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Spagnuolo Hierarchical mesh segmentation based on fitting primitives
| Content Provider | Semantic Scholar |
|---|---|
| Author | Attene, Marco Falcidieno, Bianca Michela |
| Abstract | ing a class of similar shapes. Broadly speaking, segmentation algorithms attempt to exploit geometric information to infer a decomposition of the surface that corresponds to the one that experts would produce manually. The concept of good segmentation, however, strongly depends on the context in which it will be used. In the broadest scenario of supporting the process of shape understanding, methods based on intrinsic characteristics of the shape, such as curvature and topology, tend to group together parts of the model having a kind of coherence and/or uniformity. In [2] and [4], for example, Morse theory is used to partition a two-manifold in regions having a prescibed topology; once such a partitioning has been determined, regions are connected together to form an extended Reeb graph structure representing the signature of the shape. The identification of regions of constant curvature has been addressed in [16], where a multi-scale method to evaluate the surface curvature has been introduced. Being a multi-scale approach, the algorithm produces several segmentations (one for each scale), so that a more complete interpretation of the shape is supported. In some particular contexts, such as the one addressed in this article, more specific and effective methods may be used that exploit an a-priori knowledge of the shape. We tackle the problem of decomposing a triangulated surface into areas with prescribed characteristics. Specifically, we present a framework to compute a hierarchical segmentation of a given shape into connected regions approximated by primitives belonging to a given set. The set of primitives to be used is arbitrary and does not influence the validity of the framework. The remainder of the paper is organized as follows. In Sect. 2, previous work on mesh segmentation is classified and discussed. In Sect. 3, the hierarchical face clustering method, which is the basis of our work, is described. Section 4 provides an overview of our framework, while in Sect. 5 the computation of the parameters of some fitting primitives is explained. Besides the mathematical foundations described in Sect. 5, we provide some suggestions for an efficient implementation in Sect. 6. Finally, Sect. 7 reviews some application contexts in which our framework is particularly useful, and we conclude the paper in Sect. 8 by discussing potential improvements of the method, extensions and future research directions. 2 Prior art on mesh segmentation In the more specific context of retrieving the underlying structure of regular models, which is the field of investigation of this paper, we can identify segmentation algorithms in two main classes: • Feature-based detection – Methods belonging to this class try to follow the same path of the human expert, and thus attempt to determine surface regions indirectly first by computing a set of feature lines and then by splitting the surface through a network of such features. • Direct region detection – Methods of this type group faces and vertices into regions through an estimation of approximating primitives. Some approaches grow the regions starting from seed faces, while some others follow a top-down paradigm and split big regions into smaller ones that can be better approximated by the primitives employed. Both algorithm classes have their advantages and drawbacks, but neither is sufficiently accurate in general and it is often necessary to refine the automatic process by a human intervention to clean the results. 2.1 Feature-based segmentation The main difficulty in this class of algorithms is the automatic detection of feature lines. When the model is a height-field, for example, lines of discontinuity are used to define the so-called surface primal sketch [18]. In the more general case of triangulated surfaces, typical methods are based on fold detection, that is, regions of the surface having a high principal curvature are used to extract feature lines. If, for example, the maximum of the two principal curvatures exceeds a prescribed threshold, the vertex is probably part of a fold [32]. In [22] morphological operators adapted to triangle meshes are used to detect the presence of folds, while in the different setting described in [30], curvature extrema are computed to identify perceptually salient surface regions which are then turned into feature lines through a skeletonization procedure. When feature lines are not actually present in the model because they have been chamfered by the sampling process, they can be reconstructed starting from the neighboring smooth regions and tagged for further processing [3]. In a different setting, the features may be not completely sharp, and surface primitives may be separated by blended edges. In these cases, a feature sensitive metric may be used as described in [19]. For the purpose of segmentation, however, none of the above-mentioned methods are generally sufficient, as they typically produce gaps in the boundaries of the regions, and such a sparsity causes serious difficulties when determining fairly bounded regions. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://page-one.springer.com/pdf/preview/10.1007/s00371-006-0375-x |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
