Efficiently estimating projective transformations

Radke, Richard J.; Ramadge, Peter J.; Echigo, Tomio; Iisaku, Shun‐ichi

doi:10.1109/icip.2000.900937

Cited by 12 publications

(4 citation statements)

References 11 publications

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“…Radke et al [96] consider the problem of estimating projective transformations associated with standard problems in image processing and computer vision. The estimation problem leads to the minimization of a nonlinear functional of eight parameters, which, through a separation argument, can be reduced to a problem in only two variables.…”

Section: Robotics and Visionmentioning

confidence: 99%

Separable nonlinear least squares: the variable projection method and its applications

2003

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In this paper we review 30 years of developments and applications of the variable projection method for solving separable nonlinear least-squares problems. These are problems for which the model function is a linear combination of nonlinear functions. Taking advantage of this special structure, the method of variable projections eliminates the linear variables obtaining a somewhat more complicated function that involves only the nonlinear parameters. This procedure not only reduces the dimension of the parameter space but also results in a better-conditioned problem. The same optimization method applied to the original and reduced problems will always converge faster for the latter. We present first a historical account of the basic theoretical work and its various computer implementations, and then report on a variety of applications from electrical engineering, medical and biological imaging, chemistry, robotics, vision, and environmental sciences. An extensive bibliography is included. The method is particularly well suited for solving real and complex exponential model fitting problems, which are pervasive in their applications and are notoriously hard to solve.

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Section: Robotics and Visionmentioning

confidence: 99%

Separable nonlinear least squares: the variable projection method and its applications

2003

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“…The projective transformations and were estimated using the efficient algorithm described in [25], using point matches extracted by the automatic feature selection algorithm described in [26]. The measurement update used an 8-pixel search neighborhood about the time-updated estimate and the Ohta-Kanade cost function.…”

Section: Resultsmentioning

confidence: 99%

Efficiently synthesizing virtual video

Radke

Ramadge

Kulkarni

et al. 2003

IEEE Trans. Circuits Syst. Video Technol.

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Given a set of synchronized video sequences of a dynamic scene taken by different cameras, we address the problem of creating a virtual video of the scene from a novel viewpoint. A key aspect of our algorithm is a method for recursively propagating dense and physically accurate correspondences between the two video sources. By exploiting temporal continuity and suitably constraining the correspondences, we provide an efficient framework for synthesizing realistic virtual video. The stability of the propagation algorithm is analyzed, and experimental results are presented.Index Terms-Correspondence, image-based rendering, view synthesis, virtual video, virtual views.

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“…Translation of the camera point of view combined with camera tilt (pitch and roll) cause perspective distortions of the acquired images that require more complex transformations such as 8 parameter projective transformation [6]. There are two means of recovering these parameters: (1) manually choosing (at least) four tie points in each image to be co-registered (perhaps by pre-arranged insertion of features into the scene) and solving eight equations for eight unknown parameters [7]; or (2) formulation of a non-quadratic minimization problem for pixel value differences and consequent numerical solution using Levenberg-Marquardt [1] or other scheme. Both methods have drawbacks: human intervention in the first, and in second case inhomogeneous illumination associated with camera and light source motion, which makes the optimization problem be ill-defined.…”

Section: Video Image Mosaicingmentioning

confidence: 99%

Sensor-assisted video mosaicing for seafloor mapping

Rzhanov

Cutter

Huff

Proceedings 2001 International Conference on Image Processing (Cat. No.01CH37205)

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This paper discusses a proposed processing technique for combining video imagery with auxiliary sensor information. The latter greatly simplifies image processing by reducing complexity of the transformation model. The mosaics produced by this technique are adequate for many applications, in particular habitat mapping. The algorithm is demonstrated through simulations and hardware configuration is described.

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Efficiently estimating projective transformations

Cited by 12 publications

References 11 publications

Separable nonlinear least squares: the variable projection method and its applications

Separable nonlinear least squares: the variable projection method and its applications

Efficiently synthesizing virtual video

Sensor-assisted video mosaicing for seafloor mapping

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