# Addressing the Gaps of IoU Loss in 3D Object Detection with IIoU
## 1 Introduction  
Object detection has become increasingly popular and contributed to the development of various applications in the autonomous vehicular industry, such as obstacle detection, collision avoidance, lane-level detection,parking assistance and pedestrian safety [1; 2; 3]. In order to perform detection tasks in autonomous vehicles, range sensors such as LiDAR, RADAR, RGB-D, and stereo vision cameras are heavily relied upon [4; 5; 6]. LiDAR and RADAR emit light pulses and radio waves to detect the presence of an object and provide data in the form of point clouds. In contrast, vision cameras capture 2D image data of the environment along with depth/distance estimation. With rapid development in deep learning, 2D and 3D detections have gathered more interest in the research community [7]. 2D networks are often termed image-based network since it heavily depends on image data to perform localization and classification tasks [8]. The bounding box coordinates of 2D objects are represented as x1, y1, x2, y2. Recently, various architectures such as SSD [9], Faster R-CNN [10], YOLO [11], FFNet [12] and VirConv-S [13] have been proposed in 2D detection challenge and are successfully backed by large-scale datasets such as KITTI [14]. Compared to 2D detection techniques, 3D object detection poses a trivial challenge because the concepts of 2D detection cannot be directly translated to the 3D domain due to its 6 Degrees-of-Freedom (DoF) [15]. 3D object detectors estimate the bounding box coordinates as (x, y, z, l, w, h, \(\theta\)). Like 2D object detectors, state-of-the-art 3D object detectors can be classified into single-stage and two-stage detectors based on the presence or absence of Regional Proposal Networks (RPN). In two-stage methods, the first stage extracts feature information generated by RPN and generates Regions of Interest (RoI). The second stage acts as a detector network that operates only on the proposed regions to create accurate predictions. On the other hand, Single-stage detectors serve as a simple and efficient end-to-endpipeline. However, single-stage detectors face a performance drop as compared to two-stage detectors. One of the primary reasons is the sparsity of point clouds, and when the network progressively scales down during the forward pass of the network, crucial spatial information is lost [1]. This causes an inability to predict the bounding box coordinates in 3D space accurately. Architectures such as PointNet [16] and VoxelNet [4] were proposed to increase the performance of single-stage detector networks. VoxelNet divides the 3D space into voxels and then applies PointNet across each voxel, followed by 3D and 2D convolution layers [17]. Following the recent success in the usage of transformers [18] in computer vision, another approach was to utilize transformer structures to address sparse irregularities in processing point cloud information [19]. During training, the predicted bounding boxes are regressed continuously to match the ground truth data [20; 21; 22]. The detector stage of single and two-stage object detectors use \(L_{norm}\) based loss functions such as L1, L2, and smooth-\(I\)\(I\) to optimize the bounding box regression problem [10; 23]. However, a performance gap exists between IoU-based evaluation metrics and distance-based loss functions. [24; 25; 26; 17; 27] have analyzed this mismatch and demonstrated that similar bounding boxes with different aspect ratios yield the same distance loss while their IoU values remain different. IoU based loss functions [27; 28; 29] were proposed to address this issue. IoU, as the name suggests, measures the Intersection Over Union area between two bounding boxes. One of the critical differences between IoU losses and distance loss is that IoU considers all the properties of bounding boxes, such as length, width, height, and orientation, and remains scale-invariant, solving scale and range differences between the boxes.