Large repositories of 3D shapes provide valuable input for data-driven analysis and modeling tools. They are especially powerful once annotated with semantic information such as salient regions and functional parts. We propose a novel active learning method capable of enriching massive geometric datasets with accurate semantic region annotations. Given a shape collection and a user-specified region label our goal is to correctly demarcate the corresponding regions with minimal manual work. Our active framework achieves this goal by cycling between manually annotating the regions, automatically propagating these annotations across the rest of the shapes, manually verifying both human and automatic annotations, and learning from the verification results to improve the automatic propagation algorithm. We use a unified utility function that explicitly models the time cost of human input across all steps of our method. This allows us to jointly optimize for the set of models to annotate and for the set of models to verify based on the predicted impact of these actions on the human efficiency. We demonstrate that incorporating verification of all produced labelings within this unified objective improves both accuracy and efficiency of the active learning procedure. We automatically propagate human labels across a dynamic shape network using a conditional random field (CRF) framework, taking advantage of global shape-to-shape similarities, local feature similarities, and point-to-point correspondences. By combining these diverse cues we achieve higher accuracy than existing alternatives. We validate our framework on existing benchmarks demonstrating it to be significantly more efficient at using human input compared to previous techniques. We further validate its efficiency and robustness by annotating a massive shape dataset, labeling over 93,000 shape parts, across multiple model classes, and providing a labeled part collection more than one order of magnitude larger than existing ones.
We present a new globally smooth parameterization method for triangulated surfaces of arbitrary topology. Given two orthogonal piecewise linear vector elds dened over the input mesh (typically the estimated principal curvature directions), our method computes two piecewise linear periodic functions, aligned with the input vector elds, by minimizing an objective function. The bivariate function they dene is a smooth parameterization almost everywhere on the surface, except in the vicinity of singular vertices, edges and triangles, where the derivatives of the parameterization vanish. We extract a quadrilateral chart layout from the parameterization function and propose an automatic procedure to detect the singularities, and x them by splitting and re-parameterizing the containing charts. Our method can construct both quasi-conformal (angle preserving) and quasi-isometric (angle and area preserving) parameterizations. The more restrictive class of quasi-isometric parameterizations is constructed at the expense of introducing more singularities. The constructed parameterizations can be used for a variety of geometry processing applications. Since we can align the parameterization with the principal curvature directions, our result is particularly suitable for surface tting and remeshing.
TechnionConformal parameterization of mesh models has numerous applications in geometry processing. Conformality is desirable for remeshing, surface reconstruction, and many other mesh processing applications. Subject to the conformality requirement, these applications typically benet from parameterizations with smaller stretch. The Angle Based Flattening (ABF) method, presented a few years ago, generates provably valid conformal parameterizations with low stretch. However, it is quite time consuming and becomes error prone for large meshes due to numerical error accumulation. This work presents ABF++, a highly ecient extension of the ABF method that overcomes these drawbacks, while maintaining all the advantages of ABF. ABF++ robustly parameterizes meshes of hundreds of thousands and millions of triangles within minutes. It is based on two main components: (1) a new numerical solution technique that dramatically reduces the dimension of the linear systems solved at each iteration, speeding up the solution; (2) an ecient hierarchical solution technique. The speedup with (1) does not come at the expense of greater distortion. The hierarchical technique (2) enables parameterization of models with millions of faces in seconds, at the expense of a minor increase in parametric distortion. The parameterization computed by ABF++ are provably valid, i.e. they contain no ipped triangles. As a result of these extensions, the ABF++ method is extremely suitable for robustly and eciently parameterizing models for geometry processing applications.
Many geometry processing applications, such as morphing, shape blending, transfer of texture or material properties, and fitting template meshes to scan data, require a bijective mapping between two or more models. This mapping, or crossparameterization, typically needs to preserve the shape and features of the parameterized models, mapping legs to legs, ears to ears, and so on. Most of the applications also require the models to be represented by compatible meshes, i.e. meshes with identical connectivity, based on the cross-parameterization. In this paper we introduce novel methods for shape preserving cross-parameterization and compatible remeshing. Our crossparameterization method computes a low-distortion bijective mapping between models that satisfies user prescribed constraints. Using this mapping, the remeshing algorithm preserves the user-defined feature vertex correspondence and the shape correlation between the models. The remeshing algorithm generates output meshes with significantly fewer elements compared to previous techniques, while accurately approximating the input geometry. As demonstrated by the examples, the compatible meshes we construct are ideally suitable for morphing and other geometry processing applications.
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