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Implicit Neural Representations (INR) use multilayer perceptrons to represent high-frequency functions in lowdimensional problem domains. Recently these representations achieved state-of-the-art results on tasks related to complex 3D objects and scenes. A core problem is the representation of highly detailed signals, which is tackled using networks with periodic activation functions (SIRENs) or applying Fourier mappings to the input. This work analyzes the connection between the two methods and shows that a Fourier mapped perceptron is structurally like one hidden layer SIREN. Furthermore, we identify the relationship between the previously proposed Fourier mapping and the general d-dimensional Fourier series, leading to an integer lattice mapping. Moreover, we modify a progressive training strategy to work on arbitrary Fourier mappings and show that it improves the generalization of the interpolation task. Lastly, we compare the different mappings on the image regression and novel view synthesis tasks. We confirm the previous finding that the main contributor to the mapping performance is the size of the embedding and standard deviation of its elements.

Multi-object tracking is a critical component in autonomous navigation, as it provides valuable information for decision-making. Many researchers tackled the 3D multiobject tracking task by filtering out the frame-by-frame 3D detections; however, their focus was mainly on finding useful features or proper matching metrics. Our work focuses on a neglected part of the tracking system: score refinement and tracklet termination. We show that manipulating the scores depending on time consistency while terminating the tracklets depending on the tracklet score improves tracking results. We do this by increasing the matched tracklets' score with score update functions and decreasing the unmatched tracklets' score. Compared to count-based methods, our method consistently produces better AMOTA and MOTA scores when utilizing various detectors and filtering algorithms on different datasets. The improvements in AMOTA score went up to 1.83 and 2.96 in MOTA. We also used our method as a late-fusion ensembling method, and it performed better than voting-based ensemble methods by a solid margin. It achieved an AMOTA score of 67.6 on nuScenes test evaluation, which is comparable to other state-of-the-art trackers. Code is publicly available at: https://github.com/cogsys-tuebingen/CBMOT.

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