Surface reconstruction from range scans is challenging in the presence of noise and outliers, as fidelity to observations must be balanced against sensitivity to measurement errors. Yet, most neural approaches discard the sensor positions and corresponding visibility information, compensating for this loss with geometric priors or regularization terms. We instead formulate surface reconstruction as robust regression of the predicted first surface intersection along each acquisition ray against its measured depth, which penalizes predicted surface intersections within the segment between the sensor and the observed point. We represent the surface as the zero set of a 1-Lipschitz multi-layer perceptron, allowing the use of linearly convergent sphere tracing to compute the first hit, and use a robust Huber loss for regression. Our formulation requires neither oriented normals, sampled off-surface points, nor an eikonal loss. Comparisons with the state of the art on synthetic and real data with varying levels of noise and outlier contamination demonstrate competitive performance on clean data and much improved fidelity and robustness under even moderate corruption. Our analysis further confirms a trade-off between fidelity and robustness: greater fitting capacity improves data fidelity in the clean case but increases sensitivity to the measurement errors inherent in real acquisitions, with a sweet spot typically emerging at intermediate capacity.

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