Estimating 3-D motion parameters from the three-dimensional point correspondences is considered in this paper. A minimum errors-in-variable formulation of the motion estimation problem is developed to obtain stable an...
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ISBN:
(纸本)0818638826
Estimating 3-D motion parameters from the three-dimensional point correspondences is considered in this paper. A minimum errors-in-variable formulation of the motion estimation problem is developed to obtain stable and accurate solutions and connected with the ordinary least squares formulation of the problem. When covariance matrices of 3-D points are known, a closed form matrix-weighted solution is derived for estimating the motion parameters in the presence of i.i.d. Gaussian noise. In a general case, a closed form approximate solution is also presented. The solutions extend two solutions proposed by Horn et al. and by Arun et al., respectively. The experimental results demonstrate that our solutions are accurate and reliable in presence of noise with different deviation.
Most stereo algorithms do not take into account discontinuities in disparity and the fact that there are half-occlusions consisting of areas seen by one eye but not the other. At the same time, very few of them are fo...
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ISBN:
(纸本)0818638826
Most stereo algorithms do not take into account discontinuities in disparity and the fact that there are half-occlusions consisting of areas seen by one eye but not the other. At the same time, very few of them are formulated using the framework of energy functionals which are so successfully used in other areas of computer vision such as image segmentation and surface representation. In this paper, a formulation is presented within such a framework taking into account the discontinuities and half-occlusions. The formulation follows directly from the assumption that when matching the left and right images, the order of points must be preserved. A model is derived consisting of two coupled energy functionals corresponding to the two eyes. They are coupled in the sense that the discontinuity locus determined by one eye also determines the occluded area in the image seen by the other eye. A nonlinear system of diffusion equations is derived by simultaneously applying gradient descent to these functionals. The diffusion equations are implemented by a straight-forward finite-difference scheme.
The Fundamental matrix is a key concept when working with uncalibrated images and multiple viewpoints. It contains all the available geometric information and enables to recover the epipolar geometry from uncalibrated...
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ISBN:
(纸本)081863880X
The Fundamental matrix is a key concept when working with uncalibrated images and multiple viewpoints. It contains all the available geometric information and enables to recover the epipolar geometry from uncalibrated perspective views. This paper is about the problem of its determination from points which lie in several planes. In that case, there is an homography between coordinates of points in the two images. We first investigate the use of different criteria to compute the homography. A very simple and important relation between the homography matrices obtained from the observation of planar surfaces and the Fundamental matrix is then established. Using simulations and real images to validate our analysis, we show that as a first consequence of this relation, the general methods to compute the fundamental matrix are unstable when the points lie close to planes. We have then proposed new algorithms to exploit this situation, through the use of the previous relation and have compared their performance to the performances of the general algorithm using a large number of noisy synthetic data and real images.
We present an algorithm for fusing monocular and stereo cues to get robust estimates of both motion and structure. Our algorithm assumes the motion to be along a smooth trajectory and the sequence of images to be dens...
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ISBN:
(纸本)0818638826
We present an algorithm for fusing monocular and stereo cues to get robust estimates of both motion and structure. Our algorithm assumes the motion to be along a smooth trajectory and the sequence of images to be dense. The algorithm starts by calculating the instantaneous FOE (focus of expansion). Knowing the FOE we calculate a MAP estimate of the displacement at each pixel and an associated confidence measure. Using the displacement estimates we calculate a relative depth map from one of the two frame sequences. By calculating the disparities at some feature points and using information about their relative depths we compute the instantaneous component of velocity in the direction perpendicular to the image plane (the Z direction). Using this information a depth map is calculated, this depth map is then used to derive a prior probability distribution for disparity that is used in matching the two frames of the stereo pairs. We use this method to estimate the disparity at each pixel independently;no assumption about smoothness are used. Experimental results on a real image sequence are given.
Expansion matching (EXM) optimizes a novel matching criterion called Discriminative Signal to Noise Ratio (DSNR) and robustly recognizes templates under conditions of noise, severe occlusion and super-position. We int...
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ISBN:
(纸本)0818638826
Expansion matching (EXM) optimizes a novel matching criterion called Discriminative Signal to Noise Ratio (DSNR) and robustly recognizes templates under conditions of noise, severe occlusion and super-position. We introduce a family of optimal DSNR edge detectors based on the expansion filter for any given edge model. Experimental comparisons show that our Step Expansion Filter (SEF) yields better results than the Canny Edge Detector (CED) in terms of DSNR even under adverse noise conditions. As for segmentation quality, the SEF also yields higher Figures of Merit (FOM) than the CED over a wide range of noise levels. Experiments on real images reveal that the SEF yields less noisy edge elements and preserves structural details accurately. EXM is also effective for feature extraction.
Thick curves arise naturally in certain applications such as magnetic resonance imaging of the brain;they can also arise in computer vision problems through morphological dilation of boundaries of objects. In this pap...
