Differentiable Space Carving for 3D Reconstruction Using Imaging Sonar

Effective 3D reconstruction utilizing imaging sonars is vital for underwater robots, particularly in turbid water conditions. The absence of elevation angles in acoustic echo measurements significantly slows down the Neural Radiance Field (NeRF) method. This is attributed to the differentiable rendering model of sonar images, which, unlike visual imagery, needs to generate samples covering a spatial sector rather than a ray for each pixel. To address this, we present a fast 3D reconstruction method using sonar images, termed Differentiable Space Carving (DSC). DSC carves the space iteratively by rendering echo probabilities instead of echo intensities, eliminating the need for the intensity network commonly found in NeRF models. The absence of occupancy-echo correspondences is effectively tackled through backpropagation guided by rendering losses. Additionally, we leverage occupancy probability grids and multiresolution hash encoding to construct differentiable occupancy models, ensuring faster convergence compared to multilayer perceptrons. The experiments have been conducted in numerically simulated environments and with datasets from a laboratory tank. Compared to existing NeRF methods, DSC reconstructs objects about ten times faster and provides more details.