Combined Wavelet and Laplacian Smoothing for Denoising of Triangle Mesh Boundary

Three-dimensional (3D) surface model applications have emerged to be an interesting research topic due to the popularity of range cameras such as the Microsoft Kinect. However, digitized surface meshes are often corrupted with noises especially at the boundary. This is due to the random missing boundary data which results in noisy transitions and ragged boundary edges. Such deformity is especially apparent in open surface meshes and needs to be treated in order to improve the visual quality of the meshes as well as to facilitate further applications. In this research, an effective denoising algorithm for triangle mesh boundary is proposed, which is an improved version of the classical Laplacian smoothing algorithm. The proposed algorithm incorporates a wavelet technique into the Laplacian smoothing algorithm to increase the efficiency of denoising. This includes increased smoothness of the output and reduced computation time. The output of the algorithm is ready to be applied in various applications in the industry including 3D printing. The proposed algorithm is evaluated and benchmarked using a metric which measures the smoothness of the boundaries of the denoised meshes. This is achieved by computing the average value of the curvature evaluated at each vertex of the mesh boundary using an invariant three-point curvature approximation method. Using the metric, numerical results are generated and the proposed algorithm is compared with several related methods in the literature. Apart from smoothness, the computation time of all methods are also compared. Both visual and numerical results show that the proposed algorithm outperforms other methods in the literature