## 5 Discussion and Conclusions  
In the second section of the paper, a description of related works is given. The methods described there, that is [8; 9; 10; 23; 24; 25; 26; 27; 28], were chosen for two main reasons--they concern action recognition and use the Weizmann database. However, the approaches used to represent a frame or a silhouette are diverse. In [23] a set of rectangular patches is used to represent a shape and in [26] only contour points are applied. Some researchers use various transforms, e.g., the authors of [24] apply Trace transform to binarized silhouettes, while in [28] the two-dimensional Fourier transform is applied to the original frames. The opposite approach is the use of cumulative silhouettes [8; 9] or cumulative skeletons [10]. Some other techniques are dense trajectories based on salient points [27] and time series [25]. The approach proposed in this paper combines simple shape descriptors with the one-dimensional Fourier transform and standard leave-one-out classification procedure. Each action sequence is firstly described by a set of simple features and represented using a predefined number of Fourier coefficients. Classification is two-stage: firstly, actions are divided into two subgroups based on trajectory length, and secondly, leave-one-sequence-out cross-validation is performed. The proposed approach yields 97.2% accuracy in the assumed application scenario and 91.12% accuracy on the entire Weizmann database. The best results were obtained with the use of features based on a minimum bounding rectangle--its area, width and perimeter. These features are simple; however, if observed over time, they carry much more information about an action. Therefore, the input data can be limited to rectangular objects of interest, representing regions where silhouettes are located. These areas can be tracked over time to extract centroid locations. With these assumptions, the calculation of convex hulls may be omitted. A comparison of some recognition rates of the proposed approach to other methods tested on the Weizmann dataset is presented in Table 3. Although our approach does not provide a perfect accuracy, it can be compared with some other solutions. It should be mentioned that the presented methods may assume other application scenarios and experimental conditions. Moreover, if we limit the number of classes, it does not always improve the results, which is proven in our experiments. When the classification of actions with changing location of a silhouette is performed for 10 classes, the highest accuracy is 95.56%, while for the limited number of classes it decreases to 94.44%. According to that, we especially refer to the results presented in [8; 23; 28] that outperformed our results obtained in the experiment concerning the assumed application scenario. The authors of [28] also employ spectral domain features, however these features are extracted from video frames using the two-dimensional Fourier Transform. In our approach the frames are represented using simple shape descriptors, which for each sequence are concatenated into a vector, and the one-dimensional Fourier Transform is applied. Therefore, the initial data dimensionality is lower. The descriptor proposed in [23] requires the extraction of rectangular regions from a human silhouette which may be problematic in case of imperfect silhouettes. The approach proposed in [8] uses accumulated silhouette representation, which requires all foreground masks from an action sequence. In our approach each foreground mask is represented separately, therefore in the case of the real-time scenario the proposed approach can be adjusted to utilise fewer frames. The proposed approach has some advantages--it can be adapted to different action types by selecting other shape features and matching measures. Action representations are small and easy to calculate because simple algorithms are applied.