9330524
Structure and pose from single images of symmetric objects with applications to robot navigation
In this paper, we provide a principled and unified explanation how knowledge in global 3-D structural invariants, typically captured by a group action on a symmetric structure, can significantly facilitate the task of reconstructing a 3-D scene from one or more images. More importantly, the "absolute" pose between the camera frame and the canonical frame that symmetric objects (e.g., buildings, hallways) provide us overwhelming clues to their orientation and position. We give the necessary and sufficient conditions under which this pose can be uniquely determined, and when such conditions are not satisfied, exactly to what extent this pose can be recovered. We show how algorithms from conventional multiple-view geometry, after properly modified and extended, can be effectively applied to perform such recovery. Since the structure, pose and even camera calibration can be recovered from a single image; the techniques naturally apply to vision-based robot navigation where global position and orientation is important.
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.
36567578
Euclidean reconstruction and reprojection up to subgroups
The necessary and sufficient conditions for being able to estimate scene structure, motion and camera calibration from a sequence of images are very rarely satisfied in practice. What exactly can be estimated in sequences of practical importance, when such conditions are not satisfied? In this paper we give a complete answer to this question. For every camera motion that fails to meet the conditions, we give explicit formulas for the ambiguities in the reconstructed scene, motion and calibration. Such a characterization is crucial both for designing robust estimation algorithms (that do not try to recover parameters that cannot be recovered), and for generating novel views of the scene by controlling the vantage point. To this end, we characterize explicitly all the vantage points that give rise to a valid Euclidean reprojection regardless of the ambiguity in the reconstruction. We also characterize vantage points that generate views that are altogether invariant to the ambiguity. All the results are presented using simple notation that involves no tensors nor complex projective geometry, and should be accessible with basic background in linear algebra.
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.
8131766
Segmentation of a piece-wise planar scene from perspective images
We study and compare two novel embedding methods for segmenting feature points of piece-wise planar structures from two (uncalibrated) perspective images. We show that a set of different homographies can be embedded in different ways to a higher-dimensional real or complex space, so that each homography corresponds to either a complex bilinear form or a real quadratic form. Each embedding reveals different algebraic properties and relations of homographies. We give a closed-form segmentation solution for each case by utilizing these properties based on subspace-segmentation methods. These theoretical results show that one can intrinsically segment a piece-wise planar scene from 2-D images without explicitly performing any 3-D reconstruction. The resulting segmentation may make subsequent 3-D reconstruction much better-conditioned. We demonstrate the proposed methods with some convincing experimental results.
2268413
Web object retrieval
The primary function of current Web search engines is essentially relevance ranking at the document level. However, myriad structured information about real-world objects is embedded in static Web pages and online Web databases. Document-level information retrieval can unfortunately lead to highly inaccurate relevance ranking in answering object-oriented queries. In this paper, we propose a paradigm shift to enable searching at the object level. In traditional information retrieval models, documents are taken as the retrieval units and the content of a document is considered reliable. However, this reliability assumption is no longer valid in the object retrieval context when multiple copies of information about the same object typically exist. These copies may be inconsistent because of diversity of Web site qualities and the limited performance of current information extraction techniques. If we simply combine the noisy and inaccurate attribute information extracted from different sources, we may not be able to achieve satisfactory retrieval performance. In this paper, we propose several language models for Web object retrieval, namely an unstructured object retrieval model, a structured object retrieval model, and a hybrid model with both structured and unstructured retrieval features. We test these models on a paper search engine and compare their performances. We conclude that the hybrid model is the superior by taking into account the extraction errors at varying levels.
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.
7189578
The Kalman Filter as the optimal linear minimum mean-squared error multiuser CDMA detector
It is shown that a first-order linear state-space model applies to the asynchronous code-division multiple-access (CDMA) channel, and thus the Kalman filter produces symbol estimates with the minimum mean-squared error (MMSE) among all linear filters, in long- or short-code systems for a given detection delay. This result may be used as a benchmark against which to compare the performance of other linear detectors in asynchronous channels. It also reveals that a time-varying recursive filter with a fixed and finite complexity implements the fixed-lag linear MMSE (LMMSE) detector, which hitherto has been assumed to require a processing window (and hence complexity) that grows with time.
33501253
A design analysis model for developing world wide web sites
This study applies reader-response criticism to examine the relationship between and among designers, text, and users of the Galter Health Sciences Library Web site. It asks such questions as "How do Web site designers construct their subject?" or, "whom do the web designers think their users are?" The study ascertains the intentions of the designers of the GHSL Web site; examines the meanings made by the users through interviews; compares the similarities and differences of designers' intentions with their organization of knowlege represented in the GHSL Web site; and compares the similarities and differences between the designers' intentions and views of the users.
14652056
A framework for refining similarity queries using learning techniques
In numerous applications that deal with similarity search, a user may not have an exact idea of his information need and/or may not be able to construct 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 the feedback on the relevance of the retrieved objects to refine the query. In this paper, we explore such a refinement strategy for a general class of SQL similarity queries. Our approach casts the refinement problem as that of learning concepts using examples. This is achieved by viewing the tuples on which a user provides feedback as a labeled training set for a learner. Under this setup, SQL query refinement consists of two learning tasks, namely learning the structure of the SQL query and learning the relative importance of the query components. The paper develops appropriate machine learning approaches suitable for these two learning tasks. The primary contribution of the paper is a general refinement framework that decides when each learner is invoked in order to quickly learn the user query. Experimental analyses over many real life datasets and queries show that our strategy outperforms the existing approaches significantly in terms of retrieval accuracy and query simplicity.