## 5 Classification  
The classification process is presented in Figure 5. Series of images of a single target (i.e., as a sequence of temporally consecutive frames of the same bird) are fed to the CNN that is applied to feature extraction. The two-step learning method is applied, i.e., the CNN is trained with the first N-1 layers viewed as feature maps and these maps are used to train a Support Vector Machine (SVM) classifier [25]. The SVM classifier makes use of one-versus-all binary learners, in which, for each binary learner, one class is positive and the rest are negative. The total number of the binary learners is the same as the number of classes. A linear classification model is applied. Stochastic gradient descent  
Figure 4: Example of binary image acquired by the segmentation process. (**a**) an original image of the Herring Gull; (**b**) respective binary image as a result of segmentation of the original image. Figure 3: Schematic diagram of the system. with 10 as the mini-batch size, and the Hinge loss function with regularization term \(1/n\), where \(n\) is a number of training examples [26; 27] are also applied. The output of the SVM is presented as \(\mathbf{P}\)-vectors as follows:  
\[\mathbf{P}_{i}=[c_{1},c_{2},...,c_{\mathrm{nc}}],i=1,...,n, \tag{1}\]  
where \(c_{j}\) is a probability of belonging to _class_\(j\), _nc_ is the number of classes and \(n\) is the number of images in each series, thus there will be one \(\mathbf{P}\)-vector for each image in any given image series. There are also two parameters based on information provided by the radar system. The size of the target bird is estimated as follows. The frame size ([width \(x\) height \(y\)], in _pixels_) of the camera and the angle of view (\(\alpha\)) of the lens are known. The distance (\(d\)) to the target bird is provided by the radar. The maximum number of horizontal (\(\sigma_{h}\)) and vertical (\(\sigma_{v}\)) _pixels_ of the target bird are calculated from the segmented image, respectively. The angle of view, \(b\), at the distance, \(d\), is calculated over a right-angled triangle (see Figure 6). The horizontal number of _pixels_/_meter_ is given by  
\[\rho_{h}=\frac{x}{b_{h}}, \tag{2}\]  
and the vertical number of _pixels_/_meter_ by  
\[\rho_{v}=\frac{y}{b_{v}}, \tag{3}\]  
where, \(b_{h}\) and \(b_{v}\) denote the horizontal and the vertical angles of view, respectively. The estimate for the size of the bird in a single image in _square meters_ as an area of rectangle is:  
\[e=\frac{\sigma_{h}}{\rho_{h}}*\frac{\sigma_{v}}{\rho_{v}}. \tag{4}\]  
Figure 5: The classification process. The size estimate is presented as a vector with elements placed according to the class order (the classes are ordered alphabetically by their names), i.e., _class 1, class 2,... class nc_, where _nc_ denotes the number of classes. The composition of the vector is following: calculate the average of the size estimates of the image series, check from the size-look-up table all the classes that contain the average size, \(e\), turn those elements to one and set the others to zero, yielding  
\[\textit{Size Estimate},\mathbf{E}=[e_{1},e_{2},...,e_{\text{nc}}], \tag{5}\]  
with elements:  
\[e_{j}=\left\{ \begin{array}{ll}1,&\text{if $e$ fits class $j$,}\\ 0,&\text{otherwise.}\end{array} \right. \tag{6}\]  
The velocity of the target bird is composed in similar way as the _E_-vector in Size Estimate (5), i.e., check from the velocity-look-up table all the classes that contain the provided velocity, \(v\), turn those elements to one and the others to zero. \[\textit{Velocity},\mathbf{V}=[v_{1},v_{2},...,v_{\text{nc}}], \tag{7}\]  
with elements:  
\[v_{j}=\left\{ \begin{array}{ll}1,&\text{if $v$ fits class $j$,}\\ 0,&\text{otherwise.}\end{array} \right. \tag{8}\]  
The final classification is achieved by a fusion between the parameters provided by the radar and the predictions from the image classifier.