## 6 Conclusions  
This paper has presented a novel method of image content representation. In our approach, we propose to encode an image as a tuple of sparse matrices that describes the intensity and position of selected visual features occurring in the image. The method was validated through a series of experiments on the MNIST data set [7]. The presented simple variant, in which each matrix was reduced to local maxima, provided the ability to generate sparse matrices where no more than 6.25% of elements were preserved. However, as revealed by further analysis, very sparse matrices with no more than five elements preserved in each \(28\times 28\) matrix (which is less than 0.64% of elements preserved) were sufficient to keep a low autoencoder error rate and obtain a classifier accuracy of 98.40%. The application of the method to the classification task provided satisfactory results, outperforming the classical sparse coding solutions [23; 25]. In our approach, the method of encoding was the same, regardless of the image class, because no class-dependent information was used in the training process. Thus, the presented method can be considered unsupervised. This is a relevant factor that has to be taken into account when comparing the results of the present study with those in [22]--our results are not as good as those of the supervised variant presented in that work but outperform those of the unsupervised variant. The presented classifier also performs better than most solutions based on spiking neural networks [28; 29]. It is not as good as some models presented in [31], but it must be emphasized that the classification accuracy comparison is not the key aspect in this particular case. Spiking neural networks possess different properties, such as the ability to handle noise [29]. Some of the models, such as LIF neurons [27; 28] or STDP learning [29], suffer from too high complexity, or unsatisfactory sparsity level of the generated representation (especially in [31]). The sparse representation based on visual features made it possible to perform a detailed analysis of the nature of the selected features. We presented both context-free feature visualizations  
Figure 17: Processing times of MF4, AF4, and AF5 models for square images of different sizes. As in the case of the standard training and test process, these results were achieved using GPU. (see Tables 8, 10, and 12) and digit-specific distribution of particular features (see Figures 8-13). Additionally, per-digit statistics of feature occurrences were discussed (see Tables 9, 11, and 13). The presented method is based solely on convolutional layers and point-wise operations (activation functions). This makes the feature detection invariant to translation. Consequently, the pretrained autoencoder can process the input images of any size, which was demonstrated on the basis of a data set with larger images, each containing multiple digits (see Section 4.4). Experiments using non-digit symbols were also performed (see Figures 11-13), in order to show that the generated features were adjusted to the selected data set--not surprisingly, the autoencoder trained in the proposed way performed markedly worse on non-digit characters. The study was based on the MNIST data set [7], which is relatively easy to analyze. However, further tests are needed to verify the applicability of the method to more complex databases, such as the ImageNet data set [37] or data from the Pascal Visual Object Classes Challenge [38]. In order to be applied to images of real-life objects, the method would have to be enhanced with the ability to recognize more complex and more numerous visual features. The different visual features used in the presented approach are sensitive to object rotation and size. In particular, the images from the MNIST data set were easy to describe with lines, and the rotation of the line was the key element that identified the features. However, the task of feature detection in different rotations can be approached in multiple ways.