Single-shot coded diffraction system for 3D object shape estimation

The three-dimensional (3D) shape reconstruction problem of an object is a task of high interest in autonomous vehicles, detection of moving objects, and precision agriculture. A common methodology to recover the 3D shape of an object is using its optical phase. However, this approach involves solving a non-convex computationally demanding inverse problem known as phase retrieval (PR) in a setup that records coded diffraction patterns (CDP). Usually, the acquisition of several snapshots from the scene is required to solve the PR problem. This work proposes a single-shot 3D shape estimation technique using the optical phase of the object from CDP. The presented approach consists on accurately estimating the optical phase of the object by low-pass-filtering the leading eigenvector of a carefully constructed matrix. Then, the estimated phase is used to infer the 3D object shape. It is important to mention that the estimation procedure does not involve a full time demanding reconstruction of the objects. Numerical results on synthetic data demonstrate that the proposed methodology closely estimates the 3D surface of an object with a normalized Mean-Square-Error of up to 0.27, under both noiseless and noisy scenarios. Additionally, the proposed method requires up to 60% less measurements to accurately estimate the 3D surface compared to a state-of-the-art methodology.