The joint bilateral filter, which enables feature-preserving signal smoothing according to the structural information from a guidance, has been applied for various tasks in geometry processing. Existing methods either rely on a static guidance that may be inconsistent with the input and lead to unsatisfactory results, or a dynamic guidance that is automatically updated but sensitive to noises and outliers. Inspired by recent advances in image filtering, we propose a new geometry filtering technique called static dynamic filter, which utilizes both static and dynamic guidances to achieve state-of-the-art results. The proposed filter is based on a nonlinear optimization that enforces smoothness of the signal within designated neighborhoods, while preserving signal variations that correspond to features of certain scales. We develop an efficient iterative solver for the problem, which unifies existing filters that are based on static or dynamic guidances. The filter can be applied to mesh face normals followed by vertex position update, to achieve scale-aware and feature-preserving filtering of mesh geometry. It also works well for other types of signals defined on mesh surfaces, such as texture colors. Extensive experimental results demonstrate the effectiveness of the proposed filter for various geometry processing applications such as mesh denoising, geometry feature enhancement, and texture color filtering.
In the past, various filtering approaches have been proposed to process mesh geometry. Early work from Taubin and applied low-pass filters on meshes, which remove high-frequency noises but also attenuate sharp features. Later, Taubin proposed a two-step approach that first performs smoothing on face normals, followed by vertex position updates using anisotropic filters. To enhance crease edges, applied anisotropic diffusion to mesh normals before updating vertex positions. Chuang and Kazhdan @cite_20 developed a framework for curvature-aware mesh filtering based on the screened Poisson equation.
@cite_20
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In this paper, we introduce a feature-preserving denoising algorithm. It is built on the premise that the underlying surface of a noisy mesh is piecewise smooth, and a sharp feature lies on the intersection of multiple smooth surface regions. A vertex close to a sharp feature is likely to have a neighborhood that includes distinct smooth segments. By defining the consistent subneighborhood as the segment whose geometry and normal orientation most consistent with those of the vertex, we can completely remove the influence from neighbors lying on other segments during denoising. Our method identifies piecewise smooth subneighborhoods using a robust density-based clustering algorithm based on shared nearest neighbors. In our method, we obtain an initial estimate of vertex normals and curvature tensors by robustly fitting a local quadric model. An anisotropic filter based on optimal estimation theory is further applied to smooth the normal field and the curvature tensor field. This is followed by second-order bilateral filtering, which better preserves curvature details and alleviates volume shrinkage during denoising. The support of these filters is defined by the consistent subneighborhood of a vertex. We have applied this algorithm to both generic and CAD models, and sharp features, such as edges and corners, are very well preserved. Most mesh denoising techniques utilize only either the facet normal field or the vertex normal field of a mesh surface. The two normal fields, though contain some redundant geometry information of the same model, can provide additional information that the other field lacks. Thus, considering only one normal field is likely to overlook some geometric features. In this paper, we take advantage of the piecewise consistent property of the two normal fields and propose an effective framework in which they are filtered and integrated using a novel method to guide the denoising process. Our key observation is that, decomposing the inconsistent field at challenging regions into multiple piecewise consistent fields makes the two fields complementary to each other and produces better results. Our approach consists of three steps: vertex classification , bi-normal filtering , and vertex position update . The classification step allows us to filter the two fields on a piecewise smooth surface rather than a surface that is smooth everywhere. Based on the piecewise consistence of the two normal fields, we filtered them using a piecewise smooth region clustering strategy. To benefit from the bi-normal filtering, we design a quadratic optimization algorithm for vertex position update. Experimental results on synthetic and real data show that our algorithm achieves higher quality results than current approaches on surfaces with multifarious geometric features and irregular surface sampling. In this paper, we propose a novel triangle mesh denoising method based on the differential coordinates. The proposed approach consists of the application of the mean filter to differential coordinates of the mesh and the reconstruction of mesh vertices' Cartesian coordinates to make them fit to the modified differential coordinates. The presented method is simple, stable and able to effectively remove large noise. Experimental results demonstrate that the proposed Mesh Mean Filter does not cause surface shrinkage and shape distortion during the denoising process, and preserves geometric detail features to a certain extent. In recent years researchers have made noticeable progresses in mesh denoising, that is, recovering high-quality 3D models from meshes corrupted with noise (raw or synthetic). Nevertheless, these state of the art approaches still fall short for robustly handling various noisy 3D models. The main technical challenge of robust mesh denoising is to remove noise while maximally preserving geometric features. In particular, this issue becomes more difficult for models with considerable amount of noise. In this paper we present a novel scheme for robust feature-preserving mesh denoising. Given a noisy mesh input, our method first estimates an initial mesh, then performs feature detection, identification and connection, and finally, iteratively updates vertex positions based on the constructed feature edges. Through many experiments, we show that our approach can robustly and effectively denoise various input mesh models with synthetic noise or raw scanned noise. The qualitative and quantitative comparisons between our method and the selected state of the art methods also show that our approach can noticeably outperform them in terms of both quality and robustness.