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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 GIM3D: A 3D Dataset for Garment Segmentation(The Eurographics Association, 2022) Musoni, Pietro; Melzi, Simone; Castellani, Umberto; Cabiddu, Daniela; Schneider, Teseo; Allegra, Dario; Catalano, Chiara Eva; Cherchi, Gianmarco; Scateni, RiccardoThe 3D cloth segmentation task is particularly challenging due to the extreme variation of shapes, even among the same category of clothes. Several data-driven methods try to cope with this problem but they have to face the lack of available data capable to generalize to the variety of real-world data. For this reason, we present GIM3D (Garments In Motion 3D), a synthetic dataset of clothed 3D human characters in different poses. The over 4000 3D models in this dataset are produced by a physical simulation of clothes with different fabrics, sizes, and tightness, using animated human avatars having a large variety of shapes. Our dataset is composed of single meshes created to simulate 3D scans, with labels for the separate clothes and the visible body parts. We also provide an evaluation of the use of GIM3D as a training set on garment segmentation tasks using state-of-the-art data-driven methods for both meshes and point clouds.Item Adjoint Bijective ZoomOut: Efficient Upsampling for Learned Linearly-invariant Embedding(The Eurographics Association, 2023) Viganò, Giulio; Melzi, Simone; Banterle, Francesco; Caggianese, Giuseppe; Capece, Nicola; Erra, Ugo; Lupinetti, Katia; Manfredi, GildaIn this paper, we present a novel method for refining correspondences between 3D point clouds. Our method is compatible with the functional map framework, so it relies on the spectral representation of the correspondence. Although, differently from other similar approaches, this algorithm is specifically for a particular functional setting, being the only refinement method compatible with a recent data-driven approach, more suitable for point cloud matching. Our algorithm arises from a different way of converting functional operators into point-to-point correspondence, which we prove to promote bijectivity between maps, exploiting a theoretical result. Iterating this procedure and performing spectral upsampling in the same way as other similar methods, ours increases the accuracy of the correspondence, leading to more bijective correspondences. We tested our method over different datasets. It outperforms the previous methods in terms of map accuracy in all the tests considered.Item PC-GAU: PCA Basis of Scattered Gaussians for Shape Matching via Functional Maps(The Eurographics Association, 2022) Colombo, Michele; Boracchi, Giacomo; Melzi, Simone; Cabiddu, Daniela; Schneider, Teseo; Allegra, Dario; Catalano, Chiara Eva; Cherchi, Gianmarco; Scateni, RiccardoShape matching is a central problem in geometry processing applications, ranging from texture transfer to statistical shape analysis. The functional maps framework provides a compact representation of correspondences between discrete surfaces, which is then converted into point-wise maps required by real-world applications. The vast majority of methods based on functional maps involve the eigenfunctions of the Laplace-Beltrami Operator (LB) as the functional basis. A primary drawback of the LB basis is that its energy does not uniformly cover the surface. This fact gives rise to regions where the estimated correspondences are inaccurate, typically at tiny parts and protrusions. For this reason, state-of-the-art procedures to convert the functional maps (represented in the LB basis) into point-wise correspondences are often error-prone. We propose PCGAU, a new functional basis whose energy spreads on the whole shape more evenly than LB. As such, PC-GAU can replace the LB basis in existing shape matching pipelines. PC-GAU consists of the principal vectors obtained by applying Principal Component Analysis (PCA) to a dictionary of sparse Gaussian functions scattered on the surfaces. Through experimental evaluation of established benchmarks, we show that our basis produces more accurate point-wise maps —- compared to LB - when employed in the same shape-matching pipeline.