## 2 Proposed Network
### Detection Head--CenterNet  
CenterNet is an anchor-free detector proposed in [14]. CenterNet identifies objects as a point at their bounding box center. During training, CenterNet converts ground truth Rols into heatmaps. For the training image a keypoint map \(K_{(x,y,c)}\) is generated in which if the coordinates \((x,y)\) belong to the center of an object then it will be activated and the rest positions will be set to zero. The keypoint map is then converted into a corresponding set of heatmaps. These heatmaps are used to train the detector with a focal loss function to classify into corresponding class (\(L_{k}\)) [31]. CenterNet also consists of an offset head for object location and a size head to regress the size of object to generate its RoIs. The final detection loss function is given as:  
\[L_{det}=L_{k}+\lambda_{size}L_{s}+\lambda_{off}L_{off} \tag{5}\]  
where \(L_{s}\) and \(L_{off}\) are \(L1\) loss functions and \(\lambda_{size}\) and \(\lambda_{off}\) are loss weights.  
\(L1\) loss or \(L1\) regularization is used to calculate the error, where error is the difference between the ground truth bounding box and the predicted bounding box coordinates. During detection, class-wise heatmaps are generated corresponding to separate categories. Then some peak points are found out in the generated class-wise heatmaps. In the normal setting, 100 peak points are considered for detection within each category. A keypoint estimator \(\hat{\gamma}\) is used to predict all center points. A set of \(n\) detected center point \(\hat{P}_{c}\) for all \(c\) classes is estimated as \(\hat{P}=\{(\hat{x_{i}},\hat{y_{i}})\}_{i=1}^{n}\) where \((\hat{x_{i}},\hat{y_{i}})\) is the integer coordinate for a keypoint location. Detection confidence score is measured using the keypoint values \(\hat{Y}_{xi,yi,c}\). A local offset is also predicted for center point location and to regress object size. For the learned model, evaluation metric in terms of mean average precision (mAP) is determined for all classes when the Intersection over Union (IoU) with the ground truth bounding box exceeds 0.5. The precision value for any given category is the percentage of correct predictions. i.e.,  
\[Precision=TruePositive/(TruePositive+FalsePositive) \tag{6}\]  
Figure 5: An overview of channel-wise attention module.  
Whereas recall measures the proportion of true positive that can be determined as:  
\[Recall=TruePositive/(TruePositive+FalseNegative) \tag{7}\]  
In general, the average precision (AR) for any given category is the area under the precision-recall curve (AUC--area under the curve). The mean average precision (mAP) is the average value of the AR for all categories of a dataset.  
In this study, we present an architecture containing spatial and channel attention modules as an extension of the our previous method. A conventional way of implementing the channel attention module is that attention blocks are added to each convolutional block during feature extraction [8; 20]. While some methods proposed to use both spatial and channel attention mechanisms within each convolutional block [22]. In our proposed method we employ both attention modules only once in parallel order just before the generation of the class-wise heatmaps, which are used to make dense predictions. The spatial attention and channel attention modules generate two sets of class-wise heatmaps. This arrangement captures strong informative spatial features along with high-level semantics features. Element-wise addition of class-wise feature maps, generated by both attention modules, is performed for better fusion of class-wise information.