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Parametric Segmentation of Nonlinear Structures in Visual Data: An Accelerated Sampling Approach

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Nonlinear Approaches in Engineering Applications 2

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Abstract

In many image processing applications, identification of nonlinear structures in image data is of particular interest. Examples include fitting multiple ellipse patterns to image data, estimation and segmentation of multiple motions in subsequent images in video, and fitting nonlinear patterns to cell images for cancer detection in biomedical applications. This chapter introduces a novel approach to calculate a first order approximation for point distances from general nonlinear structures. We also propose an accelerated sampling method for robust segmentation of multiple structures. Our sampling method is substantially faster than random sampling used in the well-known RANSAC method as it effectively makes use of the spatial proximity of the points belonging to each structure. A fast high-breakdown robust estimator called Accelerated-LKS (A-LKS) is devised using the accelerated search to minimize the kth order statistics of squared distances. A number of experiments on homography estimation problems are presented. Those experiments include cases with up to eight different motions and we benchmark the performance of the proposed estimator in comparison with a number of state-of-the-art robust estimators. We also show the result of applying A-LKS to solve ellipse fitting and motion segmentation in practical applications.

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Notes

  1. 1.

    It is important to note that the dimension of data space is not always equal to the dimension of the parameter space denoted by p in this chapter. More precisely, p is the minimum number of data points that can specify a unique model candidate, which is not necessarily equal to the dimension of the data points. For instance in the fundamental estimation problem, each data point includes a pair of matching pixels and the dimension of each data point is 4, but the dimension of the parameter space is 8.

  2. 2.

    It is important to note that ε is the ratio of gross outliers and in the presence of several structures, it is far less than \({\epsilon }^{{\prime}}\) in Eqs. (9.27) and (9.28) which equals the sum of gross and pseudo outlier ratios. In the presence of n obj structures with an equal number of inliers, \({\epsilon }^{{\prime}} =\epsilon +(1-\epsilon )(1 - 1/n_{\mathrm{obj}})\). For instance, if ε = 5% of data are gross outliers and there are n obj = 8 structures, we have \({\epsilon }^{{\prime}} = 88\%.\)

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Authors and Affiliations

  1. School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, Bundoora, VIC, 3083, Australia

    Reza Hoseinnezhad & Alireza Bab-Hadiashar

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  1. Reza Hoseinnezhad
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  2. Alireza Bab-Hadiashar
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Correspondence to Reza Hoseinnezhad .

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Editors and Affiliations

  1. Aerospace, Mechanical and Manufacturing Engineering, RMIT University Bundoora East Campus, Bundoora, Victoria, Australia

    Reza N. Jazar

  2. Industrial Systems Engineering, University of Regina, Regina, Saskatchewan, Canada

    Liming Dai

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Hoseinnezhad, R., Bab-Hadiashar, A. (2014). Parametric Segmentation of Nonlinear Structures in Visual Data: An Accelerated Sampling Approach. In: Jazar, R., Dai, L. (eds) Nonlinear Approaches in Engineering Applications 2. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6877-6_9

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  • DOI: https://doi.org/10.1007/978-1-4614-6877-6_9

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