Persistence-Based Structural Recognition

Li, Chunyuan; Ovsjanikov, Maks; Chazal, Frédéric

doi:10.1109/cvpr.2014.257

Cited by 94 publications

(94 citation statements)

References 34 publications

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“…Finally, notice that the definition of our signature holds more generally for compact metric spaces, so our signature can be used on a much wider class of spaces than 3D shapes, and in potentially many applications. In particular, our mapping of PDs to vectors could be used on the global signatures of [CCSG*09b], or even for characterizing objects of different nature, like images as in [LOC14]. Moreover, note that our family of growing balls can be seen as the sublevel sets of a distance function to the base point.…”

Section: Signature Definitionmentioning

confidence: 89%

“…Our topological signatures make heavy use of the so‐called persistence diagrams (PDs), which have been recently employed in a number of tasks in computer graphics and vision [CCSG*09b, SOCG10, LOC14]. These diagrams are easy to compute and enjoy many nice theoretical properties, and in particular characterize topological features in a stable and informative way.…”

Section: Introductionmentioning

confidence: 99%

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Stable Topological Signatures for Points on 3D Shapes

Carrière

Oudot

Ovsjanikov

2015

Computer Graphics Forum

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Figure 1: Our signatures characterize a point x by the birth (leftmost) and death (second left) of the topological features (here, non-trivial loops) in the neighborhood of x in a provably stable way. We show how to compactly encode these events in a vector without losing the stability properties. This is useful in a variety of contexts, including shape segmentation and labeling (as shown on the right) using linear classifiers such as SVM. AbstractComparing points on 3D shapes is among the fundamental operations in shape analysis. To facilitate this task, a great number of local point signatures or descriptors have been proposed in the past decades. However, the vast majority of these descriptors concentrate on the local geometry of the shape around the point, and thus are insensitive to its connectivity structure. By contrast, several global signatures have been proposed that successfully capture the overall topology of the shape and thus characterize the shape as a whole. In this paper, we propose the first point descriptor that captures the topology structure of the shape as 'seen' from a single point, in a multiscale and provably stable way. We also demonstrate how a large class of topological signatures, including ours, can be mapped to vectors, opening the door to many classical analysis and learning methods. We illustrate the performance of this approach on the problems of supervised shape labeling and shape matching. We show that our signatures provide complementary information to existing ones and allow to achieve better performance with less training data in both applications.

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Section: Signature Definitionmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Stable Topological Signatures for Points on 3D Shapes

Carrière

Oudot

Ovsjanikov

2015

Computer Graphics Forum

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“…The method provides a principled way to qualitatively visualize and measure the topological struc tures via the feature functions defined on the shape surface. Topological Persistence recently became of interest for shape retrieval tasks [33,34] partially due to the popularity of topolog ical data analysis [35].…”

Section: Graph Based Techniquesmentioning

confidence: 99%

A comparison of 3D shape retrieval methods based on a large-scale benchmark supporting multimodal queries

et al. 2015

Computer Vision and Image Understanding

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120

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a b s t r a c tLarge scale 3D shape retrieval has become an important research direction in content based 3D shape retrieval. To promote this research area, two Shape Retrieval Contest (SHREC) tracks on large scale com prehensive and sketch based 3D model retrieval have been organized by us in 2014. Both tracks were based on a unified large scale benchmark that supports multimodal queries (3D models and sketches). This benchmark contains 13680 sketches and 8987 3D models, divided into 171 distinct classes. It was compiled to be a superset of existing benchmarks and presents a new challenge to retrieval methods as it comprises generic models as well as domain specific model types. Twelve and six distinct 3D shape retrieval methods have competed with each other in these two contests, respectively. To measure and compare the performance of the participating and other promising Query by Model or Query by Sketch 3D shape retrieval methods and to solicit state of the art approaches, we perform a more comprehensive comparison of twenty six (eighteen originally participating algorithms and eight additional state of the art or new) retrieval methods by evaluating them on the common benchmark. The benchmark, results, and evaluation tools are publicly available at our websites

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“…In this case, topological approaches [16,21] offer a modular framework in which it is possible to plug in multiple shape properties in the form of different real functions, so as to describe shapes and measure their (dis)similarity up to different notions of invariance. Examples of these descriptions are Reeb graphs [6,61], size functions [7], persistence diagrams [42,11] and persistence spaces [10]. Recently, topological descriptors have been shown to be a viable option for comparing shapes endowed with colourimetric information [5].…”

Section: Related Literaturementioning

confidence: 99%

Retrieval and classification methods for textured 3D models: a comparative study

et al. 2015

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This paper presents a comparative study of six methods for the retrieval and classification of textured 3D models, which have been selected as representative of the state of the art. To better analyse and control how methods deal with specific classes of geometric and texture deformations, we built a collection of 572 synthetic textured mesh models, in which each class includes multiple texture and geometric modifications of a small set of null models. Results show a challenging, yet lively, scenario and also reveal interesting insights in how to deal with texture information according to different approaches, possibly working in the CIELab as well as in modifications of the RGB colour space.

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Persistence-Based Structural Recognition

Abstract: This paper presents a framework for object recognition using topological persistence.

Cited by 94 publications

References 34 publications

Stable Topological Signatures for Points on 3D Shapes

Stable Topological Signatures for Points on 3D Shapes

A comparison of 3D shape retrieval methods based on a large-scale benchmark supporting multimodal queries

Retrieval and classification methods for textured 3D models: a comparative study

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