Near-optimal Active Reconstruction (2503.18999v1)

Abstract: With the growing practical interest in vision-based tasks for autonomous systems, the need for efficient and complex methods becomes increasingly larger. In the rush to develop new methods with the aim to outperform the current state of the art, an analysis of the underlying theory is often neglected and simply replaced with empirical evaluations in simulated or real-world experiments. While such methods might yield favorable performance in practice, they are often less well understood, which prevents them from being applied in safety-critical systems. The goal of this work is to design an algorithm for the Next Best View (NBV) problem in the context of active object reconstruction, for which we can provide qualitative performance guarantees with respect to true optimality. To the best of our knowledge, no previous work in this field addresses such an analysis for their proposed methods. Based on existing work on Gaussian process optimization, we rigorously derive sublinear bounds for the cumulative regret of our algorithm, which guarantees near-optimality. Complementing this, we evaluate the performance of our algorithm empirically within our simulation framework. We further provide additional insights through an extensive study of potential objective functions and analyze the differences to the results of related work.