Kinetic collision detection between two simple polygons

AbstractWe design a kinetic data structure for detecting collisions between two simple polygons in motion. In order to do so, we create a planar subdivision of the free space between the two polygons, called the external relative geodesic triangulation, which certifies their disjointness. We show how this subdivision can be maintained as a kinetic data structure when the polygons are moving, and analyze its performance in the kinetic setting

Localizing Polygonal Objects in Man-Made Environments

Object detection is a significant challenge in Computer Vision and has received a lot of attention in the field. One such challenge addressed in this thesis is the detection of polygonal objects, which are prevalent in man-made environments. Shape analysis is an important cue to detect these objects. We propose a contour-based object detection framework to deal with the related challenges, including how to efficiently detect polygonal shapes and how to exploit them for object detection. First, we propose an efficient component tree segmentation framework for stable region extraction and a multi-resolution line segment detection algorithm, which form the bases of our detection framework. Our component tree segmentation algorithm explores the optimal threshold for each branch of the component tree, and achieves a significant improvement over image thresholding segmentation, and comparable performance to more sophisticated methods but only at a fraction of computation time. Our line segment detector overcomes several inherent limitations of the Hough transform, and achieves a comparable performance to the state-of-the-art line segment detectors. However, our approach can better capture dominant structures and is more stable against low-quality imaging conditions. Second, we propose a global shape analysis measurement for simple polygon detection and use it to develop an approach for real-time landing site detection in unconstrained man-made environments. Since the task of detecting landing sites must be performed in a few seconds or less, existing methods are often limited to simple local intensity and edge variation cues. By contrast, we show how to efficiently take into account the potential sitesâ global shape, which is a critical cue in man-made scenes. Our method relies on component tree segmentation algorithm and a new shape regularity measure to look for polygonal regions in video sequences. In this way we enforce both temporal consistency and geometric regularity, resulting in reliable and consistent detections. Third, we propose a generic contour grouping based object detection approach by exploring promising cycles in a line fragment graph. Previous contour-based methods are limited to use additive scoring functions. In this thesis, we propose an approximate search approach that eliminates this restriction. Given a weighted line fragment graph, we prune its cycle space by removing cycles containing weak nodes or weak edges, until the upper bound of the cycle space is less than the threshold defined by the cyclomatic number. Object contours are then detected as maximally scoring elementary circuits in the pruned cycle space. Furthermore, we propose another more efficient algorithm, which reconstructs the graph by grouping the strongest edges iteratively until the number of the cycles reaches the upper bound. Our approximate search approaches can be used with any cycle scoring function. Moreover, unlike other contour grouping based approaches, our approach does not rely on a greedy strategy for finding multiple candidates and is capable of finding multiple candidates sharing common line fragments. We demonstrate that our approach significantly outperforms the state-of-the-art

TwinTex: Geometry-aware Texture Generation for Abstracted 3D Architectural Models

Coarse architectural models are often generated at scales ranging from individual buildings to scenes for downstream applications such as Digital Twin City, Metaverse, LODs, etc. Such piece-wise planar models can be abstracted as twins from 3D dense reconstructions. However, these models typically lack realistic texture relative to the real building or scene, making them unsuitable for vivid display or direct reference. In this paper, we present TwinTex, the first automatic texture mapping framework to generate a photo-realistic texture for a piece-wise planar proxy. Our method addresses most challenges occurring in such twin texture generation. Specifically, for each primitive plane, we first select a small set of photos with greedy heuristics considering photometric quality, perspective quality and facade texture completeness. Then, different levels of line features (LoLs) are extracted from the set of selected photos to generate guidance for later steps. With LoLs, we employ optimization algorithms to align texture with geometry from local to global. Finally, we fine-tune a diffusion model with a multi-mask initialization component and a new dataset to inpaint the missing region. Experimental results on many buildings, indoor scenes and man-made objects of varying complexity demonstrate the generalization ability of our algorithm. Our approach surpasses state-of-the-art texture mapping methods in terms of high-fidelity quality and reaches a human-expert production level with much less effort. Project page: https://vcc.tech/research/2023/TwinTex.Comment: Accepted to SIGGRAPH ASIA 202

Conservative occlusion culling for urban visualization using a slice-wise data structure

Cataloged from PDF version of article.In this paper, we propose a framework for urban visualization using a conservative from-region visibility algorithm based on occluder shrinking. The visible geometry in a typical urban walkthrough mainly consists of partially visible buildings. Occlusion-culling algorithms, in which the granularity is buildings, process these partially visible buildings as if they are completely visible. To address the problem of partial visibility, we propose a data structure, called slice-wise data structure, that represents buildings in terms of slices parallel to the coordinate axes. We observe that the visible parts of the objects usually have simple shapes. This observation establishes the base for occlusion-culling where the occlusion granularity is individual slices. The proposed slice-wise data structure has minimal storage requirements. We also propose to shrink general 3D occluders in a scene to find volumetric occlusion. Empirical results show that significant increase in frame rates and decrease in the number of processed polygons can be achieved using the proposed slice-wise occlusion-culling as compared to an occlusion-culling method where the granularity is individual buildings. © 2007 Elsevier Inc. All rights reserved

Voronoi diagrams in the max-norm: algorithms, implementation, and applications

Voronoi diagrams and their numerous variants are well-established objects in computational geometry. They have proven to be extremely useful to tackle geometric problems in various domains such as VLSI CAD, Computer Graphics, Pattern Recognition, Information Retrieval, etc. In this dissertation, we study generalized Voronoi diagram of line segments as motivated by applications in VLSI Computer Aided Design. Our work has three directions: algorithms, implementation, and applications of the line-segment Voronoi diagrams. Our results are as follows: (1) Algorithms for the farthest Voronoi diagram of line segments in the Lp metric, 1 ≤ p ≤ ∞. Our main interest is the L2 (Euclidean) and the L∞ metric. We first introduce the farthest line-segment hull and its Gaussian map to characterize the regions of the farthest line-segment Voronoi diagram at infinity. We then adapt well-known techniques for the construction of a convex hull to compute the farthest line-segment hull, and therefore, the farthest segment Voronoi diagram. Our approach unifies techniques to compute farthest Voronoi diagrams for points and line segments. (2) The implementation of the L∞ Voronoi diagram of line segments in the Computational Geometry Algorithms Library (CGAL). Our software (approximately 17K lines of C++ code) is built on top of the existing CGAL package on the L2 (Euclidean) Voronoi diagram of line segments. It is accepted and integrated in the upcoming version of the library CGAL-4.7 and will be released in september 2015. We performed the implementation in the L∞ metric because we target applications in VLSI design, where shapes are predominantly rectilinear, and the L∞ segment Voronoi diagram is computationally simpler. (3) The application of our Voronoi software to tackle proximity-related problems in VLSI pattern analysis. In particular, we use the Voronoi diagram to identify critical locations in patterns of VLSI layout, which can be faulty during the printing process of a VLSI chip. We present experiments involving layout pieces that were provided by IBM Research, Zurich. Our Voronoi-based method was able to find all problematic locations in the provided layout pieces, very fast, and without any manual intervention

Prior knowledge and preferential structures in gradient descent learning algorithms

A family of gradient descent algorithms for learning linear functions in an online setting is considered. The family includes the classical LMS algorithm as well as new variants such as the Exponentiated Gradient (EG) algorithm due to Kivinen and Warmuth. The algorithms are based on prior distributions defined on the weight space. Techniques from differential geometry are used to develop the algorithms as gradient descent iterations with respect to the natural gradient in the Riemannian structure induced by the prior distribution. The proposed framework subsumes the notion of "link-functions"