# Multi-Resolution and Semantic-Aware Bidirectional Adapter for Multi-Scale Object Detection
## 3 The Proposed Method
### Multi-Resolution Cascaded Fusion  
FPN employs a single-resolution image as its input to create a feature pyramid. It can partially mitigate the challenge of scale variation. However, this approach is limited since a single-resolution image can only offer a restricted amount of object information within a specific scale. Using high-resolution images as input can be advantageous for detecting small objects, yet it might lead to relatively lower performance in detecting larger objects. Conversely, utilizing low-resolution images as input may lead to subpar performance in detecting small objects. Consequently, employing a single-resolution image as input might not suffice for effectively detecting objects across various scales. Hence, the inclusion of a multi-scale image input is crucial for detectors to gather a broader spectrum of object information across different resolutions. This observation motivates our introduction of the multi-resolution cascaded fusion, which integrates multi-resolution data into the network architecture, as illustrated in Figure 1(a). Initially, the input image undergoes both backbone processing and direct downsampling to align with the size of \(C_{i}=\{C_{2},C_{3},C_{4},C_{5}\}\) from the backbone as \(Cd_{i}^{\prime}=\{Cd_{2}^{\prime},Cd_{3}^{\prime},Cd_{4}^{\prime},Cd_{5}^{ \prime}\}\). Following this, the downsampled multi-resolution images undergo a sequence of convolution, batch normalization, and activation operations, culminating in the creation of corresponding features imbued with both coarse-grained spatial details and semantic insights. Furthermore, we employ a matching gate to adaptively manage the fusion process between the generated  
Figure 2: The overall architecture of MSBA. There are three components: multi-resolution cascaded fusion (MCF), semantic-aware refinement transformer (SRT) and bidirectional fine-grained interaction (BFI). MCF performs an adaptive fusion of multi-receptive-field and multi-resolution features, providing ample multi-scale information. Subsequently, SRT refines the features by amplifying long-range semantic information. Moreover, BFI ensures robust interaction by establishing two opposing directions of guidance for features containing fine-grained information. The pixel-level filter establishes a bottom-up pathway to convey spatial information from high-resolution levels. Concurrently, the channel-wise prompt guides low-level semantic information via the top-down structure. multi-resolution features and the multi-stage features derived from the backbone. This procedure can be described as:  
\[C_{i}^{\prime}=\sum_{\Psi_{i}\in CBR}\Psi_{i}(Cds_{i}^{\prime}). \tag{4}\]  
Here, \(Cds_{i}^{\prime}\) refers to the input image that has been downsampled to align with the suitable spatial dimensions of \(C_{i}\), with \(i\) representing the feature level index from the backbone. \(\Psi_{i}(\cdot)\) represents a sequence of operations, including a 3 \(\times\) 3 Conv, BN, and ReLU to produce semantic features. Subsequently, we leverage \(C_{i}^{\prime}\) to merge with the corresponding \(C_{i}\) using a matching gate, thereby generating a feature that is more effective. Additionally, we formulate a multi-receptive-field cascaded fusion strategy to extract multi-scale spatial information from the lower-level features. The entire procedure can be expressed as follows:  
\[M_{i}^{\prime}=\mathcal{G}(C_{i}^{\prime},C_{i})+R_{i}(\mathcal{G}(C_{i-1}^{ \prime},C_{i-1}))\quad i=(3,4,5), \tag{5}\]  
where \(R_{i}^{\prime}\) signifies the convolution operator applied with different dilation rates. \(M_{i}^{\prime}\) corresponds to the input for the subsequent stage, enriched with ample coarse-grained and multi-scale spatial information. Notably, \(M_{2}^{\prime}\) is derived from the matching gate without the incorporation of dilated convolution. Generally, our multi-resolution cascaded fusion supplies diverse resolution information. The proposed MCF is advantageous for object instances of varying scales.