The Experts below are selected from a list of 38652 Experts worldwide ranked by ideXlab platform
Takeo Kanade - One of the best experts on this subject based on the ideXlab platform.
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Shape and motion from image streams : a Factorization Method.
2018Co-Authors: Carlo Tomasi, Takeo KanadeAbstract:Abstract: "Inferring the depth and shape of remote objects and the complete camera motion from a stream of images is possible, but is an ill-conditioned problem when the objects are distant with respect to their size. To overcome this difficulty, we have developed a Factorization Method to decompose an image stream directly into object shape and camera motion, without computing depth as an intermediate step. The Factorization Method is explored in a series of technical reports, going from basic principles through implementation. This is the first report in the series, and presents basic concepts in the case of planar motion, in which images are single scanlines.In this situation, an image stream can be represented by the F [cross] P matrix of the image coordinates of P points tracked through F frames. We show that under orthographic projection this measurement matrix is of rank 3. Using this observation, we develop an algorithm to recover shape and camera motion, based on the singular value decomposition of the measurement matrix. Noise is defeated by applying a well-conditioned computation to the highly redundant input represented by an image stream. No assumptions are made about smoothness or regularity of the camera motion, and even sudden jumps in the camera velocity are faithfully reproduced in the computed output.
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A Multibody Factorization Method for Independently Moving Objects
International Journal of Computer Vision, 1998Co-Authors: João Paulo Costeira, Takeo KanadeAbstract:The structure-from-motion problem has been extensively studied in the field of computer vision. Yet, the bulk of the existing work assumes that the scene contains only a single moving object. The more realistic case where an unknown number of objects move in the scene has received little attention, especially for its theoretical treatment. In this paper we present a new Method for separating and recovering the motion and shape of multiple independently moving objects in a sequence of images. The Method does not require prior knowledge of the number of objects, nor is dependent on any grouping of features into an object at the image level. For this purpose, we introduce a mathematical construct of object shapes, called the shape interaction matrix, which is invariant to both the object motions and the selection of coordinate systems. This invariant structure is computable solely from the observed trajectories of image features without grouping them into individual objects. Once the matrix is computed, it allows for segmenting features into objects by the process of transforming it into a canonical form, as well as recovering the shape and motion of each object. The theory works under a broad set of projection models (scaled orthography, paraperspective and affine) but they must be linear, so it excludes projective “cameras”.
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a sequential Factorization Method for recovering shape and motion from image streams
IEEE Transactions on Pattern Analysis and Machine Intelligence, 1997Co-Authors: T Morita, Takeo KanadeAbstract:We present a sequential Factorization Method for recovering the three-dimensional shape of an object and the motion of the camera from a sequence of images, using tracked features. The Factorization Method originally proposed by Tomasi and Kanade (1992) produces robust and accurate results incorporating the singular value decomposition. However, it is still difficult to apply the Method to real-time applications, since it is based on a batch-type operation and the cost of the singular value decomposition is large. We develop the Factorization Method into a sequential Method by regarding the feature positions as a vector time series. The new Method produces estimates of shape and motion at each frame. The singular value decomposition is replaced with an updating computation of only three dominant eigenvectors, which can be performed in O(P/sup 2/) time, while the complete singular value decomposition requires O(FP/sup 2/) operations for an F/spl times/P matrix. Also, the Method is able to handle infinite sequences, since it does not store any increasingly large matrices. Experiments using synthetic and real images illustrate that the Method has nearly the same accuracy and robustness as the original Method.
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a paraperspective Factorization Method for shape and motion recovery
IEEE Transactions on Pattern Analysis and Machine Intelligence, 1997Co-Authors: Conrad J Poelman, Takeo KanadeAbstract:The Factorization Method, first developed by Tomasi and Kanade (1992), recovers both the shape of an object and its motion from a sequence of images, using many images and tracking many feature points to obtain highly redundant feature position information. The Method robustly processes the feature trajectory information using singular value decomposition (SVD), taking advantage of the linear algebraic properties of orthographic projection. However, an orthographic formulation limits the range of motions the Method can accommodate. Paraperspective projection, first introduced by Ohta et al. (1981), is a projection model that closely approximates perspective projection by modeling several effects not modeled under orthographic projection, while retaining linear algebraic properties. Our paraperspective Factorization Method can be applied to a much wider range of motion scenarios, including image sequences containing motion toward the camera and aerial image sequences of terrain taken from a low-altitude airplane.
