## 1 Introduction  
The digital analysis of medical microscopic images is very important from an application point of view. The designing of such systems is necessary for improving patient condition analysis and to reducing human errors. Advances in image acquisition of microscopic slides have improved the performance of CADx (Computer-Aided Diagnosis) [1; 2]. CADx systems are large data systems, because microscopic slides are very large images and many of them are processed in a typical workflow. A typical microscope slide is approximately 75 \(\times\) 26 mm and submicrometer resolution can be achievedusing optical scanners. In most cases, the biological content does not occupy the entire slide, but image size is still large enough. The problem of image size is important, but automated analysis is much more significant. Large data sets require fully automated or computer-assisted processing (Human in The Loop). The extraction of important parameters for medical analysis of a patient is a very complicated task. The essential problem is complexity of visible structures and their variability in different patients. The designing of CADx systems is seemingly one of the most challenging tasks for researchers nowadays. Reliable CADx systems are available for the morphologically simplest biological structures. A good example is the use of liquid cytology with removed artefacts instead of traditional pap smear in cervical cancer screening, which leads to clearer background of obtained cytological images and therefore enables preliminary computer interpretation of cytology for example with Focal Point BS, Burlington, NC, [3]. Automated microscopy system Cellavision DM96 is also used for the examination of peripheral blood smears essential in hematological diagnosis [4; 5]. A typical CADx system is based on a data classification system with numerous application-oriented complex algorithms. One of them is the estimation of a type of microscopic structure and the determination of malignancy. This could be achieved by analyzing microscopic structures, which are tissue dependent. The analysis of lung microscopic slides shows the importance of fractal structures for classification purposes. Quantitative analysis of the fractal dimension seems to be a promising method, but the segmentation of an acquired image is needed. Additional image analysis algorithms as well as a large data set are required for the design of CADx systems. Two main approaches could be applied for the design of a CADx system. The first one is the black-box approach using machine learning methods, where overall process is based on training using a large data set. The primary drawback of this approach is the need for a very large data set with man-made segmentation. The secondary drawback is the lack of knowledge about obtained data processing details, therefore such a system is a black box and determination of reliability of such a CADx system is questionable. The second approach is the hierarchical system which is much more promising, because particular parts of the system could be tested independently, thus the determination of reliability of such a CADx system is possible. The hierarchical system allows the reduction of the data set, because increased control of particular algorithms is possible. This work uses hierarchical design. The first hierarchy level is based on segmentation using dedicated HistAENN (Histogram-based Autoencoder Neural Network) and semisupervised learning principle. The second hierarchy level is the fractal-based estimator for complex structure analysis. The field of research has a broad spectrum of application, and therefore the contribution is listed in a few main points:  
* This work assumes hierarchical design using autoencoder neural network (the first hierarchy level) and the fractal-based estimator for complex structure analysis (the second hierarchy level) of segmented images and shows how to select or preselect algorithms in the second hierarchy level algorithm using small data sets and the semisupervised training principle.