Implicit representations allow to use a parametric function that maps (spatial) coordinates to the value that is traditionally stored in each pixel, e.g. RGB values, instead of a discrete grid. This has recently proven quite advantageous as an internal representation for images or scenes for deep learning models. Yet, its potential to ensure certain properties of the solution has not yet been fully explored. In this work, we demonstrate that implicit representations are a powerful tool for enforcing a variety of different geometric constraints in image segmentation. While convexity, star-shape, path-connectedness, periodicity, or symmetry of the (spatial or space-time) region to be segmented are very challenging to enforce for pixel-wise discretizations, a suitable parametrization of an implicit representation, mapping spatial or spatio-temporal coordinates to the likeliness of a pixel belonging to the fore- or background, allows to **provably** ensure such constraints. Several numerical examples demonstrate that challenging segmentation scenarios can benefit from the inclusion of application-specific constraints, e.g. when occlusions prevent a faithful segmentation with classical approaches.

Our research aims to reduce the cost of pressure sensor calibration through machine learning. Pressure sensor calibration is a standard process whereby freshly manufactured pressure sensors are subjected to various controlled temperature and pressure setpoints to compute a mapping between the sensor's output and true pressure. Traditionally this mapping is calculated by fitting a polynomial with calibration data. Obtaining this data is costly since a large spectrum of temperature and pressure setpoints are required to model the sensor's behavior. We present a machine learning approach to predict a pre-defined calibration polynomial's parameters while requiring only one-third of the calibration data. Our method learns a pattern from past calibration sessions to predict the calibration polynomial's parameters from partial calibration setpoints for any newly manufactured sensor. We design a novel polynomial hypernetwork coupled with Fourier features and a weighted loss to solve this problem. We perform extensive evaluations and show that the current industry-standard method fails under similar conditions. In contrast, our approach saves two-thirds of the calibration time and cost. Furthermore, we conduct comprehensive ablations to study the effect of Fourier mapping and weighted loss. Code and a novel calibration dataset validated by calibration engineers are also made public.

Anticipation of accidents ahead of time in autonomous and non -autonomous vehicles aids in accident avoidance. In order to recognize abnormal events such as traffic accidents in a video sequence, it is important that the network takes into account interactions of objects in a given frame. We propose a novel Feature Aggregation (FA) block that refines each object's features by computing a weighted sum of the features of all objects in a frame. We use FA block along with Long Short Term Memory (LSTM) network to anticipate accidents in the video sequences. We report mean Average Precision (mAP) and Average Time-to-Accident (ATTA) on Street Accident (SA) dataset. Our proposed method achieves the highest score for risk anticipation by predicting accidents 0.32 sec and 0.75 sec earlier compared to the best results with Adaptive Loss and dynamic parameter prediction based methods respectively.