## 6 Discussion
### Invariant Image Representation and Neural Networks  
One of the most important problems of neural network-based system is the selection of architecture of the neural network. The invariance of input image on the scale, rotation, skew, and other image transformations is crucial for the correct processing of real images. Sometimes a physical relationof objects and acquisition system (camera) guarantees fixed relation for some of the transformations. The system should be non-sensitive to the object transformations. There are two possible approaches for achieving this extremely important property:  
* Invariant transformations guaranteed by machine learning,
* Invariant transformations guaranteed by preprocessing algorithms.  
The first approach may be achieved by neural network, using augmentation of data with different combinations of scale, rotation, skews, and other transformations. Data augmentation requires a great deal of additional computation power for the preparation of augmented images and learning time is also significantly increased. Moreover, the achieving of input image invariance requires additional layers.  
An alternative approach is used in hierarchical systems, which are designed with the knowledge about possible image transformations, when object-to-acquisition system relations could be estimated. Preprocessing algorithms could be applied for achieving image transformation invariance. Such algorithms use image features as control points for the desired transformation. Achieved compensation reduces learning cost, which is the main advantage of this approach. It is important for users of the system, because the selected segmentation is based on semisupervised learning (one particular image, one learning process). The drawback is the lack of feature points in microscopic lung images, due to isotropy, so rotational invariance should be achieved without control points.  
The problem of rotational invariance is addressed in this work by the conversion of input image part from particular sliding window position to another space. This technique is very often applied for images or non-image input data. Statistical parameters, such as mean, standard deviation, etc. are independent of the data order, so desired rotational invariance may be achieved. Some researchers use tens of these parameters for input data preprocessing, instead of directly processing a part of the image.  
The selection of parameters is not trivial. Another difficulty is the correlation of multiple statistical parameters used at the same time. Mean and standard deviations are not correlated, but for example mean and median values could share some properties. Output results may depend on one parameter or multiple parameters with some weights. Another problem lies in the possibility of interpolation, not the approximation (data generalization) due to redundant preprocessing parameters.  
Non-parametric statistical approach is selected in this paper (SWLH). Histograms preserve information about the distribution using a set of values using a less reductive approach. Details about distribution, including modal properties, are preserved that could be important for segmentation purposes. Different image classes could be very often described by different distributions, due to differences in local brightness and contrast. Edge regions are their mixture. The hypothesis concerning a possibility of preprocessing of input image by the SWLH is also empirically tested in this work.