LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

ARCHITECTURE ESTIMATION FROM SPARSE IMAGES USING GRAMMATICAL SHAPE PRIORS FOR CULTURAL HERITAGE

The estimation and reconstruction of 3D architectural structures is of great in- terest in computer vision, as well as cultural heritage. This dissertation proposes a novel approach to solve the di??cult problem of estimating architectural structures from sparse images and e??ciently generating 3D models from estimation results for cultural heritage. This approach takes as input one plan drawing image and a few fac¸ade images, and provides as output the volumetric 3D models which represent the structures in the sparse images. Support of this research goal has motivated new investigations in underlying structure estimation problems including detecting structural feature points in 2D images, decomposing plan drawings into semantically meaningful shapes for medieval castles, estimating rectangular and Gothic fac¸ades using shape priors, and estimating complete 3D models for architectural structures using a novel volumetric shape grammar. Major outstanding challenges in each of these topic areas are addressed resulting in contributions to current state-of-the-art as it applied to these di??cult problems

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum

Part decomposition of 3D surfaces

This dissertation describes a general algorithm that automatically decomposes realworld scenes and objects into visual parts. The input to the algorithm is a 3 D triangle mesh that approximates the surfaces of a scene or object. This geometric mesh completely specifies the shape of interest. The output of the algorithm is a set of boundary contours that dissect the mesh into parts where these parts agree with human perception. In this algorithm, shape alone defines the location of a bom1dary contour for a part. The algorithm leverages a human vision theory known as the minima rule that states that human visual perception tends to decompose shapes into parts along lines of negative curvature minima. Specifically, the minima rule governs the location of part boundaries, and as a result the algorithm is known as the Minima Rule Algorithm. Previous computer vision methods have attempted to implement this rule but have used pseudo measures of surface curvature. Thus, these prior methods are not true implementations of the rule. The Minima Rule Algorithm is a three step process that consists of curvature estimation, mesh segmentation, and quality evaluation. These steps have led to three novel algorithms known as Normal Vector Voting, Fast Marching Watersheds, and Part Saliency Metric, respectively. For each algorithm, this dissertation presents both the supporting theory and experimental results. The results demonstrate the effectiveness of the algorithm using both synthetic and real data and include comparisons with previous methods from the research literature. Finally, the dissertation concludes with a summary of the contributions to the state of the art

Discrete Mathematics and Symmetry

Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group

Explorative Graph Visualization

Netzwerkstrukturen (Graphen) sind heutzutage weit verbreitet. Ihre Untersuchung dient dazu, ein besseres Verständnis ihrer Struktur und der durch sie modellierten realen Aspekte zu gewinnen. Die Exploration solcher Netzwerke wird zumeist mit Visualisierungstechniken unterstützt. Ziel dieser Arbeit ist es, einen Überblick über die Probleme dieser Visualisierungen zu geben und konkrete Lösungsansätze aufzuzeigen. Dabei werden neue Visualisierungstechniken eingeführt, um den Nutzen der geführten Diskussion für die explorative Graphvisualisierung am konkreten Beispiel zu belegen.Network structures (graphs) have become a natural part of everyday life and their analysis helps to gain an understanding of their inherent structure and the real-world aspects thereby expressed. The exploration of graphs is largely supported and driven by visual means. The aim of this thesis is to give a comprehensive view on the problems associated with these visual means and to detail concrete solution approaches for them. Concrete visualization techniques are introduced to underline the value of this comprehensive discussion for supporting explorative graph visualization