Abstract
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.
Highlights
Recent advances in 3D scanning technology have led to the increasing use of 3D models in many fields, including the entertainment industry, archaeology, computer vision, and medical imaging.These models are usually captured in the form of point clouds or polygonal meshes [1], but they are often corrupted by noise during the data acquisition stage
Surface denoising methods can be classified into two major categories: isotropic and anisotropic. The former techniques filter the noisy data independently of direction, while the latter methods modify the diffusion equation to make it nonlinear or anisotropic in order to preserve the sharp features of a 3D mesh surface
Motivated by the good performance of the similarity-based image denoising framework proposed in reference [12], we introduce a simple, yet effective, feature-preserving approach to 3D mesh denoising
Summary
Recent advances in 3D scanning technology have led to the increasing use of 3D models in many fields, including the entertainment industry, archaeology, computer vision, and medical imaging. These models are usually captured in the form of point clouds or polygonal meshes [1], but they are often corrupted by noise during the data acquisition stage. Surface denoising methods can be classified into two major categories: isotropic and anisotropic The former techniques filter the noisy data independently of direction, while the latter methods modify the diffusion equation to make it nonlinear or anisotropic in order to preserve the sharp features of a 3D mesh surface. The simplest surface denoising method is the Laplacian flow which repeatedly and simultaneously adjusts the location of each mesh vertex to the geometric center of its neighboring vertices [2]
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