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33
Fully automatic registration of 3d point clouds
 IN CVPR ’06: PROCEEDINGS OF THE 2006 IEEE COMPUTER SOCIETY CONFERENCE ON COMPUTER VISION AND PATTERN RECOGNITION
, 2006
"... We propose a novel technique for the registration of 3D point clouds which makes very few assumptions: we avoid any manual rough alignment or the use of landmarks, displacement can be arbitrarily large, and the two point sets can have very little overlap. Crude alignment is achieved by estimation of ..."
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Cited by 45 (0 self)
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We propose a novel technique for the registration of 3D point clouds which makes very few assumptions: we avoid any manual rough alignment or the use of landmarks, displacement can be arbitrarily large, and the two point sets can have very little overlap. Crude alignment is achieved by estimation of the 3Drotation from two Extended Gaussian Images even when the data sets inducing them have partial overlap. The technique is based on the correlation of the two EGIs in the Fourier domain and makes use of the spherical and rotational harmonic transforms. For pairs with low overlap which fail a critical verification step, the rotational alignment can be obtained by the alignment of constellation images generated from the EGIs. Rotationally aligned sets are matched by correlation using the Fourier transform of volumetric functions. A fine alignment is acquired in the final step by running Iterative Closest Points with just few iterations.
Shape Representations and Algorithms for 3D Model Retrieval
, 2004
"... With recent improvements in methods for the acquisition and rendering of 3D models, the need for retrieval of models from large repositories of 3D shapes has gained prominence in the graphics and vision communities. A variety of methods have been proposed that enable the efficient querying of model ..."
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Cited by 15 (1 self)
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With recent improvements in methods for the acquisition and rendering of 3D models, the need for retrieval of models from large repositories of 3D shapes has gained prominence in the graphics and vision communities. A variety of methods have been proposed that enable the efficient querying of model repositories for a desired 3D shape. Many of these methods use a 3D model as a query and attempt to retrieve models from the database that have a similar shape.
Complex data processing: Fast wavelet analysis on the sphere
 J. Fourier Anal. and Appl
"... and P. Vielva ..."
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Invertible Filter Banks on the 2Sphere
, 2006
"... Multiscale filtering methods, such as wavelets and steerable pyramids, have been widely used in processing and analysis of planar images and promise similar benefits in application to spherical images. While recent advances have extended some filtering methods to the sphere, many key challenges rema ..."
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Cited by 8 (2 self)
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Multiscale filtering methods, such as wavelets and steerable pyramids, have been widely used in processing and analysis of planar images and promise similar benefits in application to spherical images. While recent advances have extended some filtering methods to the sphere, many key challenges remain. This paper focuses on the selfinvertibility property of filter banks, particularly desirable if images are modified in the wavelet domain. More specifically, we develop conditions for invertibility of spherical filter banks for both continuous and discrete convolution and illustrate how such conditions can be incorporated into the design of multiscale axissymmetric wavelets.
Correspondencefree Structure from Motion
, 2007
"... We present a novel approach for the estimation of 3Dmotion directly from two images using the Radon transform. The feasibility of any camera motion is computed by integrating over all feature pairs that satisfy the epipolar constraint. This integration is equivalent to taking the inner product of a ..."
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Cited by 5 (1 self)
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We present a novel approach for the estimation of 3Dmotion directly from two images using the Radon transform. The feasibility of any camera motion is computed by integrating over all feature pairs that satisfy the epipolar constraint. This integration is equivalent to taking the inner product of a similarity function on feature pairs with a Dirac function embedding the epipolar constraint. The maxima in this five dimensional motion space will correspond to compatible rigid motions. The main novelty is in the realization that the Radon transform is a filtering operator: If we assume that the similarity and Dirac functions are defined on spheres and the epipolar constraint is a group action of rotations on spheres, then the Radon transform is a correlation integral. We propose a new algorithm to compute this integral from the spherical Fourier transform of the similarity and Dirac functions. Generating the similarity function now becomes a preprocessing step which reduces the complexity of the Radon computation by a factor equal to the number of feature pairs processed. The strength of the algorithm is in avoiding a commitment to correspondences, thus being robust to erroneous feature detection, outliers, and multiple motions.
