Abstract Given a point cloud, which is assumed to be a sampling of a continuous surface, and a viewpoint, which points are visible from that viewpoint? Since points do not occlude each other, the real question is which points would be visible if the surface they were sampled from were known. While an existing approximation method addresses this problem, it is unsuitable for use in optimization processes or learning models due to its lack of differentiability. To overcome this limitation, the paper introduces a novel differentiable approximation method. It is based on identifying the extreme points of a point set in a differentiable manner. This approach can be effectively integrated into optimization algorithms or used as a layer in neural networks, allowing for the computation and utilization of visible points in various tasks, such as optimal viewpoint selection. The paper also provides theoretical proofs of the operator's correctness in the limit, further validating its effectiveness. The code is available at https://github.com/sagikatz/HPRO

Recent works have shown that depth information can be obtained from Dual-Pixel (DP) sensors. A DP arrangement provides two views in a single shot, thus resembling a stereo image pair with a tiny baseline. However, the different point spread function (PSF) per view, as well as the small disparity range, makes the use of typical stereo matching algorithms problematic. To address the above shortcomings, we propose a Continuous Cost Aggregation (CCA) scheme within a semi-global matching framework that is able to provide accurate continuous disparities from DP images. The proposed algorithm fits parabolas to matching costs and aggregates parabola coefficients along image paths. The aggregation step is performed subject to a quadratic constraint that not only enforces the disparity smoothness but also maintains the quadratic form of the total costs. This gives rise to an inherently efficient disparity propagation scheme with a pixel-wise minimization in closed-form. Furthermore, the continuous form allows for a robust multi-scale aggregation that better compensates for the varying PSF. Experiments on DP data from both DSLR and phone cameras show that the proposed scheme attains state-of-the-art performance in DP disparity estimation.

This paper re-visits classical problems in document enhancement. Rather than proposing a new algorithm for a specific problem, we introduce a novel general approach. The key idea is to modify any state-of-the-art algorithm, by providing it with new information (input), improving its own results. Interestingly, this information is based on a solution to a seemingly unrelated problem of visibility detection in R3. We show that a simple representation of an image as a 3D point cloud, gives visibility detection on this cloud a new interpretation. What does it mean for a point to be visible? Although this question has been widely studied within computer vision, it has always been assumed that the point set is a sampling of a real scene. We show that the answer to this question in our context reveals unique and useful information about the image. We demonstrate the benefit of this idea for document binarization and for unshadowing.

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 function's 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.

Point sets are the standard output of many 3D scanning systems and depth cameras. Presenting the set of points as is, might "hide" the prominent features of the object from which the points are sampled. Our goal is to reduce the number of points in a point set, for improving the visual comprehension from a given viewpoint. This is done by controlling the density of the reduced point set, so as to create bright regions (low density) and dark regions (high density), producing an effect of shading. This data reduction is achieved by leveraging a limitation of a solution to the classical problem of determining visibility from a viewpoint. In addition, we introduce a new dual problem, for determining visibility of a point from infinity, and show how a limitation of its solution can be leveraged in a similar way.

This paper proposes a simple and fast operator, the "Hidden" Point Removal operator, which determines the visible points in a point cloud, as viewed from a given viewpoint. Visibility is determined without reconstructing a surface or estimating normals. It is shown that extracting the points that reside on the convex hull of a transformed point cloud, amounts to determining the visible points. This operator is general - it can be applied to point clouds at various dimensions, on both sparse and dense point clouds, and on viewpoints internal as well as external to the cloud. It is demonstrated that the operator is useful in visualizing point clouds, in view-dependent reconstruction and in shadow casting.

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

Cutting up a complex object into simpler sub-objects is a fundamental problem in various disciplines. In image processing, images are segmented while in computational geometry, solid polyhedra are decomposed. In recent years, in computer graphics, polygonal meshes are decomposed into sub-meshes. In this paper we propose a novel hierarchical mesh decomposition algorithm. Our algorithm computes a decomposition into the meaningful components of a given mesh, which generally refers to segmentation at regions of deep concavities. The algorithm also avoids over-segmentation and jaggy boundaries between the components. Finally, we demonstrate the utility of the algorithm in control-skeleton extraction.

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. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computational Geometry and Object Modeling]: Boundary representations I.3.7 [Three-Dimensional Graphics and Realism]: Animation