Final Report Summary - IRON (Robust Geometry Processing) The initial great promise of Digital Geometry Processing (DGP) was to achieve for shapes what had been done in Digital Signal Processing (DSP) for sound and images. Central research themes in the field of DGP include conversions between physical and digital representations. These conversions, referred to as reconstruction and approximation, formed two central themes of the ERC-funded IRON project. The lack of robustness and guarantees in current conversion approaches makes it impossible to streamline the processing pipeline. Stringent requirements for input data and a lack of guarantees for the outputs prevent the current technological solutions from working together seamlessly. Practitioners are thus obliged to use an iterative process of trial and error to repair imperfect data. For instance, a computational engineer who needs to perform a thermal computational simulation on an outdoor urban scene often takes weeks just to render the digital model defect-free and ready for simulation. In our quest for robust shape reconstruction, we pioneered novel formulations based on the theory of optimal transportation. As such, the input geometric measurements are regarded as discrete measures (a distribution of masses), and the reconstruction problem is reformulated as a mass transportation problem, offering unrivaled resilience to noise and outliers. Our approach has potential to offer both resilience to imperfect inputs and guarantees for outputs, while using automation to reduce the task duration from weeks to hours. This translates to a net gain in terms of wall clock time (as opposed to computing clock time), which is what matters most in industrial applications.
