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278
A Framework for Robust Subspace Learning
 International Journal of Computer Vision
, 2003
"... Many computer vision, signal processing and statistical problems can be posed as problems of learning low dimensional linear or multilinear models. These models have been widely used for the representation of shape, appearance, motion, etc, in computer vision applications. ..."
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Cited by 177 (10 self)
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Many computer vision, signal processing and statistical problems can be posed as problems of learning low dimensional linear or multilinear models. These models have been widely used for the representation of shape, appearance, motion, etc, in computer vision applications.
Segmenting foreground objects from a dynamic textured background via a robust kalman filter
 in IEEE Proceedings of the International Conference on Computer Vision
, 2003
"... The algorithm presented in this paper aims to segment the foreground objects in video (e.g., people) given timevarying, textured backgrounds. Examples of timevarying backgrounds include waves on water, clouds moving, trees waving in the wind, automobile trafc, moving crowds, escalators, etc. We ha ..."
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Cited by 100 (0 self)
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The algorithm presented in this paper aims to segment the foreground objects in video (e.g., people) given timevarying, textured backgrounds. Examples of timevarying backgrounds include waves on water, clouds moving, trees waving in the wind, automobile trafc, moving crowds, escalators, etc. We have developed a novel foregroundbackground segmentation algorithm that explicitly accounts for the nonstationary nature and clutterlike appearance of many dynamic textures. The dynamic texture is modeled by an Autoregressive Moving Average Model (ARMA). A robust Kalman lter algorithm iteratively estimates the intrinsic appearance of the dynamic texture, as well as the regions of the foreground objects. Preliminary experiments with this method have demonstrated promising results. 1
Heteroscedastic Regression in Computer Vision: Problems with Bilinear Constraint
 International Journal of Computer Vision
"... We present an algorithm to estimate the parameters of a linear model in the presence of heteroscedastic noise, i.e., each data point having a different covariance matrix. ..."
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Cited by 97 (7 self)
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We present an algorithm to estimate the parameters of a linear model in the presence of heteroscedastic noise, i.e., each data point having a different covariance matrix.
Geometric Properties of Central Catadioptric Line Images and their Application in Calibration
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2005
"... Abstract—In central catadioptric systems, lines in a scene are projected to conic curves in the image. This work studies the geometry of the central catadioptric projection of lines and its use in calibration. It is shown that the conic curves where the lines are mapped possess several projective in ..."
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Cited by 80 (9 self)
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Abstract—In central catadioptric systems, lines in a scene are projected to conic curves in the image. This work studies the geometry of the central catadioptric projection of lines and its use in calibration. It is shown that the conic curves where the lines are mapped possess several projective invariant properties. From these properties, it follows that any central catadioptric system can be fully calibrated from an image of three or more lines. The image of the absolute conic, the relative pose between the camera and the mirror, and the shape of the reflective surface can be recovered using a geometric construction based on the conic loci where the lines are projected. This result is valid for any central catadioptric system and generalizes previous results for paracatadioptric sensors. Moreover, it is proven that systems with a hyperbolic/elliptical mirror can be calibrated from the image of two lines. If both the shape and the pose of the mirror are known, then two line images are enough to determine the image of the absolute conic encoding the camera’s intrinsic parameters. The sensitivity to errors is evaluated and the approach is used to calibrate a real camera. Index Terms—Catadioptric, omnidirectional vision, projective geometry, lines, calibration. 1
On the fitting of surfaces to data with covariances
 IEEE Trans. Patt. Anal. Mach. Intell
, 2000
"... AbstractÐWe consider the problem of estimating parameters of a model described by an equation of special form. Specific models arise in the analysis of a wide class of computer vision problems, including conic fitting and estimation of the fundamental matrix. We assume that noisy data are accompanie ..."
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Cited by 78 (19 self)
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AbstractÐWe consider the problem of estimating parameters of a model described by an equation of special form. Specific models arise in the analysis of a wide class of computer vision problems, including conic fitting and estimation of the fundamental matrix. We assume that noisy data are accompanied by (known) covariance matrices characterizing the uncertainty of the measurements. A cost function is first obtained by considering a maximumlikelihood formulation and applying certain necessary approximations that render the problem tractable. A novel, Newtonlike iterative scheme is then generated for determining a minimizer of the cost function. Unlike alternative approaches such as Sampson's method or the renormalization technique, the new scheme has as its theoretical limit the minimizer of the cost function. Furthermore, the scheme is simply expressed, efficient, and unsurpassed as a general technique in our testing. An important feature of the method is that it can serve as a basis for conducting theoretical comparison of various estimation approaches.
Catadioptric SelfCalibration
, 2000
"... We have assembled astandH460 movable system that can capture long sequences ofomnid ectional images (up to 1,500 images at 6.7 Hzand a resolution of 1140 1030). The goal of this system is to reconstruct complex large environments, such as an entire floor of a buildH4 from the captured images on ..."
