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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.

Figure 1: Composite images of segment boundaries selected by different people (the darker the seam the more people have chosen a cut along that edge). One example is shown for each of the 19 object categories considered in this study. AbstractThis paper describes a benchmark for evaluation of 3D mesh segmentation algorithms. The benchmark comprises a data set with 4,300 manually generated segmentations for 380 surface meshes of 19 different object categories, and it includes software for analyzing 11 geometric properties of segmentations and producing 4 quantitative metrics for comparison of segmentations. The paper investigates the design decisions made in building the benchmark, analyzes properties of human-generated and computer-generated segmentations, and provides quantitative comparisons of 7 recently published mesh segmentation algorithms. Our results suggest that people are remarkably consistent in the way that they segment most 3D surface meshes, that no one automatic segmentation algorithm is better than the others for all types of objects, and that algorithms based on non-local shape features seem to produce segmentations that most closely resemble ones made by humans.

We introduce the Symmetry Factored Embedding (SFE) and the Symmetry Factored Distance (SFD) as new tools to analyze and represent symmetries in a point set. The SFE provides new coordinates in which symmetry is "factored out," and the SFD is the Euclidean distance in that space. These constructions characterize the space of symmetric correspondences between points -i.e., orbits. A key observation is that a set of points in the same orbit appears as a clique in a correspondence graph induced by pairwise similarities. As a result, the problem of finding approximate and partial symmetries in a point set reduces to the problem of measuring connectedness in the correspondence graph, a well-studied problem for which spectral methods provide a robust solution. We provide methods for computing the SFE and SFD for extrinsic global symmetries and then extend them to consider partial extrinsic and intrinsic cases. During experiments with difficult examples, we find that the proposed methods can characterize symmetries in inputs with noise, missing data, non-rigid deformations, and complex symmetries, without a priori knowledge of the symmetry group. As such, we believe that it provides a useful tool for automatic shape analysis in applications such as segmentation and stationary point detection.

The goal of our work is to develop an algorithm for automatic and robust detection of global intrinsic symmetries in 3D surface meshes. Our approach is based on two core observations. First, symmetry invariant point sets can be detected robustly using critical points of the Average Geodesic Distance (AGD) function. Second, intrinsic symmetries are self-isometries of surfaces and as such are contained in the low dimensional group of Möbius transformations. Based on these observations, we propose an algorithm that: 1) generates a set of symmetric points by detecting critical points of the AGD function, 2) enumerates small subsets of those feature points to generate candidate Möbius transformations,and 3) selects among those candidate Möbius transformations the one(s) that best map the surface onto itself. The main advantages of this algorithm stem from the stability of the AGD in predicting potential symmetric point features and the low dimensionality of the Möbius group for enumerating potential self-mappings. During experiments with a benchmark set of meshes augmented with human-specified symmetric correspondences, we find that the algorithm is able to find intrinsic symmetries for a wide variety of object types with moderate deviations from perfect symmetry.