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this means that the syntactic analysis procedures have to be derived independently.
For the ETPL(k) graph grammar presented here, an effective parsing algorithm of
a multinomial complexity is known [3]. This allows us to develop very productive
analysers that make it possible to verify the graph representations analysed to
check if they constitute elements of the language defined by the graph grammar
introduced. A significant benefit of using an ETPL(k) graph grammar is the possi-
bility of introducing derivational rules with simple semantic actions. This makes it
possible, in addition, to determine significant morphometric parameters of the ana-
lysed 3D reconstructions of coronary arteries. The entire syntactic/semantic analy-
sis is carried out in a multinomial time, both for patterns unambiguously defined
and for fuzzy, ambiguous patterns, as the above grammar classes can be extended
into probabilistic forms [16]. This is a very desirable property, particularly when it
is necessary to analyse cases not considered before.
5 Picture Grammars in Classification and Semantic
Interpretation of 3D Coronary Vessels Visualisations
5.1 Characteristics of the Image Data
Research work was conducted on images from diagnostic examinations made us-
ing 64-slice spiral computed tomography [4] in the form of animations saved as
AVI (MPEG4) files with the 512x512 pixel format. Such sequences were obtained
for various patients during diagnostic examinations of the heart and
present in a
very clear manner all morphologic changes of individual sections of arteries in any
plane.
C
oronary vessels were visualized without the accompanying muscle tissue
of the heart.
5.2 Preliminary Analysis of 3D Coronary Vascularisation
Reconstructions
To enable creating linguistic representations of 3D reconstructions of coronary
vascularisation, images showing the coronary arteries being examined undergo a
series of operations as part of the image pre-processing stage. The first step in the
preliminary analysis of the images analysed is segmentation, which allows areas
meeting certain homogeneity criteria (e.g. brightness, colour, texture) to be delim-
ited, which usually boils down to distinguishing individual objects making up the
image. In this case, segmentation consists in extracting coronary arteries while ob-
scuring needless elements from the image background so that later it is possible to
span the appropriate graph modelling the analysed structure. What is important is
that this pre-processing stage is executed using dedicated software integrated with
the CT scanner [4] and allows high quality images showing the coronary vascu-
larisation of the examined patient, free from marginal elements, to be obtained.
For this reason we can skip this pre-processing stage and focus straight away on
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