Surface Reconstruction Based on the Modified Gauss Formula

In this article, we introduce a surface reconstruction method that has excellent performance despite nonuniformly distributed, noisy, and sparse data. We reconstruct the surface by estimating an implicit function and then obtain a triangle mesh by extracting an iso-surface. Our implicit function takes advantage of both the indicator function and the signed distance function. The implicit function is dominated by the indicator function at the regions away from the surface and is approximated (up to scaling) by the signed distance function near the surface. On one hand, the implicit function is well defined over the entire space for the extracted iso-surface to remain near the underlying true surface. On the other hand, a smooth iso-surface can be extracted using the marching cubes algorithm with simple linear interpolations due to the properties of the signed distance function. Moreover, our implicit function can be estimated directly from an explicit integral formula without solving any linear system. An approach called disk integration is also incorporated to improve the accuracy of the implicit function. Our method can be parallelized with small overhead and shows compelling performance in a GPU version by implementing this direct and simple approach. We apply our method to synthetic and real-world scanned data to demonstrate the accuracy, noise resilience, and efficiency of this method. The performance of the proposed method is also compared with several state-of-the-art methods.