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.
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.
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.
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.
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.
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.
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.
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.
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.