14267213
Geometric segmentation of perspective images based on symmetry groups
Symmetry is an effective geometric cue to facilitate conventional segmentation techniques on images of man-made environment. Based on three fundamental principles that summarize the relations between symmetry and perspective imaging, namely, structure from symmetry, symmetry hypothesis testing, and global symmetry testing, we develop a prototype system which is able to automatically segment symmetric objects in space from single 2D perspective images. The result of such a segmentation is a hierarchy of geometric primitives, called symmetry cells and complexes, whose 3D structure and pose are fully recovered. Such a geometrically meaningful segmentation may greatly facilitate applications such as feature matching and robot navigation.
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.
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.
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.
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.
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.
2798845
Modeling and querying uncertain spatial information for situational awareness applications
Situational awareness (SA) applications monitor the real world and the entities therein to support tasks such as rapid decision-making, reasoning, and analysis. Raw input about unfolding events may arrive from variety of sources in the form of sensor data, video streams, human observations, and so on, from which events of interest are extracted. Location is one of the most important attributes of events, useful for a variety of SA tasks. In this paper, we propose an approach to model and represent (potentially uncertain) event locations described by human reporters in the form of free text. We analyze several types of spatial queries of interest in SA applications. Our experimental evaluation demonstrates the effectiveness of our approach.
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.
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.
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.