Concordia Institute for Information Systems Engineering, Concordia University, Montreal, QC H3G 1M8, Canada.
Sensors (Basel). 2018 Jul 21;18(7):2379. doi: 10.3390/s18072379.
We present a geometric framework for surface denoising using graph signal processing, which is an emerging field that aims to develop new tools for processing and analyzing graph-structured data. The proposed approach is formulated as a constrained optimization problem whose objective function consists of a fidelity term specified by a noise model and a regularization term associated with prior data. Both terms are weighted by a normalized mesh Laplacian, which is defined in terms of a data-adaptive kernel similarity matrix in conjunction with matrix balancing. Minimizing the objective function reduces it to iteratively solve a sparse system of linear equations via the conjugate gradient method. Extensive experiments on noisy carpal bone surfaces demonstrate the effectiveness of our approach in comparison with existing methods. We perform both qualitative and quantitative comparisons using various evaluation metrics.
我们提出了一种基于图信号处理的曲面去噪的几何框架，这是一个新兴的领域，旨在开发用于处理和分析图结构数据的新工具。所提出的方法被公式化为一个约束优化问题，其目标函数由噪声模型指定的保真度项和与先验数据相关的正则化项组成。这两个项都由归一化网格拉普拉斯加权，该拉普拉斯是根据数据自适应核相似矩阵并结合矩阵平衡来定义的。通过共轭梯度法，最小化目标函数可以将其简化为迭代求解稀疏线性方程组。在嘈杂的腕骨表面上进行的广泛实验表明，与现有方法相比，我们的方法具有有效性。我们使用各种评估指标进行定性和定量比较。
