Sagi Katz

Mesh segmentation using feature point and core extraction

Mesh segmentation has become a necessary ingredient in many applications in computer graphics. This paper proposes a novel hierarchical mesh segmentation algorithm, which is based on new methods for prominent feature point and core extraction. The algorithm has several benefits. First, it is invariant both to the pose of the model and to different proportions between the model’s components. Second, it produces correct hierarchical segmentations of meshes, both in the coarse levels of the hierarchy and in the fine levels, where tiny segments are extracted. Finally, the boundaries between the segments go along the natural seams of the models.

Mesh Segmentation - A Comparative Study

Mesh segmentation has become an important component in many applications in computer graphics. In the last several years, many algorithms have been proposed in this growing area, offering a diversity of methods and various evaluation criteria. This paper provides a comparative study of some of the latest algorithms and results, along several axes. We evaluate only algorithms whose code is available to us, and thus it is not a comprehensive study. Yet, it sheds some light on the vital properties of the methods and on the challenges that future algorithms should face

Metamorphosis of Polyhedral Surfaces using Decomposition

This paper describes an algorithm for morphing polyhedral surfaces based on their decompositions into patches. The given surfaces need neither be genus‐zero nor two‐manifolds. We present a new algorithm for decomposing surfaces into patches. We also present a new projection scheme that handles topologically cylinder‐like polyhedral surfaces. We show how these two new techniques can be used within a general framework and result with morph sequences that maintain the distinctive features of the input models.

On the Visibility of Point Clouds

Is it possible to determine the visible subset of points directly from a given point cloud? Interestingly, it was shown that this is indeed the case - despite the fact that points cannot occlude each other, this task can be performed without surface reconstruction or normal estimation. The operator is very simple - it first transforms the points to a new domain and then constructs the convex hull in that domain. Points that lie on the convex hull of the transformed set of points are the images of the visible points. This operator found numerous applications in computer vision, including face reconstruction, keypoint detection, finding the best viewpoints, reduction of points, and many more. The current paper addresses a fundamental question: What properties should a transformation function satisfy, in order to be utilized in this operator? We show that three such properties are sufficient: the sign of the function, monotonicity, and a condition regarding the functions parameter. The correctness of an algorithm that satisfies these three properties is proved. Finally, we show an interesting application of the operator - assignment of visibility-confidence score. This feature is missing from previous approaches, where a binary yes/no visibility is determined. This score can be utilized in various applications, we illustrate its use in view-dependent curvature estimation.

On visibility and empty-region graphs

Abstract Empty-region graphs are well-studied in Computer Graphics, Geometric Modeling, Computational Geometry, as well as in Robotics and Computer Vision. The vertices of these graphs are points in space, and two vertices are connected by an arc if there exists an empty region of a certain shape and size between them. In most of the graphs discussed in the literature, the empty region is assumed to be a circle or the union/intersection of circles. In this paper we propose a new type of empty-region graphs—the γ-visibility graph. This graph can accommodate a variety of shapes of empty regions and may be defined in any dimension. Interestingly, we will show that commonly-used shapes are a special case of our graph. In this sense, our graph generalizes some empty-region graphs. Though this paper is mostly theoretical, it may have practical implication—the numerous applications that make use of empty-region graphs would be able to select the best shape that suits the problem at hand.