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.
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.
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.
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.
6626830
Optimization Criteria and Geometric Algorithms for Motion and Structure Estimation
Prevailing efforts to study the standard formulation of motion and structure recovery have recently been 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 motion and structure recovery: the choice of objective function, optimization techniques and 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,” all of which can be unified in a new “optimal triangulation” procedure. Regardless of various choices of the objective function, the optimization problems all inherit the same unknown parameter space, the so-called “essential manifold.” Based on recent developments of optimization techniques on Riemannian manifolds, in particular on Stiefel or Grassmann manifolds, we propose a Riemannian Newton algorithm to solve the motion and structure recovery problem, making use of the natural differential geometric structure of the essential manifold.We provide a clear account of sensitivity and robustness of the proposed linear and nonlinear optimization techniques and study the analytical and practical equivalence of different objective functions. The geometric characterization of critical points and the simulation results clarify the difference between the effect of bas-relief ambiguity, rotation and translation confounding and other types of local minima. This leads to consistent interpretations of simulation results over a large range of signal-to-noise ratio and variety of configurations.
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.
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.
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.
7391513
Asymptotic performance of hybrid-selection/maximal-ratio combining over fading channels
In this letter, we study the asymptotic performance of hybrid-selection/maximal-ratio combining (HS/MRC) and postdetection HS/equal-gain combining (HS/EGC) over generalized fading channels for large average signal-to-noise ratios (ASNRs). By evaluating the asymptotic moment generating function of the HS/MRC output SNR at high ASNR, we derive the diversity and coding gains for HS/MRC for a large class of modulation formats and versatile fading conditions, including different types of fading channels and nonidentical SNR statistics across diversity branches. Our analytical results reveal that the diversity gains of HS/MRC and HS/EGC are equivalent to that of MRC, and the difference in the coding gains for different modulation formats is manifested in terms of a modulation factor defined in this letter. Some new analytical results about effects of the number of combined branches for HS/MRC and noncoherent combining loss of HS/EGC are also provided.