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Item An Approach to the Decomposition of Solids with Voids via Morse Theory(The Eurographics Association, 2023) Pareja-Corcho, Juan; Montoya-Zapata, Diego; Moreno, Aitor; Cadavid, Carlos; Posada, Jorge; Arenas-Tobon, Ketzare; Ruiz-Salguero, Oscar; Banterle, Francesco; Caggianese, Giuseppe; Capece, Nicola; Erra, Ugo; Lupinetti, Katia; Manfredi, GildaThe decomposition of solids is a problem of interest in areas of engineering such as feature recognition or manufacturing planning. The problem can be stated as finding a set of smaller and simpler pieces that glued together amount to the initial solid. This decomposition can be guided by geometrical or topological criteria and be applied to either surfaces or solids (embedded manifolds). Most topological decompositions rely on Morse theory to identify changes in the topology of a manifold. A Morse function f is defined on the manifold and the manifold's topology is studied by studying the behaviour of the critical points of f . A popular structure used to encode this behaviour is the Reeb graph. Reeb graph-based decompositions have proven to work well for surfaces and for solids without inner voids, but fail to consider solids with inner voids. In this work we present a methodology based on the handle-decomposition of a manifold that can encode changes in the topology of solids both with and without inner voids. Our methodology uses the Boundary Representation of the solid and a shape similarity criteria to identify changes in the topology of both the outer and inner boundary(ies) of the solid. Our methodology is defined for Morse functions that produce parallel planar level sets and we do not consider the case of annidated solids (i.e. solids within other solids). We present an algorithm to implement our methodology and execute experiments on several datasets. Future work includes the testing of the methodology with functions different to the height function and the speed up of the algorithm's data structure.Item Spectral-based Segmentation for Functional Shape-matching(The Eurographics Association, 2023) Mancinelli, Claudio; Melzi, Simone; Banterle, Francesco; Caggianese, Giuseppe; Capece, Nicola; Erra, Ugo; Lupinetti, Katia; Manfredi, GildaIn Computer Graphics and Computer Vision, shape co-segmentation and shape-matching are fundamental tasks with diverse applications, from statistical shape analysis to human-robot interaction. These problems respectively target establishing segmentto- segment and point-to-point correspondences between shapes, which are crucial task for numerous practical scenarios. Notably, co-segmentation can aid in point-wise correspondence estimation in shape-matching pipelines like the functional maps framework. Our paper introduces an innovative shape segmentation pipeline which provides coherent segmentation for shapes within the same class. Through comprehensive evaluation on a diverse test set comprising shapes from various datasets and classes, we demonstrate the coherence of our segmentation approach. Moreover, our method significantly improves accuracy in shape matching scenarios, as evidenced by comparisons with the original functional maps approach. Importantly, these enhancements come with minimal computational overhead. Our work not only introduces a novel coherent segmentation method and a valuable tool for improving correspondence accuracy within functional maps, but also contributes to the theoretical foundations of this impactful field, inspiring further research.Item Semantic Segmentation of High-resolution Point Clouds Representing Urban Contexts(The Eurographics Association, 2023) Romanengo, Chiara; Cabiddu, Daniela; Pittaluga, Simone; Mortara, Michela; Banterle, Francesco; Caggianese, Giuseppe; Capece, Nicola; Erra, Ugo; Lupinetti, Katia; Manfredi, GildaPoint clouds are becoming an increasingly common digital representation of real-world objects, and they are particularly efficient when dealing with large-scale objects and/or when extremely high-resolution is required. The focus of our work is on the analysis, 3D feature extraction and semantic annotation of point clouds representing urban scenes, coming from various acquisition technologies, e.g., terrestrial (fixed or mobile) or aerial laser scanning or photogrammetry; the task is challenging, due to data dimensionality and noise. In particular, we present a pipeline to segment high-resolution point clouds representing urban environments into geometric primitives; we focus on planes, cylinders and spheres, which are the main features of buildings (walls, roofs, arches, ...) and ground surfaces (streets, pavements, platforms), and identify the unique parameters of each instance. This paper focuses on the semantic segmentation of buildings, but the approach is currently being generalised to manage extended urban areas. Given a dense point cloud representing a specific building, we firstly apply a binary space partitioning method to obtain small enough sub-clouds that can be processed. Then, a combination of the well-known RANSAC algorithm and a recognition method based on the Hough transform (HT) is applied to each sub-cloud to obtain a semantic segmentation into salient elements, like façades, walls and roofs. The parameters of primitive instances are saved as metadata to document the structural element of buildings for further thematic analyses, e.g., energy efficiency. We present a case study on the city of Catania, Italy, where two buildings of historical and artistic value have been digitized at very high resolution. Our approach is able to semantically segment these huge point clouds and it proves robust to uneven sampling density, input noise and outliers.