Data-Driven Shape Analysis and Processing

Data-driven methods play an increasingly important role in discovering geometric, structural, and semantic relationships between 3D shapes in collections, and applying this analysis to support intelligent modeling, editing, and visualization of geometric data. In contrast to traditional approaches, a key feature of data-driven approaches is that they aggregate information from a collection of shapes to improve the analysis and processing of individual shapes. In addition, they are able to learn models that reason about properties and relationships of shapes without relying on hard-coded rules or explicitly programmed instructions. We provide an overview of the main concepts and components of these techniques, and discuss their application to shape classification, segmentation, matching, reconstruction, modeling and exploration, as well as scene analysis and synthesis, through reviewing the literature and relating the existing works with both qualitative and numerical comparisons. We conclude our report with ideas that can inspire future research in data-driven shape analysis and processing.Comment: 10 pages, 19 figure

Co-skeletons:Consistent curve skeletons for shape families

We present co-skeletons, a new method that computes consistent curve skeletons for 3D shapes from a given family. We compute co-skeletons in terms of sampling density and semantic relevance, while preserving the desired characteristics of traditional, per-shape curve skeletonization approaches. We take the curve skeletons extracted by traditional approaches for all shapes from a family as input, and compute semantic correlation information of individual skeleton branches to guide an edge-pruning process via skeleton-based descriptors, clustering, and a voting algorithm. Our approach achieves more concise and family-consistent skeletons when compared to traditional per-shape methods. We show the utility of our method by using co-skeletons for shape segmentation and shape blending on real-world data

Second-order Shape Optimization for Geometric Inverse Problems in Vision

We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian, which is generally hard to compute and suffers from a series of degeneracies. Our analysis highlights the role of mean curvature motion in comparison with first-order schemes: instead of surface area, our approach penalizes deformation, either by its Dirichlet energy or total variation. Latter regularizer sparks the development of an alternating direction method of multipliers on triangular meshes. Therein, a conjugate-gradients solver enables us to bypass formation of the Gaussian normal equations appearing in the course of the overall optimization. We combine all of the aforementioned ideas in a versatile geometric variation-regularized Levenberg-Marquardt-type method applicable to a variety of shape functionals, depending on intrinsic properties of the surface such as normal field and curvature as well as its embedding into space. Promising experimental results are reported

Persistent topology for natural data analysis - A survey

Natural data offer a hard challenge to data analysis. One set of tools is being developed by several teams to face this difficult task: Persistent topology. After a brief introduction to this theory, some applications to the analysis and classification of cells, lesions, music pieces, gait, oil and gas reservoirs, cyclones, galaxies, bones, brain connections, languages, handwritten and gestured letters are shown

Report on shape analysis and matching and on semantic matching

In GRAVITATE, two disparate specialities will come together in one working platform for the archaeologist: the fields of shape analysis, and of metadata search. These fields are relatively disjoint at the moment, and the research and development challenge of GRAVITATE is precisely to merge them for our chosen tasks. As shown in chapter 7 the small amount of literature that already attempts join 3D geometry and semantics is not related to the cultural heritage domain. Therefore, after the project is done, there should be a clear ‘before-GRAVITATE’ and ‘after-GRAVITATE’ split in how these two aspects of a cultural heritage artefact are treated.This state of the art report (SOTA) is ‘before-GRAVITATE’. Shape analysis and metadata description are described separately, as currently in the literature and we end the report with common recommendations in chapter 8 on possible or plausible cross-connections that suggest themselves. These considerations will be refined for the Roadmap for Research deliverable.Within the project, a jargon is developing in which ‘geometry’ stands for the physical properties of an artefact (not only its shape, but also its colour and material) and ‘metadata’ is used as a general shorthand for the semantic description of the provenance, location, ownership, classification, use etc. of the artefact. As we proceed in the project, we will find a need to refine those broad divisions, and find intermediate classes (such as a semantic description of certain colour patterns), but for now the terminology is convenient – not least because it highlights the interesting area where both aspects meet.On the ‘geometry’ side, the GRAVITATE partners are UVA, Technion, CNR/IMATI; on the metadata side, IT Innovation, British Museum and Cyprus Institute; the latter two of course also playing the role of internal users, and representatives of the Cultural Heritage (CH) data and target user’s group. CNR/IMATI’s experience in shape analysis and similarity will be an important bridge between the two worlds for geometry and metadata. The authorship and styles of this SOTA reflect these specialisms: the first part (chapters 3 and 4) purely by the geometry partners (mostly IMATI and UVA), the second part (chapters 5 and 6) by the metadata partners, especially IT Innovation while the joint overview on 3D geometry and semantics is mainly by IT Innovation and IMATI. The common section on Perspectives was written with the contribution of all

Similarity reasoning for local surface analysis and recognition

This thesis addresses the similarity assessment of digital shapes, contributing to the analysis of surface characteristics that are independent of the global shape but are crucial to identify a model as belonging to the same manufacture, the same origin/culture or the same typology (color, common decorations, common feature elements, compatible style elements, etc.). To face this problem, the interpretation of the local surface properties is crucial. We go beyond the retrieval of models or surface patches in a collection of models, facing the recognition of geometric patterns across digital models with different overall shape. To address this challenging problem, the use of both engineered and learning-based descriptions are investigated, building one of the first contributions towards the localization and identification of geometric patterns on digital surfaces. Finally, the recognition of patterns adds a further perspective in the exploration of (large) 3D data collections, especially in the cultural heritage domain. Our work contributes to the definition of methods able to locally characterize the geometric and colorimetric surface decorations. Moreover, we showcase our benchmarking activity carried out in recent years on the identification of geometric features and the retrieval of digital models completely characterized by geometric or colorimetric patterns

Matching 3D face scans using interest points and local histogram descriptors

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