A Markov random field based method for removing invalid unwrapping phase points in 3D reconstruction

Abstract

Fringe projection profilometry is widely used in 3D structured light due to its fast speed and accuracy. However, in the process of phase unwrapping, it is easy to cause invalid points in the edges and shadows of objects, which leads to error points in 3D reconstruction. To solve this problem, we propose an invalid points removal method based on Markov random fields. Specifically, the proposed method formulates unwrapped phase and mask maps as energy functions and uses iterative methods to minimize them. Furthermore, we validate the proposed method in a monocular structured light system and compare it with existing algorithms. Results show that the proposed method effectively identifies edges and shadows while preserving valid points, and has strong robustness and correctness.

An improved image segmentation algorithm based on MRF and Sobel operator

“…Since in images, adjacent pixels often exhibit similar colors, textures, and other features, according to The Hammersley-Clifford Theorem, we know that a random field is a Markov field if and only if the prior probability P(ω) follows a Gibbs distribution [6]. The probability distribution of a Gibbs random field takes the following form:…”

“… arg min_ ( ) y yE y  (6) In each iteration, the algorithm adjusts the weights to find the segmentation that minimizes the energy. This is achieved by comparing the energy associated with different labels and selecting the new label for each pixel.…”