Owing to the many possible errors that may occur during real‐world mapping, point set maps often present a huge amount of outliers and large levels of noise. We present two robust surface reconstruction techniques dealing with corrupted point sets without resorting to any prefiltering step. They are based on building an unsigned distance function, discretely evaluated on an adaptive tetrahedral grid, and defined from an outlier‐robust splat representation. To extract the surface from this volumetric view, the space is partitioned into two subsets, the surface of interest being at the boundary separating them. While both methods are based on a similar graph definition derived from the above‐mentioned grid, they differ in the partitioning procedure. First, we propose a method using S‐T cuts to separate the inside and outside of the mapped area. Second, we use a normalized cut approach to partition the volume using only the values of the unsigned distance function. We prove the validity of our methods by applying them to challenging underwater data sets (sonar and image based), and we benchmark their results against the approaches in the state of the art.