17940922
Symmetry-based 3-D reconstruction from perspective images
Symmetry is an important geometric cue for 3-D reconstruction from perspective images. In this paper, we introduce a unified theoretical framework for extracting poses and structures of 2-D symmetric patterns in space from calibrated images. The framework uniformly encompasses all three fundamental types of symmetry, i.e., reflective, rotational, and translational, based on a systematic study of the homography groups in image induced by the symmetry groups in space. We claim that if a planar object admits rich enough symmetry, no 3-D geometric information is lost through perspective imaging. Based on two fundamental principles that utilize common spatial relations among symmetric objects, we have developed a prototype system which can automatically extract and segment multiple 2-D symmetric patterns present in a single perspective image. The result of such a segmentation is a hierarchy of new geometric primitives, called symmetry cells and complexes, whose 3-D structures and poses are fully recovered. Finally, we propose a new symmetry-based matching technique, which can effectively establish correspondences among the extracted symmetry cells across multiple images. We demonstrate the application of the proposed algorithms on image segmentation, matching, and 3-D reconstruction with extensive experimental results. The algorithms and systems are more accurate and easier to implement than existing point-or line-based methods.
13369249
Reconstruction of 3-D Symmetric Curves from Perspective Images without Discrete Features
The shapes of many natural and man-made objects have curved contours. The images of such contours usually do not have sufficient distinctive features to apply conventional feature-based reconstruction algorithms. This paper shows that both the shape of curves in 3-D space and the camera poses can be accurately reconstructed from their perspective images with unknown point correspondences given that the curves have certain invariant properties such as symmetry. We show that in such cases the minimum number of views needed for a solution is remarkably small: one for planar curves and two for nonplanar curves (of arbitrary shapes), which is significantly less than what is required by most existing algorithms for general curves. Our solutions rely on minimizing the L 2-distance between the shapes of the curves reconstructed via the “epipolar geometry” of symmetric curves. Both simulations and experiments on real images are presented to demonstrate the effectiveness of our approach.
696914
Generalized principal component analysis (GPCA)
This paper presents an algebro-geometric solution to the problem of segmenting an unknown number of subspaces of unknown and varying dimensions from sample data points. We represent the subspaces with a set of homogeneous polynomials whose degree is the number of subspaces and whose derivatives at a data point give normal vectors to the subspace passing through the point. When the number of subspaces is known, we show that these polynomials can be estimated linearly from data; hence, subspace segmentation is reduced to classifying one point per subspace. We select these points optimally from the data set by minimizing certain distance function, thus dealing automatically with moderate noise in the data. A basis for the complement of each subspace is then recovered by applying standard PCA to the collection of derivatives (normal vectors). Extensions of GPCA that deal with data in a high-dimensional space and with an unknown number of subspaces are also presented. Our experiments on low-dimensional data show that GPCA outperforms existing algebraic algorithms based on polynomial factorization and provides a good initialization to iterative techniques such as k-subspaces and expectation maximization. We also present applications of GPCA to computer vision problems such as face clustering, temporal video segmentation, and 3D motion segmentation from point correspondences in multiple affine views.
7027764
Optimization Criteria, Sensitivity and Robustness of Motion and Structure Estimation
The prevailing efforts to study the standard formulation of motion and structure recovery have been recently focused on issues of sensitivity and robustness of existing techniques. While many cogent observations have been made and verified experimentally, many statements do not hold in general settings and make a comparison of existing techniques difficult. With an ultimate goal of clarifying these issues we study the main aspects of the problem: the choice of objective functions, optimization techniques and the sensitivity and robustness issues in the presence of noise. 
 
We clearly reveal the relationship among different objective functions, such as "(normalized) epipolar constraints", "reprojection error" or "triangulation", which can all be be unified in a new "optimal triangulation" procedure formulated as a constrained optimization problem. Regardless of various choices of the objective function, the optimization problems all inherit the same unknown parameter space, the so called "essential manifold", making the new optimization techniques on Riemanian manifolds directly applicable. 
 
Using these analytical results we provide a clear account of sensitivity and robustness of the proposed linear and nonlinear optimization techniques and study the analyticaland practical equivalence of different objective functions. The geometric characterization of critical points of a function defined on essential manifold and the simulation results clarify the difference between the effect of bas relief ambiguity and other types of local minima leading to a consistent interpretations of simulation results over large range of signal-to-noise ratio and variety of configurations.
