Adaptive depth measurement based on adversarial relevance vector regression for fringe projection profilometry

•An ARVR framework is proposed for depth measurement.•An adaptive adjustment is designed based on the adversarial posterior variance.•Quantitative and qualitative experiments are used to verify the proposed ARVR framework.•The ARVR framework has better performance than other phase-depth models. Fringe projection profilometry (FPP) is a structured light technique widely used for the depth measurement of object surfaces. For FPP systems, it is essential to establish the mapping from phases to depths, known as phase-depth models. Imaging system noise and camera defocus can disrupt the fringe order and wrapped phase relationship, potentially causing errors in phase unwrapping that may limit the effectiveness of traditional phase-depth models. To address this issue, we propose an adaptive depth measurement framework for FPP systems with using adversarial relevance vector regression (ARVR). The core principle of the ARVR framework is the predictive distribution of depths. Specifically, we first use the sparse kernel-based RVR algorithm to establish two types of local RVR-based phase-depth models and obtain the predictive distribution of depths. Then, we design an adversarial strategy of the posterior variance to calculate more reasonable depth measurements through adaptive adjustments. Experiment results demonstrated that the ARVR framework outperforms traditional phase-depth models.