## 1 Introduction
In this work, we trained a U-Net [22] model on the 3D-printed heart phantom to segment a radiopaque marker at the tip of the catheter. A postprocessing step was used to analytically calculate the Z-coordinate by leveraging the two simultaneous views of the catheter. Although this was an accurate method to perform the tip detection of a catheter, it is not scalable to many types of catheters and/or devices, since semantic segmentation models require the time-consuming manual annotation of ground truth images. Annotating masks (i.e., selecting all pixels in the catheter tip) takes ~50 times longer than defining the landmark as a single point on the image. We, therefore, explored the use of coordinate regression models that directly output the X- and Y-coordinate of the catheter tip, while utilizing the same analytical Z-coordinate calculation. This method has the benefits of simpler ground truth annotations and mitigating the need for the postprocessing of the output mask. Deep convolutional neural networks (CNNs) have been applied to a multitude of computer vision problems. In medical imaging, CNNs have been effective in many tasks, such as classification [23], localization [24], tracking [25], and image segmentation [22; 26]. [PERSON] et al. [22] proposed the U-Net [22], which replaced the pooling operators in fully convolutional networks (FCNs) [27] with up-sampling operators, allowing the input image resolution to be retained in the output. The performance of the U-Net [22] for segmenting medical images, notably with even small training datasets, demonstratedthe potential of such an encoder-decoder architecture. The U-Net [22] was later applied to other medical settings, including the Xenopus kidney [28], MRI volume segmentation of the prostate [29], retinal vessels, liver and tumors in CT scans, ischemic stroke lesion, and intervertebral disc and pancreas [30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41]. Landmark localization plays a vital role in medical image analysis. Several deep learning methods have been proposed for landmark localization that employ regression or classification [42; 43; 44; 45; 46; 47; 48]. In regression-based localization, a hard threshold is utilized to detect the presence of a landmark in image slices, patches, or voxels. This threshold converts the model's coordinate prediction (pixel-wise or mm-based) to the assigned annotated labels. Therefore, these methods usually rely on the careful consideration of a final threshold value, which may be data- or task-specific. [PERSON] et al. [49] localized a landmark by classifying image voxels with multilayer perceptrons, while [PERSON] et al. [50] localized landmarks based on their relative position (up, down, left, or right) to the landmark of interest. In another work, [PERSON] et al. [51] predicted the location of a landmark based on intersecting the classification outputs from all axial, coronal, and sagittal image slices. Another existing approach for coordinate regression is to generate a heatmap output from a CNN and apply a loss directly to the heatmap rather than the numerical coordinates [52]. Even though this approach offers good spatial generalization, it has the drawback that gradient flow begins at the heatmap rather than at the numerical coordinates. This creates a disconnect between the heatmap loss optimization and the true goal of reducing the coordinate error distances [52]. Another coordinate regression approach is to utilize fully connected (FC) layers that produce numerical coordinates [53]. Most notably, FC layers allow end-to-end backpropagation from the predicted numerical coordinates to the input image. However, the fully connected layer weights are highly dependent on the spatial distribution of the inputs during training. To address this issue, our group used another approach that leveraged a segmentation network followed by a postprocessing step [17].