Phase Unwrapping Using Flood-Fill Algorithm Based on Branch-Cut Method

Phase unwrapping is a critical technique in image processing for recovering true phase information, particularly widely applied in interferometric measurement and 3D reconstruction. The branch-cut based flood-fill unwrapping method effectively resolves phase jump issues by integrating mathematical optimization with region-growing strategies. Its core workflow can be divided into three key steps: Residue Calculation The first step involves locating discontinuity points (residues) in the phase map by calculating phase gradient integrals along local closed paths. The presence of positive and negative residues causes cumulative errors during unwrapping, requiring special handling. In code implementation, this typically involves convolving the phase map with a 2x2 kernel to compute residue polarity, where nonzero values indicate problematic pixels. Branch-Cut Placement This step forms "cut lines" by connecting adjacent positive and negative residues, forcibly constraining the flood-fill path to avoid crossing these boundaries. Optimal cut placement prevents the unwrapping path from bypassing residue areas, thereby blocking error propagation. Algorithmically, this can be implemented using minimum-spanning-tree approaches to minimize total cut length while balancing residue connectivity. Flood-Fill Unwrapping Starting from low-noise seed points, the algorithm expands pixel-by-pixel like flood propagation, correcting 2π integer jumps based on phase values of adjacent unwrapped pixels. The cut lines act as "dams" ensuring the fill doesn't traverse high-error regions. Code implementation typically uses queue-based breadth-first search with phase difference thresholding, where pixels are processed only when their phase gradient exceeds predefined tolerance values. The method's advantage lies in balancing computational efficiency and accuracy: the branch-cut method reduces residue processing load, while flood-fill's local adaptability preserves detail. Practical applications require careful seed point selection strategies and cut-line optimization, which are crucial for stability in complex noise scenarios. Programmers should implement robustness checks for handling isolated residues and boundary conditions during the flooding process.