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280
A spectral approach to shapebased retrieval of articulated 3D models
 CAD
, 2007
"... We present an approach to robust shape retrieval from databases containing articulated 3D models. Each shape is represented by the eigenvectors of an appropriately defined affinity matrix, forming a spectral embedding which achieves normalization against rigidbody transformations, uniform scaling, ..."
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Cited by 56 (1 self)
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We present an approach to robust shape retrieval from databases containing articulated 3D models. Each shape is represented by the eigenvectors of an appropriately defined affinity matrix, forming a spectral embedding which achieves normalization against rigidbody transformations, uniform scaling, and shape articulation (bending). Retrieval is performed in the spectral domain using global shape descriptors. On the McGill database of articulated 3D shapes, the spectral approach leads to absolute improvement in retrieval performance for both the spherical harmonic and the light field shape descriptors. The best retrieval results are obtained using a simple and novel eigenvaluebased descriptor we propose.
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 51 (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.
Exploring collections of 3D models using fuzzy correspondences
"... Large collections of 3D models from the same object class (e.g., chairs, cars, animals) are now commonly available via many public repositories, but exploring the range of shape variations across such collections remains a challenging task. In this work, we present a new exploration interface that a ..."
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Cited by 45 (17 self)
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Large collections of 3D models from the same object class (e.g., chairs, cars, animals) are now commonly available via many public repositories, but exploring the range of shape variations across such collections remains a challenging task. In this work, we present a new exploration interface that allows users to browse collections based on similarities and differences between shapes in userspecified regions of interest (ROIs). To support this interactive system, we introduce a novel analysis method for computing similarity relationships between points on 3D shapes across a collection. We encode the inherent ambiguity in these relationships using fuzzy point correspondences and propose a robust and efficient computational framework that estimates fuzzy correspondences using only a sparse set of pairwise model alignments. We evaluate our analysis method on a range of correspondence benchmarks and report substantial improvements in both speed and accuracy over existing alternatives. In addition, we demonstrate how fuzzy correspondences enable key features in our exploration tool, such as automated view alignment, ROIbased similarity search, and faceted browsing.
ExpressionInvariant Representations of Faces
 IEEE TRANS. PAMI
, 2007
"... Addressed here is the problem of constructing and analyzing expressioninvariant representations of human faces. We demonstrate and justify experimentally a simple geometric model that allows to describe facial expressions as isometric deformations of the facial surface. The main step in the constru ..."
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Cited by 45 (6 self)
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Addressed here is the problem of constructing and analyzing expressioninvariant representations of human faces. We demonstrate and justify experimentally a simple geometric model that allows to describe facial expressions as isometric deformations of the facial surface. The main step in the construction of expressioninvariant representation of a face involves embedding of the facial intrinsic geometric structure into some convenient lowdimensional space. We study the influence of the embedding space geometry and dimensionality choice on the representation accuracy and argue that compared to its Euclidean counterpart, spherical embedding leads to notably smaller metric distortions. We experimentally support our claim showing that a smaller embedding error leads to better recognition.
Upright orientation of manmade objects
 ACM Trans. Graphics
, 2008
"... Figure 1: Left: A manmade model with unnatural orientation. Middle: Six orientations obtained by aligning the model into a canonical coordinate frame using Principal Component Analysis. Right: Our method automatically detects the upright orientation of the model from its geometry alone. Humans usua ..."
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Cited by 43 (13 self)
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Figure 1: Left: A manmade model with unnatural orientation. Middle: Six orientations obtained by aligning the model into a canonical coordinate frame using Principal Component Analysis. Right: Our method automatically detects the upright orientation of the model from its geometry alone. Humans usually associate an upright orientation with objects, placing them in a way that they are most commonly seen in our surroundings. While it is an open challenge to recover the functionality of a shape from its geometry alone, this paper shows that it is often possible to infer its upright orientation by analyzing its geometry. Our key idea is to reduce the twodimensional (spherical) orientation space to a small set of orientation candidates using functionalityrelated geometric properties of the object, and then determine the best orientation using an assessment function of several functional geometric attributes defined with respect to each candidate. Specifically we focus on obtaining the upright orientation for manmade objects that typically stand on some flat surface (ground, floor, table, etc.), which include the vast majority of objects in our everyday surroundings. For these types of models orientation candidates can be defined according to static equilibrium. For each candidate, we introduce a set of discriminative attributes linking shape to function. We learn an assessment function of these attributes from a training set using a combination of Random Forest classifier and Support Vector Machine classifier. Experiments demonstrate that our method generalizes well and achieves about 90 % prediction accuracy for both a 10fold crossvalidation over the training set and a validation with an independent test set. 1
Modeling LSH for Performance Tuning
"... Although LocalitySensitive Hashing (LSH) is a promising approach to similarity search in highdimensional spaces, it has not been considered practical partly because its search quality is sensitive to several parameters that are quite data dependent. Previous research on LSH, though obtained intere ..."