354989
Symmetry-based photo editing
Based on high-level geometric knowledge, especially symmetry, imposed upon objects in images, we demonstrate how to edit images in terms of correct 3-D shape and relationships of the objects, without explicitly performing full 3-D reconstruction. Symmetry is proposed as the central notation that unifies both conceptually and algorithmically all types of geometric regularities such as parallelism, orthogonality, and similarity. The methods are extremely simple, accurate and easy to implement, and they demonstrate the power of applying scene knowledge.
43689222
Symmetry-based photo-editing
In this paper, we demonstrate how to edit digital photos based on the understanding of high-level geometric knowledge imposed upon objects in the photos. This is achieved by the correct recovery of the 3-D shape and relationships of the objects, without explicitly performing full 3-D reconstruction. Symmetry is proposed as the central notion that unifies both conceptually and algorithmically all types of geometric regularities such as parallelism, orthogonality, and similarity. The methods are extremely simple, accurate, easy to implement, and they demonstrate the utility of applying scene knowledge to image understanding and editing.
1141862
Integrating Similarity Retrieval and Skyline Exploration Via Relevance Feedback
Similarity retrieval have been widely used in many practical search applications. A similarity query model can be viewed as a logical combination of a set of similarity predicates. A user can initialize a query model, but model parameters or the model itself may be inadequately specified. As a result, a retrieval system cannot guarantee that it has presented all the relevant tuples to the user. In this paper, we propose a framework that integrates the similarity retrieval and skyline exploration. Using the relevance feedback as a way to constrain the search space, our framework can intelligently explore only a necessary portion of data that contains all the relevant tuples. Our framework is also flexible enough to incorporate model refinement techniques to retrieving relevant results as early as possible.
14511860
Index for fast retrieval of uncertain spatial point data
Location information gathered from a variety of sources in the form of sensor data, video streams, human observations, and so on, is often imprecise and uncertain and needs to be represented approximately. To represent such uncertain location information, the use of a probabilistic model that captures the imprecise location as a probability density function (pdf) has been recently proposed. The pdfs can be arbitrarily complex depending on the type of application and the source of imprecision. Hence, efficiently representing, storing and querying pdfs is a very challenging task. While the current state of the art indexing approaches treat the representation and storage of pdfs as a black box, in this paper, we take the challenge of representing and storing any complex pdf in an efficient way. We further develop techniques to index such pdfs to support the efficient processing of location queries. Our extensive experiments demonstrate that our indexing techniques significantly outperform the best existing solutions.
47404061
Diversity and Multiplexing Tradeoff in General Fading Channels
The optimal tradeoff between diversity gain and multiplexing gain for multiple-inputmultiple-output (MIMO) channels has been studied recently under the independent and identically distributed (i.i.d.) Rayleigh-fading assumption. In this correspondence, this result is extended and the optimal tradeoff performance is derived for generalized fading channel conditions, including different fading types, nonidentical fading distributions, spatial correlation, and nonzero channel means. Our results include many known models as special cases and shed light on the effects of different channel parameters on the optimal tradeoff performance
42056704
RAF: An Activation Framework for Refining Similarity Queries Using Learning Techniques
In numerous applications that deal with similarity search, a user may not have an exact specification of his information need and/or may not be able to formulate a query that exactly captures his notion of similarity. A promising approach to mitigate this problem is to enable the user to submit a rough approximation of the desired query and use relevance feedback on retrieved objects to refine the query. In this paper, we explore such a refinement strategy for a general class of structured similarity queries. Our approach casts the refinement problem as that of learning concepts using the tuples on which the user provides feedback as a labeled training set. Under this setup, similarity query refinement consists of two learning tasks: learning the structure of the query and learning the relative importance of query components. The paper develops machine learning approaches suitable for the two learning tasks. The primary contribution of the paper is the Refinement Activation Framework (RAF) that decides when each learner is invoked. Experimental analysis over many real life datasets shows that our strategy significantly outperforms existing approaches in terms of retrieval quality.
5996048
Scaling up all pairs similarity search
Given a large collection of sparse vector data in a high dimensional space, we investigate the problem of finding all pairs of vectors whose similarity score (as determined by a function such as cosine distance) is above a given threshold. We propose a simple algorithm based on novel indexing and optimization strategies that solves this problem without relying on approximation methods or extensive parameter tuning. We show the approach efficiently handles a variety of datasets across a wide setting of similarity thresholds, with large speedups over previous state-of-the-art approaches.