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ISBN:
(纸本)0818638826
Thick curves arise naturally in certain applications such as magnetic resonance imaging of the brain;they can also arise in computer vision problems through morphological dilation of boundaries of objects. In this paper we describe two new adaptive active contour algorithms for the extraction and mapping of the skeleton of a thick curve. They are based on conditions that have been derived in previous work which guarantee uniqueness and fidelity of the solution. Both algorithms modify the regularization constant Ko in attempt to maintain convexity of the energy function while simultaneously improving the fidelity of the result. The first algorithm changes Ko over time while the second adapts Ko spatially. We evaluate both algorithms on experiments with synthetic curves;both demonstrate an improved performance compared to a fixed parameter active contour algorithm.
We introduce a new algorithm for discontinuity-preserving visual surface reconstruction, inspired on the well known formulation of the problem as the fitting of a weak membrane to the conserved data. The method works ...
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ISBN:
(纸本)0818638826
We introduce a new algorithm for discontinuity-preserving visual surface reconstruction, inspired on the well known formulation of the problem as the fitting of a weak membrane to the conserved data. The method works by slowly applying the data `force' to a weak membrane which is allowed to tear when the tension exceeds a certain threshold;accordingly, the algorithm is named `simulated tearing' (ST). Formally, ST is a deterministic continuation method, i.e. the problem to be solved is embedded in a family of problems, of which the first member has a simple solution. The proposed method is tested and compared with mean field annealing (MFA), using real and synthetic images. Conclusions are that ST is simpler, faster and slightly out performs MFA. Furthermore, ST allows implementation based on integer arithmetic.
Estimation of curvature from noisy sampled data is a fundamental problem in digital arc segmentation. The facet approach in curvature estimation involves least square fitting the observed data points to a parametric c...
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ISBN:
(纸本)0818638826
Estimation of curvature from noisy sampled data is a fundamental problem in digital arc segmentation. The facet approach in curvature estimation involves least square fitting the observed data points to a parametric cubic polynomial and calculating the curvature analytically from the fitted parametric coefficients. Due to the fitting, there exists systematic error or bias between curvature calculated analytically from the parameterization of a circle and one calculated analytically based on the coefficients of the fitted cubic polynomial, even when the data is sampled from noiseless circle. We show how to compensate this bias by estimating it with the coefficients of the fitted cubic polynomial, which gives more accurate curvature value. We introduce small perturbations to the sampled data from a noiseless circle, and we analytically trace how the perturbation propagates through coefficients of the fitted polynomials and results in perturbation error of the curvature.
This paper studies the error sensitivity in the estimation of the 3D-motion and the normal of a planar surface from an instantaneous motion field. We use the statistical theory of the Cramer-Rao lower bound for the er...
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ISBN:
(纸本)0818638826
This paper studies the error sensitivity in the estimation of the 3D-motion and the normal of a planar surface from an instantaneous motion field. We use the statistical theory of the Cramer-Rao lower bound for the error covariance in the estimated motion and structure parameters which enables the derivation of results valid for any unbiased estimator under the assumption of Gaussian noise in the motion field. The obtained lower-bound-matrix is studied analytically with respect to the measurement noise, size of the field of view and the motion-geometry configuration. The main result of this analysis is the coupling between translation and rotation which is exacerbated if the field of view and the slant of the plane become smaller and the deviation of the translation from the viewing direction becomes larger. By-products of this study are the relationships of the uncertainty bounds for every unknown motion parameter to the angle between translation and the plane-normal, the size of the field of view, the distance from the perceived plane and the translation magnitude.
Underlying recognition is an organization of objects and their parts into classes and hierarchies. A representation of parts for recognition requires that parts be invariant to rigid transformations, robust in the pre...
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ISBN:
(纸本)0818638826
Underlying recognition is an organization of objects and their parts into classes and hierarchies. A representation of parts for recognition requires that parts be invariant to rigid transformations, robust in the presence of occlusions, stable with changes in viewing geometry, and be arranged in a hierarchy. These constraints are captured in a general framework using notions of a PART-LINE and a PARTITIONING SCHEME. A proposed general principle of `form from function' motivates a particular partitioning scheme involving two types of parts, NECK-BASED and LIMB-BASED, whose psychophysical relevance was demonstrated in literature. Neck-based parts arise from narrowings in shape, or the local minima in distance between two points on the boundary, while limb-based parts arise from a pair of negative curvature extrema which have `co-circular' tangents. In this paper, we present computational support for the limb-based and neck-based parts by showing that they are invariant, robust, stable and yield a hierarchy of parts. Examples illustrate that the resulting decompositions are robust in the presence of occlusion and noise for a range of man-made and natural objects, and lead to natural and intuitive parts which can be used for recognition.
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