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Cited by 39 (1 self)
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Although LocalitySensitive Hashing (LSH) is a promising approach to similarity search in highdimensional spaces, it has not been considered practical partly because its search quality is sensitive to several parameters that are quite data dependent. Previous research on LSH, though obtained interesting asymptotic results, provides little guidance on how these parameters should be chosen, and tuning parameters for a given dataset remains a tedious process. To address this problem, we present a statistical performance model of Multiprobe LSH, a stateoftheart variance of LSH. Our model can accurately predict the average search quality and latency given a small sample dataset. Apart from automatic parameter tuning with the performance model, we also use the model to devise an adaptive LSH search algorithm to determine the probing parameter dynamically for each query. The adaptive probing method addresses the problem that even though the average performance is tuned for optimal, the variance of the performance is extremely high. We experimented with three different datasets including audio, images and 3D shapes to evaluate our methods. The results show the accuracy of the proposed model: the recall errors predicted are within 5 % from the real values for most cases; the adaptive search method reduces the standard deviation of recall by about 50 % over the existing method.
Ffts on the rotation group
 Santa Fe Institute Working Papers Series Paper
, 2003
"... Earlier work by Driscoll and Healy [4] has produced an efficient O(B 2 log 2 B) algorithm for computing the Fourier transform of bandlimited functions on the 2sphere. In this paper, we discuss an implementation of an O(B 4) algorithm for the numerical computation of Fourier transforms of functions ..."
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Cited by 37 (0 self)
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Earlier work by Driscoll and Healy [4] has produced an efficient O(B 2 log 2 B) algorithm for computing the Fourier transform of bandlimited functions on the 2sphere. In this paper, we discuss an implementation of an O(B 4) algorithm for the numerical computation of Fourier transforms of functions defined on the rotation group, SO(3). This compares with the direct O(B 6) approach. The algorithm we implemented is based on the “Separation of Variables ” technique, e.g. as presented by Maslen and Rockmore [19]. In conjunction with the techniques developed in [4], the SO(3) algorithm we implemented may be made truly fast, O(B 3 log 2 B). Basic results will be presented establishing the algorithm’s numerical stability, and examples of applications will be presented. 1
3D object retrieval using manytomany matching of curve skeletons
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, 2005
"... We present a 3D matching framework based on a manytomany matching algorithm that works with skeletal representations of 3D volumetric objects. We demonstrate the performance of this approach on a large database of 3D objects containing more than 1000 exemplars. The method is especially suited t ..."
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Cited by 37 (3 self)
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We present a 3D matching framework based on a manytomany matching algorithm that works with skeletal representations of 3D volumetric objects. We demonstrate the performance of this approach on a large database of 3D objects containing more than 1000 exemplars. The method is especially suited to matching objects with distinct part structure and is invariant to part articulation. Skeletal matching has an intuitive quality that helps in defining the search and visualizing the results. In particular, the matching algorithm produces a direct correspondence between two skeletons and their parts, which can be used for registration and juxtaposition. 1.
T.: Selecting distinctive 3D shape descriptors for similarity retrieval
 In: Proc. IEEE Int. Conf. on Shape Model. and Appl. SMI ’06
, 2006
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TopologyInvariant Similarity of Nonrigid Shapes
, 2009
"... This paper explores the problem of similarity criteria between nonrigid shapes. Broadly speaking, such criteria are divided into intrinsic and extrinsic, the first referring to the metric structure of the object and the latter to how it is laid out in the Euclidean space. Both criteria have their ..."
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Cited by 33 (3 self)
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This paper explores the problem of similarity criteria between nonrigid shapes. Broadly speaking, such criteria are divided into intrinsic and extrinsic, the first referring to the metric structure of the object and the latter to how it is laid out in the Euclidean space. Both criteria have their advantages and disadvantages: extrinsic similarity is sensitive to nonrigid deformations, while intrinsic similarity is sensitive to topological noise. In this paper, we approach the problem from the perspective of metric geometry. We show that by unifying the extrinsic and intrinsic similarity criteria, it is possible to obtain a stronger topologyinvariant similarity, suitable for comparing deformed shapes with different topology. We construct this new joint criterion as a tradeoff between the extrinsic and intrinsic similarity and use it as a setvalued distance. Numerical results demonstrate the efficiency of our approach in cases where using either extrinsic or intrinsic criteria alone would fail.