We perform co-analysis of a set of man-made 3D objects to allow the creation of novel instances derived from the set. We analyze the objects at the part level and treat the anisotropic part scales as a shape style. The co-analysis then allows style transfer to synthesize new objects. The key to co-analysis is part correspondence, where a major challenge is the handling of large style variations and diverse geometric content in the shape set. We propose style-content separation as a means to address this challenge. Specifically, we define a correspondence-free style signature for style clustering. We show that confining analysis to within a style cluster facilitates tasks such as co-segmentation, content classification, and deformation-driven part correspondence. With part correspondence between each pair of shapes in the set, style transfer can be easily performed. We demonstrate our analysis and synthesis results on several sets of man-made objects with style and content variations.

We introduce an algorithm for unsupervised co-segmentation of a set of shapes so as to reveal the semantic shape parts and establish their correspondence across the set. The input set may exhibit significant shape variability where the shapes do not admit proper spatial alignment and the corresponding parts in any pair of shapes may be geometrically dissimilar. Our algorithm can handle such challenging input sets since, first, we perform co-analysis in a descriptor space, where a combination of shape descriptors relates the parts independently of their pose, location, and cardinality. Secondly, we exploit a key enabling feature of the input set, namely, dissimilar parts may be “linked ” through third-parties present in the set. The links are derived from the pairwise similarities between the parts ’ descriptors. To reveal such linkages, which may manifest themselves as anisotropic and non-linear structures in the descriptor space, we perform spectral clustering with the aid of diffusion maps. We show that with our approach, we are able to co-segment sets of shapes that possess significant variability, achieving results that are close to those of a supervised approach. Keywords: Co-segmentation, shape correspondence, spectral clustering, diffusion maps. Links: DL PDF 1

Classical approaches to shape correspondence base their computation purely on the properties, in particular geometric similarity, of the shapes in question. Their performance still falls far short of that of humans in challenging cases where corresponding shape parts may differ significantly in geometry or even topology. We stipulate that in these cases, shape correspondence by humans involves recognition of the shape parts where prior knowledge on the parts would play a more dominant role than geometric similarity. We introduce an approach to part correspondence which incorporates prior knowledge imparted by a training set of pre-segmented, labeled models and combines the knowledge with content-driven analysis based on geometric similarity between the matched shapes. First, the prior knowledge is learned from the training set in the form of per-label classifiers. Next, given two query shapes to be matched, we apply the classifiers to assign a probabilistic label to each shape face. Finally, by means of a joint labeling scheme, the probabilistic labels are used synergistically with pairwise assignments derived from geometric similarity to provide the resulting part correspondence. We show that the incorporation of knowledge is especially effective in dealing with shapes exhibiting large intra-class variations. We also show that combining knowledge and content analyses outperforms approaches guided by either attribute alone. 1.

A geodesic is a parameterized curve on a Riemannian manifold governed by a second order partial differential equation. Geodesics are notoriously unstable: small perturbations of the underlying manifold may lead to dramaticchangesofthecourseofageodesic.Suchinstabilitymakesitdifficulttousegeodesicsinmanyapplications, in particular in the world of discrete geometry. In this paper, we consider a geodesic as the indicator function of the set of the points on the geodesic. From this perspective, we present a new concept called fuzzy geodesics and showthatfuzzygeodesicsarestablewithrespecttotheGromov-Hausdorffdistance.Basedonfuzzygeodesics,we proposeanewobjectcalled the intersection configurationforasetofpointsonashapeanddemonstrateitseffectivenessintheapplicationoffindingconsistentcorrespondencesbetweensparsesetsofpointsonshapesdiffering byextreme deformations. Categories and Subject Descriptors (according to ACM CCS): Generation—Line and curve generation

In this paper, we introduce a novel approach for global registration of partially overlapping point clouds. The approach identifies feature points of matching objects based on surface-approximating polynomials and finds an initial transformation depending on these polynomials. We compute an extended set of rotationally-invariant features for polynomials. In contrast to purely feature-based approaches, we do not only compute transformations based on the invariant properties of polynomials, but actually transform the polynomials into a common coordinate system and compare the transformed coefficients. This results in an improved correspondence analysis of local surfaces. Hence, using transformed polynomials, we gain more discriminating information about different structures. Therefore, the approach can handle partial scans of different objects simultaneously. Each partial scan is assigned to one of the objects and registered accordingly. Moreover, the approach is robust against noise and can process real data.

