An improvement of rotation invariant 3D-shape based on functions on concentric spheres

Vranić, Dejan V.

doi:10.1109/icip.2003.1247355

Cited by 115 publications

(97 citation statements)

References 6 publications

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“…Spherical harmonics and moments representation of the spherical extent function were tested in [4], indicating better performance in the first case. In the same context, a more general approach was introduced by Vranic et al [5,6] known as the layered depth spheres descriptor (also known as radialized spherical extent function). Here, the 3D model is described by a spherical function which decomposes the model into a sum of concentric shells and gives the maximal distance of the model from the center of mass as a function of angle and the radius of the equivalent shell.…”

Section: Related Workmentioning

confidence: 99%

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

Papadakis

Pratikakis

Perantonis

et al. 2007

Pattern Recognition

167

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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Section: Related Workmentioning

confidence: 99%

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

Papadakis

Pratikakis

Perantonis

et al. 2007

Pattern Recognition

167

105

View full text Add to dashboard Cite

show abstract

“…This approach is not robust to noise and needs a high dimension of feature vectors, this is why the authors construct the feature vectors from the complex function on a sphere, composed with ray based feature vectors and shading based feature vectors, presented in frequency domain by applying the spherical harmonics [14]. In order to capture the information in the interior of a 3-D model, the authors proposed the descriptor named Layered Depth Spheres [13], where they use the property of spherical harmonics to achieve the rotation invariance.…”

Section: Introductionmentioning

confidence: 99%

A 3-D Search engine based on Fourier series

Lmaati¹,

Oirrak²,

Aboutajdine³

et al. 2010

Computer Vision and Image Understanding

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The size of 3-D data stored around the Web has become bigger. Therefore the development of recognition applications and retrieval systems of 3-D models is important. In this paper we propose a new scheme to measure similarity between 3-D models. The main idea is to reconstruct a 3-D closed curve that represents a 3-D model given by a polygonal mesh, and to extract a signature from this 3-D closed curve using the Fourier series. The proposed descriptor needs CPCA (Continuous Principal Component Analysis) to align 3-D models into a canonical position. The feature vectors constructed using this method, named FSD (Fourier Series Descriptor) are invariants under rigid transformations composed of translation, rotation, flipping and scale; robust to noise and level of detail. A 3-D polygonal mesh model serves as a query for search by shape similarity in a large collection of 3-D models database using an interactive 3-D search engine.

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“…For example in the area of shape description and retrieval, various invariant shape-features which have been proposed are based on spherical functions [1] [2] [3] [4]. For biomedical applications, many algorithms including invariant 3D features [5] or rigid 3D registration for 3D volume data analysis have their mathematical foundations in the rotation group SO(3) which directly implies the use of functions on spheres.…”

Section: Introductionmentioning

confidence: 99%

Fast and Accurate Rotation Estimation on the 2-Sphere without Correspondences

Fehr

Reisert

Burkhardt

2008

Lecture Notes in Computer Science

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Abstract. We present a refined method for rotation estimation of signals on the 2-Sphere. Our approach utilizes a fast correlation in the harmonic domain to estimate rotation angles of arbitrary size and resolution. The method is able to achieve great accuracy even for very low spherical harmonic expansions of the input signals without using correspondences or any other kind of a priori information. The rotation parameters are computed analytically without additional iterative postprocessing or "fine tuning".The theoretical advances presented in this paper can be applied to a wide range of practical problems such as: shape description and shape retrieval, 3D rigid registration, robot positioning with omni-directional cameras or 3D invariant feature design.

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An improvement of rotation invariant 3D-shape based on functions on concentric spheres

Cited by 115 publications

References 6 publications

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

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

A 3-D Search engine based on Fourier series

Fast and Accurate Rotation Estimation on the 2-Sphere without Correspondences

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