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Cited by 73 (0 self)
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We have assembled astandH460 movable system that can capture long sequences ofomnid ectional images (up to 1,500 images at 6.7 Hzand a resolution of 1140 1030). The goal of this system is to reconstruct complex large environments, such as an entire floor of a buildH4 from the captured images only. In this paper, wead ess the important issue of how to calibrate such a system. Our method uses images of the environment to calibrate the camera, without the use of a y specia ca93fl68900 pa93fl6 knowledge ofca08G motion, or knowledge of scene geometry. It uses the consistency of pairwise tracked point features across a sequence based on the characteristics of catad4H35 imaging. We also show how the projection equation for this catad0H30 camera can be formulated to be equivalent to that of a typical rectilinear perspective camera with just a simple transformation. 1 Introduction The visua63fl07'9 as modeling ofla00 environments is increa06DG' becominga aoming32 e proposition, due tof...
InputDependent Estimation of Generalization Error under Covariate Shift
 STATISTICS & DECISIONS, VOL.23, NO.4, PP.249–279, 2005
, 2005
"... A common assumption in supervised learning is that the training and test input points follow the same probability distribution. However, this assumption is not fulfilled, e.g., in interpolation, extrapolation, active learning, or classification with imbalanced data. The violation of this assumption— ..."
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Cited by 61 (32 self)
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A common assumption in supervised learning is that the training and test input points follow the same probability distribution. However, this assumption is not fulfilled, e.g., in interpolation, extrapolation, active learning, or classification with imbalanced data. The violation of this assumption—known as the covariate shift— causes a heavy bias in standard generalization error estimation schemes such as crossvalidation or Akaike’s information criterion, and thus they result in poor model selection. In this paper, we propose an alternative estimator of the generalization error for the squared loss function when training and test distributions are different. The proposed generalization error estimator is shown to be exactly unbiased for finite samples if the learning target function is realizable and asymptotically unbiased in general. We also show that, in addition to the unbiasedness, the proposed generalization error estimator can accurately estimate the difference of the generalization error among different models, which is a desirable property in model selection. Numerical studies show that the proposed method compares favorably with existing model selection methods in regression for extrapolation and in classification with imbalanced data.
Path Detection in Video Surveillance
 Image and Vision Computing
, 2002
"... This paper addresses the problem of automatically extracting frequently used pedestrian pathways from video sequences of natural outdoor scenes. Path models are learnt from the accumulation of trajectory data over long time periods, and can be used to augment the classification of subsequent track d ..."
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Cited by 55 (5 self)
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This paper addresses the problem of automatically extracting frequently used pedestrian pathways from video sequences of natural outdoor scenes. Path models are learnt from the accumulation of trajectory data over long time periods, and can be used to augment the classification of subsequent track data. In particular, labelled paths provide an efficient means for compressing the trajectory data for logging purposes. In addition, the model can be used to compute a probabilistic prediction of the pedestrian's location many timesteps ahead, and to aid the recognition of unusual behaviour identified as atypical object motion.
Catadioptric camera calibration using geometric invariants
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2004
"... Abstract—Central catadioptric cameras are imaging devices that use mirrors to enhance the field of view while preserving a single effective viewpoint. In this paper, we propose a novel method for the calibration of central catadioptric cameras using geometric invariants. Lines and spheres in space a ..."
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Cited by 47 (7 self)
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Abstract—Central catadioptric cameras are imaging devices that use mirrors to enhance the field of view while preserving a single effective viewpoint. In this paper, we propose a novel method for the calibration of central catadioptric cameras using geometric invariants. Lines and spheres in space are all projected into conics in the catadioptric image plane. We prove that the projection of a line can provide three invariants whereas the projection of a sphere can only provide two. From these invariants, constraint equations for the intrinsic parameters of catadioptric camera are derived. Therefore, there are two kinds of variants of this novel method. The first one uses projections of lines and the second one uses projections of spheres. In general, the projections of two lines or three spheres are sufficient to achieve catadioptric camera calibration. One important conclusion in this paper is that the method based on projections of spheres is more robust and has higher accuracy than that based on projections of lines. The performances of our method are demonstrated by both the results of simulations and experiments with real images. Index Terms—Camera calibration, catadioptric camera, geometric invariant, omnidirectional vision, panoramic vision. 1
Robust Active Shape Model Search
 In Proceedings of the European Conference on Computer Vision
, 2002
"... Active shape models (ASMs) have been shown to be a powerful tool to aid the interpretation of images. ASM model parameter estimation is based on the assumption that residuals between model fit and data have a Gaussian distribution. However, in many real applications, specifically those found in the ..."
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Cited by 47 (1 self)
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Active shape models (ASMs) have been shown to be a powerful tool to aid the interpretation of images. ASM model parameter estimation is based on the assumption that residuals between model fit and data have a Gaussian distribution. However, in many real applications, specifically those found in the area of medical image analysis, this assumption may be inaccurate. Robust parameter estimation methods have been used elsewhere in machine vision and provide a promising method of improving ASM search performance. This paper formulates Mestimator and random sampling approaches to robust parameter estimation in the context of ASM search. These methods have been applied to several sets of medical images where ASM search robustness problems have previously been encountered. Robust parameter estimation is shown to increase tolerance to outliers, which can lead to improved search robustness and accuracy.