81 research outputs found
Robust Feature-Preserving Mesh Denoising Based on Consistent Sub-Neighborhoods
published_or_final_versio
Robust feature-preserving mesh denoising based on consistent subneighborhoods
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. © 2010 IEEE.link_to_subscribed_fulltex
Comprehensive Use of Curvature for Robust and Accurate Online Surface Reconstruction
Interactive real-time scene acquisition from hand-held depth cameras has recently developed much momentum, enabling
applications in ad-hoc object acquisition, augmented reality and other fields. A key challenge to online reconstruction remains
error accumulation in the reconstructed camera trajectory, due to drift-inducing instabilities in the range scan alignments of the
underlying iterative-closest-point (ICP) algorithm. Various strategies have been proposed to mitigate that drift, including SIFT-based
pre-alignment, color-based weighting of ICP pairs, stronger weighting of edge features, and so on. In our work, we focus on surface
curvature as a feature that is detectable on range scans alone and hence does not depend on accurate multi-sensor alignment. In
contrast to previous work that took curvature into consideration, however, we treat curvature as an independent quantity that we
consistently incorporate into every stage of the real-time reconstruction pipeline, including densely curvature-weighted ICP, range
image fusion, local surface reconstruction, and rendering. Using multiple benchmark sequences, and in direct comparison to other
state-of-the-art online acquisition systems, we show that our approach significantly reduces drift, both when analyzing individual
pipeline stages in isolation, as well as seen across the online reconstruction pipeline as a whole
O zakrivljenostima na trokutnim mrežama
A face-based curvature estimation on triangle meshes is presented in
this paper. A flexible disk is laid on the mesh around a given
triangle. Such a bent disk is used as a geodesic neighborhood of the
face for approximating normal and principal curvatures. The radius
of the disk is free input data in the algorithm. Its influence on
the curvature values and the stability of estimated principal
directions are investigated in the examples.U članku je prikazana procjena zakrivljenosti na trokutnim mrežama, bazirana na stranicama. Gipki disk položen je na
mrežu oko danog trokuta. Takav prilagodljiv disk koristi se
kao geodetska okolina stranice za aproksimaciju normalnih i
glavnih zakrivljenosti. Polumjer diska je nezavisni ulazni
podatak u algoritmu. U primjerima se istražuje njegov utjecaj na vrijednosti zakrivljenosti i na stabilnost procijenjenih glavnih
smjerova
Feature Lines for Illustrating Medical Surface Models: Mathematical Background and Survey
This paper provides a tutorial and survey for a specific kind of illustrative
visualization technique: feature lines. We examine different feature line
methods. For this, we provide the differential geometry behind these concepts
and adapt this mathematical field to the discrete differential geometry. All
discrete differential geometry terms are explained for triangulated surface
meshes. These utilities serve as basis for the feature line methods. We provide
the reader with all knowledge to re-implement every feature line method.
Furthermore, we summarize the methods and suggest a guideline for which kind of
surface which feature line algorithm is best suited. Our work is motivated by,
but not restricted to, medical and biological surface models.Comment: 33 page
Invariant Reconstruction of Curves and Surfaces with Discontinuities with Applications in Computer Vision
The reconstruction of curves and surfaces from sparse data is an important task in many applications. In computer vision problems the reconstructed curves and surfaces generally represent some physical property of a real object in a scene. For instance, the sparse data that is collected may represent locations along the boundary between an object and a background. It may be desirable to reconstruct the complete boundary from this sparse data. Since the curves and surfaces represent physical properties, the characteristics of the reconstruction process differs from straight forward fitting of smooth curves and surfaces to a set of data in two important areas. First, since the collected data is represented in an arbitrarily chosen coordinate system, the reconstruction process should be invariant to the choice of the coordinate system (except for the transformation between the two coordinate systems). Secondly, in many reconstruction applications the curve or surface that is being represented may be discontinuous. For example in the object recognition problem if the object is a box there is a discontinuity in the boundary curve at the comer of the box. The reconstruction problem will be cast as an ill-posed inverse problem which must be stabilized using a priori information relative to the constraint formation. Tikhonov regularization is used to form a well posed mathematical problem statement and conditions for an invariant reconstruction are given. In the case where coordinate system invariance is incorporated into the problem, the resulting functional minimization problems are shown to be nonconvex. To form a valid convex approximation to the invariant functional minimization problem a two step algorithm is proposed. The first step forms an approximation to the curve (surface) which is piecewise linear (planar). This approximation is used to estimate curve (surface) characteristics which are then used to form an approximation of the nonconvex functional with a convex functional. Several example applications in computer vision for which the invariant property is important are presented to demonstrate the effectiveness of the algorithms. To incorporate the fact that the curves and surfaces may have discontinuities the minimizing functional is modified. An important property of the resulting functional minimization problems is that convexity is maintained. Therefore, the computational complexity of the resulting algorithms are not significantly increased. Examples are provided to demonstrate the characteristics of the algorithm
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