1995].

100 95 8 90 5 85 t 75 ^ 70 65 60 ■ 3 inputs ■ 6 inputs □ 9 inputs S 3 inputs B 6 inputs □ 9 inputs ^ 70 BV TCN BG BV TCN BG

Figure 5.9 Classification performance of the Kohonen network for the 3

histological patterns in tissue section samples of high (a) and low (h) staining quality respectively.

In contrast to the blood vessels, the netw ork presented w orse classification results for the TCN class. A lthough this very little affects the vessel

Chapter 5_______________________________________________________ Vascular Image Analysis

segmentation outcome, it probably originates from the fact that m any tissue sections contained cell nuclei w ith very w eak and heterogeneous staining. Note that tum our cell nuclei are hardly visible in images w ith low staining quality (see Fig. 5.8(b)), as the haematoxylin stain is absorbed in very low quantities (indicated in Fig. 5.8(b) by the arrow). However, in tissue sections w ith good staining quality, haematoxylin is absorbed more intensively (see Fig. 5.8(a)), b u t on the other hand there are m any regions in the full-scale histological image w ith a wide range of blue intensities, all of which is difficult to include in the training samples.

Similar rem arks apply also to the histological background, which on many occasions contained cellular debris and colour variations leading to a low classification score, b u t clearly higher than that of the cell nuclei. In addition, it is evident that the colour distributions for the sample w ith low staining quality, shown in Fig. 5.7(d), exhibit a significant overlap betw een the TCN and BG distributions, and thus a high num ber of misclassifications is inevitable. This also highlights the intrinsically probabilistic nature of our colour classification problem, as the haematoxylin stain exhibited considerable variability, and thus perfect classification of new examples w as not always feasible.

Finally, using a large num ber of colour features lengthened the feature extraction process as well as the time required for training the network, rendering its use impracticable. Moreover, as the dimensionality of the netw ork system grows, a larger num ber of training samples is also required. In our histological data the RGB colour features yielded a high num ber of correct classifications even in tissue sections w here blood vessels were stained weakly and non-uniformly.

5.7

Application of N N Segmentation

The Kohonen netw ork was tested on a num ber of histological images w ith various qualities of staining, and all of them containing variable vascular physiognom y as can be seen in the full-histological images of Fig. 5.8 and 5.10.

chapter 5_______________________________________________________ Vascular Image Analysis

The latter was also the main reason for not combining potentially useful information that could be extracted from shape analysis, w ith the colour features of the vascular structures. Blood vessels may appear circular, elongated, and generally w ithout having specific geometrical properties, as a result of different cutting angles of the biopsy, and of their tortuous shape in the tum our region. Thus their shape is random , as only a small section (or sections) of an entire vessel may be contained in the histological image.

Fig. 5.10(a) and (b) are two large-scale histological images of high and low quality of staining respectively, containing tum our cells (in blue) and blood vessels (in brown). Vessels in (a) have clearly more uniform staining com pared to those in (b), w here the binding of the m arker is w eak (denoted by the arrows). Cell nuclei in (b) are also less distinguishable, having a light blue colour, com pared to those show n in (a) w hich exhibit more intensive staining. The previous rem arks regarding the variable geometry of the vessels, partly due to the chaotic organisation of the vascular netw ork in the tum our, are also evident in both images, as they contain m any vascular structures w ith random shapes.

Fig. 5.10(c) to (h), show the three class segmentation results for the histological images (a) and (b), w hen 3 (R,G,B), 6 (r,g,b,Mr,Mg,Mb) and 9

(R,C,B,Mr,Mg,Mb,Gr,Og,Oy) colour features w ere applied as inputs to the network. The sample images used for training the netw ork are shown w ith the dashed lines. It can be seen, that the netw ork produced the best results for image (a), w hereas the netw ork's efficiency decreases as more colour features are added, something which can be verified also by the classification results show n in Table 5.1. The cell nuclei and histological background contained in image (b), cannot be identified as separate classes, probably because they exhibit similar colour properties, due to the w eak staining of the cells. The system could not also distinguish cellular regions in image (a), w hen 9 colour inputs were used for training and classification. In contrast, the nuclei in image (a) are clearly better labelled w hen colour vectors of RGB inputs are presented to the network, although some of them (mainly those stained

Chapter 5 Vascular Image Analysis

(a) (b)

H -,

o _{' ■}

J

Figure 5.10 Image segmentation results for high (a), and low (b), staining quality when using 3 (c,d), 6 (e,fl and 9 (g,h) colour features.

Chapter 5_______________________________________________________ Vascular Image Analysis

weakly) are included mistakenly in the BG class. However, as m entioned previously, misclassifications of tum our nuclei have little effect on the vessel segmentation outcome, which is essentially the m ain objective. Brown stained blood vessels are classified adequately for the image w ith the high staining quality, although classification decreases w hen m ore features are added to the system. The latter applies also to image (b), which contains m any vessels or vessel-sections w ith inhomogeneous staining. Most of the vascular structures are labelled correctly w hen the RGB features w ere used, although there are m any vessels w ith poor staining.

Another advantage of pixel classification using N N is that it is not restricted to multi-dimensional colour information. If only a grey-level image is available, the intensity signal defines a ID feature space. Fig. 5.11(a) shows the intensity com ponent of the image show n in Fig. 5.10(a), where it can be noticed that the contrast of the displayed structures is lower than that in the colour image, w hereas the vessels appear as dark objects over a light grey background.

Fig. 5.11(b) to (d) are the output images w hen 1 (I), 2 (I, Mi) and 3 (I, Mi, ,0 ;)

grey-scale features were used respectively. I corresponds to the intensity value only, w hereas Mi and Oj are the average and standard deviation grey-level respectively, in a 3 x 3 local region. In this case it can be seen that in contrast to the colour space, vessel segmentation is im proved as more features are added to the system during training. Using just one feature (i.e. the intensity component only) is not enough to label correctly the vessel sections, since m any cell nuclei are ill-classified in the BV class. Two features (I, Mi) produce slightly fewer misclassifications, whereas w hen the (I, Mi, o j feature vectors w ere used, the blood vessels are segmented accurately, although the Kohonen netw ork is still incapable of identifying TGN and BG as separate classes.

Chapter 5 Vascular Image Analysis