A fast Fourier algorithm on the rotation group
, 2007
"... In this paper we present an algorithm for the fast Fourier transform on the rotation group SO(3) which is based on the fast Fourier transform for nonequispaced nodes on the threedimensional torus. This algorithm allows to evaluate the SO(3) Fourier transform of Bbandlimited functions at M arbitra ..."
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Cited by 4 (1 self)
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In this paper we present an algorithm for the fast Fourier transform on the rotation group SO(3) which is based on the fast Fourier transform for nonequispaced nodes on the threedimensional torus. This algorithm allows to evaluate the SO(3) Fourier transform of Bbandlimited functions at M arbitrary input nodes in O(M + B³ log² B) flops instead of O(MB 3). Some numerical results will be presented establishing the algorithm’s numerical stability and time requirements.
Correspondenceless Structure from Motion
"... We present a novel approach for the estimation of 3Dmotion directly from two images using the Radon transform. The feasibility of any camera motion is computed by integrating over all feature pairs that satisfy the epipolar constraint. This integration is equivalent to taking the inner product of a ..."
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Cited by 3 (0 self)
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We present a novel approach for the estimation of 3Dmotion directly from two images using the Radon transform. The feasibility of any camera motion is computed by integrating over all feature pairs that satisfy the epipolar constraint. This integration is equivalent to taking the inner product of a similarity function on feature pairs with a Dirac function embedding the epipolar constraint. The maxima in this five dimensional motion space will correspond to compatible rigid motions. The main novelty is in the realization that the Radon transform is a filtering operator: If we assume that the similarity and Dirac functions are defined on spheres and the epipolar constraint is a group action of rotations on spheres, then the Radon transform is a correlation integral. We propose a new algorithm to compute this integral from the spherical harmonics of the similarity and Dirac functions. Generating the similarity function now becomes a preprocessing step which reduces the complexity of the Radon computation by a factor equal to the number of feature pairs processed. The strength of the algorithm is in avoiding a commitment to correspondences, thus being robust to erroneous feature detection, outliers, and multiple motions.
Spherical Correlation of Visual Representations for 3D Model Retrieval
"... In recent years we have seen a tremendous growth in the amount of freely available 3D content, in part due to breakthroughs for 3D model design and acquisition. For example, advances in range sensor technology and design software have dramatically reduced the manual labor required to construct 3D m ..."
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Cited by 2 (0 self)
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In recent years we have seen a tremendous growth in the amount of freely available 3D content, in part due to breakthroughs for 3D model design and acquisition. For example, advances in range sensor technology and design software have dramatically reduced the manual labor required to construct 3D models. As collections of 3D content continue to grow rapidly, the ability to perform fast and accurate retrieval from a database of models has become a necessity. At the core of this retrieval task is the fundamental challenge of defining and evaluating similarity between 3D shapes. Some effective methods dealing with this challenge consider similarity measures based on the visual appearance of models. While collections of rendered images are discriminative for retrieval tasks, such representations come with a few inherent limitations such as restrictions in the image viewpoint sampling and high computational costs. In this paper we present a novel algorithm for model similarity that addresses these issues. Our proposed method exploits techniques from spherical signal processing to efficiently evaluate a visual similarity measure between models. Extensive evaluations on multiple datasets are provided.
HARMONIC SILHOUETTE MATCHING FOR 3D MODELS
"... The ability to perform fast retrieval from a database of 3D models is becoming a growing necessity as the number of models in circulation is rapidly increasing. Several of the many existing methods dealing with this problem consider similarity measures based on visual appearance. This idea of compar ..."
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Cited by 2 (1 self)
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The ability to perform fast retrieval from a database of 3D models is becoming a growing necessity as the number of models in circulation is rapidly increasing. Several of the many existing methods dealing with this problem consider similarity measures based on visual appearance. This idea of comparing models using their respective silhouettes performs well on a number of benchmarks, but comes with a few inherent limitations, the biggest of which is that at the time of comparison all possible rotational alignments between two models need to be considered. In this paper we present two retrieval algorithms based on a silhouette representation. The first method shows how model similarity can be computed using fast harmonic matching techniques, and the second method reduces the problem to fast vector differencing using rotationinvariant properties of the representations. 1.
Probabilistic MarcinkiewiczZygmund inequalities on the rotation group
, 2009
"... on the rotation group ..."