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a multi body Factorization Method for motion analysis
International Conference on Computer Vision, 1995Co-Authors: João Paulo Costeira, Takeo KanadeAbstract:The structure from motion problem has been extensively studied in the field of computer vision. Yet, the bulk of the existing work assumes that the scene contains only a single moving object. The more realistic case where an unknown number of objects move in the scene has received little attention, especially for its theoretical treatment. We present a new Method for separating and recovering the motion and shape of multiple independently moving objects in a sequence of images. The Method does not require prior knowledge of the number of objects, nor is dependent on any grouping of features into an object at the image level. For this purpose, we introduce a mathematical construct of object shapes, called the shape interaction matrix, which is invariant to both the object motions and the selection of coordinate systems. This invariant structure is computable solely from the observed trajectories of image features without grouping them into individual objects. Once the structure is computed, it allows for segmenting features into objects by the process of transforming it into a canonical form, as well as recovering the shape and motion of each object. >
N Ichimura - One of the best experts on this subject based on the ideXlab platform.
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motion segmentation based on Factorization Method and discriminant criterion
International Conference on Computer Vision, 1999Co-Authors: N IchimuraAbstract:A motion segmentation algorithm based on Factorization Method and discriminant criterion is proposed. This Method uses a feature with the most useful similarities for grouping, selected using motion information calculated by Factorization Method and discriminant criterion. A group is extracted based on discriminant analysis for the selected feature's similarities. The same procedure is applied recursively to the remaining features to extract other groups. This grouping is robust against noise and outliers because features with no useful information are automatically rejected. Numerical computation is simple and stable. No prior knowledge is needed on the number of objects. Experimental results are shown for synthetic data and real image sequences.
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motion segmentation based on Factorization Method and discriminant criterion
International Conference on Computer Vision, 1999Co-Authors: N IchimuraAbstract:A motion segmentation algorithm based on Factorization Method and discriminant criterion is proposed. This Method uses a feature with the most useful similarities for grouping, selected using motion information calculated by Factorization Method and discriminant criterion. A group is extracted based on discriminant analysis for the selected feature's similarities. The same procedure is applied recursively to the remaining features to extract other groups. This grouping is robust against noise and outliers because features with no useful information are automatically rejected. Numerical computation is simple and stable. No prior knowledge is needed on the number of objects. Experimental results are shown for synthetic data and real image sequences.
Xiaodong Liu - One of the best experts on this subject based on the ideXlab platform.
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the Factorization Method for inverse acoustic scattering by a penetrable anisotropic obstacle
Mathematical Methods in The Applied Sciences, 2014Co-Authors: Andreas Kirsch, Xiaodong LiuAbstract:This paper is devoted to studying the Factorization Method applied to the inverse problem of reconstructing a penetrable anisotropic obstacle from far fleld patterns. We proved the validity of the Factorization Method. Copyright c ∞ 2012 John Wiley & Sons, Ltd.
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the Factorization Method for cavities
Inverse Problems, 2014Co-Authors: Xiaodong LiuAbstract:The inverse acoustic scattering of point sources by an impenetrable cavity is considered. The scattered fields incited by point source waves are measured on a closed curve inside the cavity. We prove the validity of the Factorization Method for reconstructing the shape of the cavity. Two explicit examples for circular cavities are given to show the feasibility and effectiveness of the Factorization Method. Finally, we present some numerical examples in 2D. The reconstructions are as satisfactory as the exterior scattering problems and change only slightly for different measurement curves, different boundary conditions and different wave numbers.
