Matching 3D models with shape distributions

Osada, Robert; Funkhouser, Thomas; Chazelle, Bernard; Dobkin, David P.

doi:10.1109/sma.2001.923386

Cited by 419 publications

(331 citation statements)

References 48 publications

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“…They show, that in most cases this is the better alternative than a normalizing approach. In [8] Reisert et al enhanced the Shape Distribution introduced by Osada [6] by SH-expansion. The currently best performing methods on the PSB are the so-called Light Field Descriptors (LFD) [2].…”

Section: Introductionmentioning

confidence: 99%

Using Irreducible Group Representations for Invariant 3D Shape Description

Reisert

Burkhardt

2006

Lecture Notes in Computer Science

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Abstract. Invariant feature representations for 3D objects are one of the basic needs in 3D object retrieval and classification. One tool to obtain rotation invariance are Spherical Harmonics, which are an orthogonal basis for the functions defined on the 2-sphere. We show that the irreducible representations of the 3D rotation group, which acts on the Spherical Harmonic representation, can give more information about the considered object than the Spherical Harmonic expansion itself. We embed our new feature extraction methods in the group integration framework and show experiments for 3D-surface data (Princeton Shape Benchmark).

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Section: Introductionmentioning

confidence: 99%

Using Irreducible Group Representations for Invariant 3D Shape Description

Reisert

Burkhardt

2006

Lecture Notes in Computer Science

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“…Since the entire shape is used for retrieval, normalization techniques can be used to remove much of the transformational ambiguity in matching, allowing for the use of the center of mass for removing translational ambiguity, radial-variance or mean-/bounding-radius for removing scaling ambiguity, and principal axes for rotational ambiguity. These methods have included: 1D histograms capturing the distribution of points [2,3,4], crease angles [5], and curvature [6] over the surface; spherical functions characterizing the distribution of surface normals [7], axes of reflective symmetry [8], conformality [9], and angular extent [10]; 3D functions characterizing the rasterization of the boundary boundary points [11] and the distance transform [12]; and even 4D plenoptic functions characterizing the 2D views of a surface [13].…”

Section: Related Workmentioning

confidence: 99%

A Shape Relationship Descriptor for Radiation Therapy Planning

Kazhdan

Simari

McNutt

et al. 2009

Medical Image Computing and Computer-Assisted Intervention – MICCAI 2009

102

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Abstract. In this paper we address the challenge of matching patient geometry to facilitate the design of patient treatment plans in radiotherapy. To this end we propose a novel shape descriptor, the Overlap Volume Histogram, which provides a rotation and translation invariant representation of a patient's organs at risk relative to the tumor volume. Using our descriptor, it is possible to accurately identify database patients with similar constellations of organ and tumor geometries, enabling the transfer of treatment plans between patients with similar geometries. We demonstrate the utility of our method for such tasks by outperforming state of the art shape descriptors in the retrieval of patients with similar treatment plans. We also preliminarily show its potential as a quality control tool by demonstrating how it is used to identify an organ at risk whose dose can be significantly reduced.

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“…The shape distributions proposed by Osada et al [22,23] is a shape descriptor where several shape characteristics can be measured for a random set of points belonging to the model, according to the selection of an appropriate shape function. There are variations of this method according to the characteristic that is measured, e.g.…”

Section: Related Workmentioning

confidence: 99%

“…Another approach to normalize a 3D model for rotation (similar to PCA), is the use of singular value decomposition (SVD) [28]. In [22,30], the SVD of the covariance matrix of the 3D model is computed and the unitary matrix is applied to the model for rotation normalization.…”

Section: Translation and Rotation Normalizationmentioning

confidence: 99%

Efficient 3D shape matching and retrieval using a concrete radialized spherical projection representation

Papadakis

Pratikakis

Perantonis

et al. 2007

Pattern Recognition

166

105

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We present a 3D shape retrieval methodology based on the theory of spherical harmonics. Using properties of spherical harmonics, scaling and axial flipping invariance is achieved. Rotation normalization is performed by employing the continuous principal component analysis along with a novel approach which applies PCA on the face normals of the model. The 3D model is decomposed into a set of spherical functions which represents not only the intersections of the corresponding surface with rays emanating from the origin but also points in the direction of each ray which are closer to the origin than the furthest intersection point. The superior performance of the proposed methodology is demonstrated through a comparison against state-of-the-art approaches on standard databases. ᭧

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Matching 3D models with shape distributions

Abstract: Measuring the similarity between 3D shapes is a fundamental problem, with applications in computer vision

Cited by 419 publications

References 48 publications

Using Irreducible Group Representations for Invariant 3D Shape Description

Using Irreducible Group Representations for Invariant 3D Shape Description

A Shape Relationship Descriptor for Radiation Therapy Planning

Efficient 3D shape matching and retrieval using a concrete radialized spherical projection representation

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