## 3 Methodology
### Proposed Architecture
#### 3.3.1 Tiny HRNet  
Our modified HRNet architecture includes four stages and four resolution levels, like the original HRNet. However, unlike [25], each stage in our architecture has only two convolutional layers at each parallel level. This simplified backbone is shown in Figure 2 and is referred to as Tiny HRNet and has significantly reduced complexity compared to HRNet [25]. The backbone includes a stem, \(n\) parallel multi-resolution convolutions at \(n\), and multi-resolution fusion. The past \(p\) chronological traffic images are first concatenated at the channel dimension, \(H\times W\times F\) (here, \(F=3\times p\)) and fed into the stem, which consists of two convolution layers, each layer with strides of \(2\times 2\), a kernel size of \(3\times 3\), and a kernel channel of C to decrease input resolution to \(\frac{H}{4}\times\frac{W}{4}\times C\). Parallel Multi-Resolution Convolution. The output of the stem is fed to the 1 st stage of the Tiny HRNet. The 1 st stage has one level \((L_{1})\) with the feature resolution of output of the stem. The 2 nd stage has two resolution levels \((L_{1}\) and \(L_{2})\) with the feature maps resolution of \(\frac{H}{4}\times\frac{W}{4}\times C\) and \(\frac{H}{8}\times\frac{W}{8}\times 2C\) at \(L_{1}\) and \(L_{2}\), respectively. While the resolution is decreased by one-half on both directions, the channel size of the feature maps is doubled. Similarly, the 3 rd stage has three resolution levels \((L_{1},L_{2}\) and \(L_{3})\) with the feature maps resolution of \(\frac{H}{4}\times\frac{W}{4}\times C\), \(\frac{H}{8}\times\frac{W}{8}\times 2C\) and \(\frac{H}{16}\times\frac{W}{16}\times 4C\) at \(L_{1}\), \(L_{2}\) and \(L_{3}\), respectively. Likewise, the 4 th stage has four resolution levels \((L_{1},L_{2},L_{3}\) and \(L_{4})\) with the feature maps resolution of \(\frac{H}{4}\times\frac{W}{4}\times C\), \(\frac{H}{8}\times\frac{W}{8}\times 2C\), \(\frac{H}{16}\times\frac{W}{16}\times 4C\), and \(\frac{H}{8}\times\frac{W}{8}\times 8C\) at \(L_{1}\), \(L_{2}\), \(L_{3}\) and \(L_{4}\), respectively. All the convolutional layers in the Tiny HRNet use a \(3\times 3\) kernel size and have a stride of \(1\times 1\), and a convolutional layer with \(2\times 2\) kernel size and \(2\times 2\) stride is used for feature map reduction. Figure 1: Road network of Seoul city with the Jam, Slow, and Free congestion levels denoted in red, yellow, and green, respectively. **(a)** A sample of raw image data capture from TOPIS website. **(b)** A sample of image after masking operation where black color represent the background. Multi-Resolution Fusion. The multi-resolution fusion is employed when the network progresses from one stage to the next. The use of multi-scale feature fusion is motivated by the fact that single-scale feature maps may not be sufficient to capture all the information, particularly when objects in the image vary in size. Fusing feature maps across multiple scales allows the network to learn from fine-grained and coarser features, which leads to more spatially precise results. The feature maps of all levels in a particular stage are fused to generate the next stage. Since the resolution of the feature maps varies at different resolution levels, the first step involves aligning these feature maps. Specifically, we aim to convert the resolution of each level in the current stage to match the feature map resolution of the target level in the next stage. This alignment process involves performing convolutional downsampling to decrease the resolution of high-resolution feature maps and bilinear upsampling operations to increase the resolution of lower-resolution feature maps. Finally, we concatenate all the feature maps obtained from the previous step. Figure 2 provides an example of multi-resolution fusion when transitioning from stage 3 to the feature map resolution level \(L_{2}\) of stage 3. Stage 3 comprises three levels \((L_{1},L_{2}\) and \(L_{3})\) with feature map resolutions that differ from the target level.