The concept of symmetry has received significant attention in computer graphics and computer vision research in recent years. Numerous methods have been proposed to find and extract geometric symmetries and exploit such high-level structural information for a wide variety of geometry processing tasks. This report surveys and classifies recent developments in symmetry detection. We focus on elucidating the similarities and differences between existing methods to gain a better understanding of a fundamental problem in digital geometry processing and shape understanding in general. We discuss a variety of applications in computer graphics and geometry that benefit from symmetry information for more effective processing. An analysis of the strengths and limitations of existing algorithms highlights the plenitude of opportunities for future research both in terms of theory and applications. 1.

This paper investigates “Schelling points ” on 3D meshes, feature points selected by people in a pure coordination game due to their salience. To collect data for this investigation, we designed an online experiment that asked people to select points on 3D surfaces that they expect will be selected by other people. We then analyzed properties of the selected points, finding that: 1) Schelling point sets are usually highly symmetric, and 2) local curvature properties (e.g., Gauss curvature) are most helpful for identifying obvious Schelling points (tips of protrusions), but 3) global properties (e.g., segment centeredness, proximity to a symmetry axis, etc.) are required to explain more subtle features. Based on these observations, we use regression analysis to combine multiple properties into an analytical model that predicts where Schelling points are likely to be on new meshes. We find that this model benefits from a variety of surface properties, particularly when training data comes from examples in the same object class.

Large collections of 3D models from the same object class (e.g., chairs, cars, animals) are now commonly available via many public repositories, but exploring the range of shape variations across such collections remains a challenging task. In this work, we present a new exploration interface that allows users to browse collections based on similarities and differences between shapes in userspecified regions of interest (ROIs). To support this interactive system, we introduce a novel analysis method for computing similarity relationships between points on 3D shapes across a collection. We encode the inherent ambiguity in these relationships using fuzzy point correspondences and propose a robust and efficient computational framework that estimates fuzzy correspondences using only a sparse set of pairwise model alignments. We evaluate our analysis method on a range of correspondence benchmarks and report substantial improvements in both speed and accuracy over existing alternatives. In addition, we demonstrate how fuzzy correspondences enable key features in our exploration tool, such as automated view alignment, ROI-based similarity search, and faceted browsing.

Figure 1: Horse algebra: the functional representation and map inference algorithm allow us to go beyond point-to-point maps. The source shape (top left corner) was mapped to the target shape (left) by posing descriptor-based functional constraints which do not disambiguate symmetries (i.e. without landmark constraints). By further adding correspondence constraints, we obtain a near isometric map which reverses orientation, mapping left to right (center). The representation allows for algebraic operations on shape maps, so we can subtract this map from the ambivalent map, to retrieve the orientation preserving near-isometry (right). Each column shows the first 20x20 block of the functional map representation (bottom), and the action of the map by transferring colors from the source shape to the target shape (top). We present a novel representation of maps between pairs of shapes that allows for efficient inference and manipulation. Key to our approach is a generalization of the notion of map that puts in correspondence real-valued functions rather than points on the shapes. By choosing a multi-scale basis for the function space on each shape, such as the eigenfunctions of its Laplace-Beltrami operator, we obtain a representation of a map that is very compact, yet fully suitable for global inference. Perhaps more remarkably, most

Abstract. Image registration is a building block for many applications in computer vision and medical imaging. However the current methods are limited when large and highly non-local deformations are present. In this paper, we introduce a new direct feature matching technique for non-parametric image registration where efficient nearest-neighbor searches find global correspondences between intensity, spatial and geometric information. We exploit graph spectral representations that are invariant to isometry under complex deformations. Our direct feature matching technique is used within the established Demons framework for diffeomorphic image registration. Our method, called Spectral Demons, can capture very large, complex and highly non-local deformations between images. We evaluate the improvements of our method on 2D and 3D images and demonstrate substantial improvement over the conventional Demons algorithm for large deformations. 1