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.
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.
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.
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.
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.
9332901
On-Demand Information Portals for Disaster Situations
This paper describes our work on developing technology for rapidly assembling information portals that provide integrated access to and analysis of information from multiple sources in the case of any disaster. Many recent disasters (the S.E. Asian Tsunamis, the London subway bombings, the Katrina hurricane, to name a few) have demonstrated that a lot of valuable information becomes available in the hours and days immediately following the disaster, and such information is indeed valuable to disaster managers or even citizens in their response. In this paper we describe our work on developing information portals for disasters in general; we describe many key information processing capabilities and challenges that we consider important in such portals and also describe our approach to developing such capabilities.
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.
9927329
CAMAS: a citizen awareness system for crisis mitigation
1 ITR-Rescue, 5251 California Avenue, Suite 210, Irvine CA 92612-2815, Phone: 949-824-1147 http://www.itr-rescue.org 2 Union Bank Building, 400 Oceangate, Suite 1050, Long Beach CA 90802 Phone: 562-628-1675, http://imagecatinc.com ABSTRACT This demo paper provides a brief description of the intuition and design philosophy of CAMAS, one of the main testbeds being developed in the context of the RESCUE (Responding to the Unexpected) project [9]. The goal of our work is to enhance the mitigation capabilities of first responders in the event of a crisis by dramatically transforming their ability to collect, store, analyze, interpret, share and disseminate data. CAMAS specifically is a system designed to allow a variety of users, including the average citizen to report incidents and potentially hazardous situations, analyze and evaluate these reports and notify appropriate personnel for further action. The multidisciplinary approach incorporates a variety of information technologies: networks; distributed systems; databases; image and video processing; GIS; and machine learning, together with subjective information obtained through social science. Besides providing an overview of the CAMAS architecture, we describe the demonstration platform and specific experiments that will illustrate issues of event extraction, ranking, access control and visualization.
1599574
Interactive Refinement of Filtering Queries on Streaming Intelligence Data
Intelligence analysis involves routinely monitoring and correlating large amount of data streaming from multiple sources. In order to detect important patterns, the analyst normally needs to look at data gathered over a certain time window. Given the size of data and rate at which it arrives, it is usually impossible to manually process every record or case. Instead, automated filtering (classification) mechanisms are employed to identify information relevant to the analyst’s task. In this paper, we present a novel system framework called FREESIA (Filter REfinement Engine for Streaming InformAtion) to effectively generate, utilize and update filtering queries on streaming data.