Descriptions of the Structures in .NET

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Descriptions of the Structures
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Figure 14.2 Operations conducted in the course of preprocessing of the examined images. At the top is the original image of a pancreatic duct showing symptoms of chronic inflammation. At the bottom, a diagram of the pancreatic duct contours with visible morphological lesions. Analysis of real, and verification of apparent, skeleton ramifications [26,27]. Smoothing the skeleton by averaging its elements [28]. The application of a specially prepared straightening transformation, transforming the external contour of the examined structures in a two-dimensional space to the form of 2D width diagrams, showing contours of the numerically straightened organ. This transformation retains all morphological details of the analyzed structures (in particular their deformations and pathological lesions) [29]. For this reason, it is a convenient starting point for further analysis of the properties of shape features of the analyzed structure and for detecting such deformations (with the use of syntactic methods of image recognition). This constitutes the basis for an automatic understanding of the nature of pathological lesions, and for a diagnosis of the disease under consideration. Recognition and automatic understanding of the looked-for lesions of organ shapes with the use of syntactic methods of image recognition [30] is possible with a prior application of the specified sequence of operations, which together constitute the previously mentioned image preprocessing stage. Details relating to individual stages of preprocessing of the analyzed images were discussed at length in the above-quoted publications of the authors. These stages have also been specified in Figure 14.2.
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3. Structural Descriptions of the Examined Structures
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Syntactic image analysis, aimed at understanding the looked-for lesions, which are symptoms of some defined diseases, has been conducted on all examples analyzed here, based only on the obtained width diagrams of vessels shown on those images (following the above-described image preprocessing). To diagnose and describe the analyzed lesions in the examined structures, we have used context-free grammars of the LR(1)-type [13,30]. These grammars allow one (with an appropriate definition of
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Medical Pattern Understanding and Cognitive Analysis
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primitive components) to diagnose and describe in an unambiguous way all lesions and pathological deformations important from the point of view of the diagnosis tasks analyzed here. The key to success in every task performed was an appropriate definition of the primitive component set (alphabet of graph primitives), allowing the recording of every examined organ shape (both correct and pathologically changed) as a regular expression in the language defined by the analyzed grammar. As has already been stressed above, this task was simplified due to the fact that primitive components were defined on the vessel width diagrams obtained (as a result of preprocessing) after an execution of the straightening transformation. This did not mean, however, that indicating the necessary primitive components (and finding terminal symbols corresponding to those components) was a very easy task. It is at the stage of selecting the primitive components that the author of the medical image understanding method described in this chapter must, for the first time (although not for the last time), cooperate closely with a team of experienced medical doctors. These experienced diagnosis experts are the only people competent to tell which features of the analyzed contour of a selected organ part are connected with some stages of natural diagnostic reasoning. The role of the producers of the optimum set of letters of the created grammar is strictly divided: a doctor can (and should!) focus his/her attention on the largest number of details possible, treating every image discussed here as a totally new, separate case. A computer scientist must try to integrate and generalize the detailed information in such a way that the result is a maximally compact set of as few primitive components as possible; the components must allow the building of a computationally effective graph grammar [12,31]. To use a concrete example, we should state that in the tasks selected and discussed here, there was a need to determine primitive components which allowed the description of pathological deformations, i.e. which edges of the analyzed structures should appear on the obtained width profiles. In accordance with the opinions of doctors with whom we consulted, shape features important for diagnostics are: pathological stenoses or dilations of the examined vessels and local changes of their contour, such as side ramifications and cysts. After analysis of many example images, it turned out that morphological lesions with very differing shapes played an identical role in the diagnostic reasoning of doctors. Therefore, for the aggregation of the various forms of deformation of the contour line of the examined vessels, it was possible to use the line approximation algorithm of the previously obtained vessel width diagram for identical sets (sequences) of primitive components. An approximation of the complete edge line of the diagram by means of a polygon is a method described in [32]. As a result of the application of this method for every diagram, we obtain a sequence of segments approximating its external contours. This sequence simplifies the analyzed image once again, yet it still retain all information important from the point of view of the constructed automatic diagnostic reasoning sequence. It is worth noticing that, at this stage, we have a very uneven compression of the primitive image information. This is beneficial for the concentration of attention of the recognizing diagram operating on these contour fragments, which are really important. If a fragment of the examined vessel at some (even very long) segment of its course has a smooth form, deprived of morphological features, which can be important for the recognition process, then the whole approximated segment is one section of a polygon and it will be represented by one symbol in a notation based on a sequence of identifiers of the discovered graphic primitives. If, on the other hand, a contour fragment is characterized by big changes of the edge line, then the proposed form of description will attribute many segments of a polygon; this will mean a big representation in the final linguistic notification. This is rightly so, since, for diagnosis, it is an important fragment! Next, depending on parameters, terminal symbols are attributed to each of the polygon segments. In the examples considered here, one parameter was enough to obtain a satisfactory specification of the description of the analyzed images. The parameter characterized every successive segment of the approximating polygon in the form of its inclination angle. To be more exact: the appropriately digitized values of the angle were given in the form of primitive components. The digitation pattern used could be treated as a counterpart of a dictionary of the introduced language of shape features. Yet, in more complex tasks, we can imagine a situation in which the set of primitive components can
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