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the Factorization Method for inverse obstacle scattering with conductive boundary condition
Inverse Problems, 2013Co-Authors: Oleksandr Bondarenko, Xiaodong LiuAbstract:The inverse acoustic scattering by a penetrable obstacle with a general conductive boundary condition is considered. Having established the well posedness of the direct problem by a variational Method, we study the Factorization Method for recovering the location and the shape of the obstacle. One by-product of the Method is an explicit proof of uniqueness of the inverse scattering problem under certain assumptions. Some numerical experiments are also presented to demonstrate the feasibility and effectiveness of the Factorization Method.
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the Factorization Method for inverse acoustic scattering in a layered medium
Inverse Problems, 2013Co-Authors: Oleksandr Bondarenko, Andreas Kirsch, Xiaodong LiuAbstract:In this paper, we consider a problem of inverse acoustic scattering by an impenetrable obstacle embedded in a layered medium. We will show that the Factorization Method can be applied to recover the embedded obstacle; that is, the equation ˜ Fg = φz is solvable if and only if the sampling point z is in the interior of the unknown obstacle. Here, ˜ F is a self-adjoint operator related to the far field operator and φz is the far field pattern of the Green function with respect to the problem of scattering by the background medium for point z. The validity of the Factorization Method is proven with the help of a mixed reciprocity principle and an application of the scattering operator. Due to the established mixed reciprocity principle, knowledge of the Green function for the background medium is no longer required, which makes the Method attractive from the computational point of view. The paper is only concerned with sound-soft obstacles, but the analysis can be easily extended for sound-hard obstacles, or obstacles with separated sound-soft and soundhard parts. Finally, we provide an explicit example for a radially symmetric case and present some numerical examples. (Some figures may appear in colour only in the online journal)
Conrad J Poelman - One of the best experts on this subject based on the ideXlab platform.
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a paraperspective Factorization Method for shape and motion recovery
IEEE Transactions on Pattern Analysis and Machine Intelligence, 1997Co-Authors: Conrad J Poelman, Takeo KanadeAbstract:The Factorization Method, first developed by Tomasi and Kanade (1992), recovers both the shape of an object and its motion from a sequence of images, using many images and tracking many feature points to obtain highly redundant feature position information. The Method robustly processes the feature trajectory information using singular value decomposition (SVD), taking advantage of the linear algebraic properties of orthographic projection. However, an orthographic formulation limits the range of motions the Method can accommodate. Paraperspective projection, first introduced by Ohta et al. (1981), is a projection model that closely approximates perspective projection by modeling several effects not modeled under orthographic projection, while retaining linear algebraic properties. Our paraperspective Factorization Method can be applied to a much wider range of motion scenarios, including image sequences containing motion toward the camera and aerial image sequences of terrain taken from a low-altitude airplane.
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a paraperspective Factorization Method for shape and motion recovery
European Conference on Computer Vision, 1994Co-Authors: Conrad J Poelman, Takeo KanadeAbstract:The Factorization Method, first developed by Tomasi and Kanade, recovers both the shape of an object and its motion from a sequence of images, using many images and tracking many feature points to obtain highly redundant feature position information. The Method robustly processes the feature trajectory information using singular value decomposition (SVD), taking advantage of the linear algebraic properties of orthographic projection. However, an orthographic formulation limits the range of motions the Method can accommodate. Paraperspective projection, first introduced by Ohta, is a projection model that closely approximates perspective projection by modelling several effects not modelled under orthographic projection, while retaining linear algebraic properties. We have developed a paraperspective Factorization Method that can be applied to a much wider range of motion scenarios, such as image sequences containing significant translational motion toward the camera or across the image. We present the results of several experiments which illustrate the Method's performance in a wide range of situations, including an aerial image sequence of terrain taken from a low-altitude airplane.
Pisin Chen - One of the best experts on this subject based on the ideXlab platform.
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nonsingular parametric oscillators darboux related to the classical harmonic oscillator
EPL, 2012Co-Authors: H C Rosu, O Cornejoperez, Pisin ChenAbstract:Interesting nonsingular parametric oscillators which are Darboux-related to the classical harmonic oscillator and have periodic dissipative/gain features are identified through a modified Factorization Method. The same Method is applied to the upside-down (hyperbolic) “oscillator” for which the obtained Darboux partners show transient underdamped features.
