# Target Identification via Multi-View Multi-Task Joint Sparse Representation
## 5 Target Identification Method Based on Multi-View Multi-Task Sparse Learning
### Multi View Multi-Task Sparse Learning Target Identification Method  
In this paper, a new target identification method called multi-view multi-task learning method (MVMT), is proposed. The method mainly includes five steps: first, read the image sequence in the captured video and sample the particles according to the particle filter sampling and resampling methods; second, select candidate templates; third, extract multiple features of particles to increase the diversity of target representation from different feature spaces; fourth, use the multi-view sparse representation method for multi-task learning to train the optimal candidate template set; fifth, for each candidate template, transform the reconstruction error into a probability problem to determine the target; finally, calibrate the target and track it in a rectangular frame. To represent the process of a multi-view multi-task learning method more intuitively, the flow chart of a multi-view multi-task sparse learning target identification method is shown in Figure 9.  
According to the flow chart in Figure 9, the target identification algorithm based on multi-task and multi-view can be divided into the following main steps:  
1. Initialize the target: Select the rectangular box of the target of interest on the first frame image;
2. Select the candidate template: Select the candidate template according to the Gaussian distribution model and process its gray image level.  
Figure 9: Flow chart of multi-view multi-task target identification method.  
\[f(x)=\frac{1}{\sqrt{2\pi\sigma}}\exp(-\frac{\left(x-\mu\right)^{2}}{2\sigma^{2}}) \tag{8}\]
3. Extract multi-view features: Extract the features of LBP, HOG, and SIFT view from the obtained candidate templates, and reduce the dimension of the extracted feature matrix;
4. Construct the redundant dictionary: Assemble the obtained single column vectors of each view of a given template into a new column vector, i.e., template vector, and cycle through other candidate templates. All the template vectors obtained are arranged in columns, and the identity matrix is added to form a redundant dictionary;
5. Multi-view multi-task sparse learning: Multi-view multi-task learning is performed on the templates in the redundant dictionary to solve the classification coefficient matrix \(C\). For several particles selected by sampling around the target, select the candidate template with a small residual to replace the bad performance in the dictionary, and finally make the candidate template in the dictionary the optimal template set. For Equation (3), a gradient descent algorithm is proposed, so the target residual can be calculated as: \[\cos t(W)=\frac{1}{2m}[\sum_{v=1}^{V}\left((A^{v}C^{v}-X^{v})^{2}+\omega_{1}|| P||_{1,2}+\omega_{2}||Q^{T}||_{1,2}\right.\] (9) For solution \(C\), the following method is used for convergence to obtain the optimal solution: \[c_{j}:=c_{j}-\alpha\frac{1}{V}\sum_{v=1}^{V}\left((A^{v}C^{v}-X^{v})\cdot A_{ j}^{v}\right)\] (10)
6. Update template: if the residual error between the training sample and the label is less than the given threshold, replace the corresponding template in the dictionary, as shown in Figure 10.
7. Determine target: Carry out probability conversion for each classification plane (each column) in matrix \(C\) and take the classification plane with the largest probability as the final target to be tracked. For the \(t\)-th frame image, the determination criteria are as follows: \[p(y_{i}|x_{t})=\frac{1}{\Gamma}\exp\{-\alpha\sum_{v=1}^{V}||Ta(1:n,i)-Y||\}\] (11) where \(\Gamma\) is the normalized factor, \(N\) represents the number of candidate templates in the dictionary, and \(Y\) represents the label. The flow chart of target judgment is shown in Figure 11.  
Figure 10: Template update schematic.  
Output box to calculate the target identification error.