Phase unwrapping is an ill-posed classical problem in many practical applications of significance such as 3D profiling through fringe projection, synthetic aperture radar and magnetic resonance imaging. Conventional phase unwrapping techniques estimate the phase either by integrating through the confined path (referred to as path-following methods) or by minimizing the energy function between the wrapped phase and the approximated true phase (referred to as minimum-norm approaches). However, these conventional methods have some critical challenges like error accumulation and high computational time and often fail under low SNR conditions. To address these problems, this paper proposes a novel deep learning framework for unwrapping the phase and is referred to as “PhaseNet 2.0”. The phase unwrapping problem is formulated as a dense classification problem and a fully convolutional DenseNet based neural network is trained to predict the wrap-count at each pixel from the wrapped phase maps. To train this network, we simulate arbitrary shapes and propose new loss function that integrates the residues by minimizing the difference of gradients and also uses L ₁ loss to overcome class imbalance problem. The proposed method, unlike our previous approach PhaseNet, does not require post-processing, highly robust to noise, accurately unwraps the phase even at the severe noise level of -5 dB, and can unwrap the phase maps even at relatively high dynamic ranges. Simulation results from the proposed framework are compared with different classes of existing phase unwrapping methods for varying SNR values and discontinuity, and these evaluations demonstrate the advantages of the proposed framework. We also demonstrate the generality of the proposed method on 3D reconstruction of synthetic CAD models that have diverse structures and finer geometric variations. Finally, the proposed method is applied to real-data for 3D profiling of objects using fringe projection technique and digital holographic interferometry. The proposed framework achieves significant improvements over existing methods while being highly efficient with interactive frame-rates on modern GPUs.

中文翻译：

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PhaseNet 2.0：基于深度学习方法的嘈杂数据的相位展开

在许多重要的实际应用中，例如通过条纹投影进行3D轮廓分析，合成孔径雷达和磁共振成像，相位展开是一个不适定的经典问题。常规的相位解缠技术通过在受限路径中积分（称为路径跟随方法）或通过使包裹相位与近似真实相位之间的能量函数最小（称为最小范数逼近）来估计相位。但是，这些常规方法面临一些关键挑战，例如错误累积和高计算时间，并且通常在低SNR条件下会失败。为了解决这些问题，本文提出了一种新颖的深度学习框架，用于展开该阶段，并称为“ PhaseNet 2.0”。相位展开问题被公式化为密集的分类问题，并且基于完全卷积的DenseNet的神经网络经过训练，可以从包裹的相位图中预测每个像素的包裹数。为了训练该网络，我们模拟了任意形状并提出了新的损失函数，该函数通过最小化梯度差来整合残差，并且还使用L _1个克服阶级失衡的问题。与我们以前的方法PhaseNet不同，所提出的方法不需要后处理，对噪声具有很高的鲁棒性，即使在-5 dB的严重噪声水平下也可以准确地解包相位，即使在相对较高的动态范围内也可以解包相位图。将所提出框架的仿真结果与不同类别的现有相位解缠方法进行比较，以改变SNR值和不连续性，这些评估证明了所提出框架的优势。我们还证明了所提出方法对具有各种结构和更精细几何变化的合成CAD模型进行3D重建的一般性。最后，将所提出的方法应用于利用条纹投影技术和数字全息干涉术对物体进行3D轮廓分析的真实数据中。