Surface coding based on Morse theory

Shinagawa, Yoshihisa; Kunii, Tosiyasu L.; Kergosien, Yannick

doi:10.1109/38.90568

Cited by 283 publications

(173 citation statements)

References 9 publications

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“…In principle, any number of efficient techniques for critical point detection [28] could be used to compute the ART and test for proper sampling. Unfortunately, we do not have access to the "true" image h(ξ, 0) (the scene radiance).…”

Section: Proper Sampling and Correspondencementioning

confidence: 99%

Video-based descriptors for object recognition

Lee

Soatto

2011

Image and Vision Computing

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Section: Proper Sampling and Correspondencementioning

confidence: 99%

Video-based descriptors for object recognition

Lee

Soatto

2011

Image and Vision Computing

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“…One-dimensional descriptors with proved topological properties, like the Reeb Graph [19], were used first in [23]. Reeb Graphs rely on Morse theory describing the extraction of critical points.…”

Section: D Descriptorsmentioning

confidence: 99%

SkelTre

2010

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Terrestrial laser scanners capture 3D geometry of real world objects as a point cloud. This paper reports on a new algorithm developed for the skeletonization of a laser scanner point cloud. The skeletonization algorithm proposed in this paper consists of three steps: (i) extraction of a graph from an octree organization, (ii) reduction of the graph to a skeleton, and (iii) embedding of the skeleton into the point cloud. For these three steps, only one input parameter is required. The results are validated on laser scanner point clouds representing 2 classes of objects; first on botanic trees as a special application and secondly on popular arbitrary objects. The presented skeleton found its first application in obtaining botanic tree parameters like length and diameter of branches and is presented here in a new, generalized version. Its definition as Reeb Graph, proofs the usefulness of the skeleton for applications like shape analysis. In this paper we show that the resulting skeleton contains the Reeb Graph and investigate the practically relevant parameters: centeredness and topological correctness. The robustness of this skeletonization method against undersampling, varying point density and systematic errors of the point cloud is demonstrated on real data examples.

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“…A Reeb graph describes the configuration of and relationship between critical points and provides a way to understand the intrinsic topological structure of a shape. Morse theory and the Reeb graph have been used in many applications such as shape matching [21], shape coding [22]- [24], surface compression [25], volume visualization [26], terrain analysis [27] and 3-D skeletonization [28], [29]. The last publication cited is particularly close to our work.…”

Section: Morse Theory and The Reeb Graphmentioning

confidence: 73%

A functional-based segmentation of human body scans in arbitrary postures

Werghi¹,

Xiao

Siebert

2006

IEEE Trans. Syst., Man, Cybern. B

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Abstract-This paper presents a general framework that aims to address the task of segmenting three-dimensional (3-D) scan data representing the human form into subsets which correspond to functional human body parts. Such a task is challenging due to the articulated and deformable nature of the human body. A salient feature of this framework is that it is able to cope with various body postures and is in addition robust to noise, holes, irregular sampling and rigid transformations. Although whole human body scanners are now capable of routinely capturing the shape of the whole body in machine readable format, they have not yet realized their potential to provide automatic extraction of key body measurements. Automated production of anthropometric databases is a prerequisite to satisfying the needs of certain industrial sectors (e.g., the clothing industry). This implies that in order to extract specific measurements of interest, whole body 3-D scan data must be segmented by machine into subsets corresponding to functional human body parts. However, previously reported attempts at automating the segmentation process suffer from various limitations, such as being restricted to a standard specific posture and being vulnerable to scan data artifacts. Our human body segmentation algorithm advances the state of the art to overcome the above limitations and we present experimental results obtained using both real and synthetic data that confirm the validity, effectiveness, and robustness of our approach.Index Terms-Human body shape analysis, Reeb graph, scattered 3-D range data segmentation, 3-D surface topology, 3-D whole-body scanners.

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Surface coding based on Morse theory

Cited by 283 publications

References 9 publications

Video-based descriptors for object recognition

Video-based descriptors for object recognition

SkelTre

A functional-based segmentation of human body scans in arbitrary postures

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