Faithful Euclidean Distance Field From Log-Gaussian Process Implicit Surfaces

In this letter, we introduce the Log-Gaussian Process Implicit Surface (Log-GPIS), a novel continuous and probabilistic mapping representation suitable for surface reconstruction local navigation. Our key contribution is realisation that regularised Eikonal equation can be simply solved by applying logarithmic transformation to GPIS formulation recover accurate Euclidean distance field (EDF) and, at same time, implicit surface. To derive proposed representation, Varadhan's formula exploited approximate non-linear partial differential (PDE) of EDF logarithm linear PDE. We show members Matérn covariance family directly satisfy The approach does not require post-processing steps EDF. Moreover, unlike sampling-based methods, Log-GPIS use sample points inside outside as derivative allow direct estimation normals gradients. benchmarked method on simulated real data against state-of-the-art frameworks also aim recovering both field. experiments produces most results comparable its computation time still allows online operations.