Elliptic Fourier features of a closed contour

Kuhl, Frank P.; Giardina, Charles R.

doi:10.1016/0146-664x(82)90034-x

Cited by 1,545 publications

(1,216 citation statements)

References 6 publications

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“…The spherical harmonic representations are first aligned and then sampled into surface meshes to establish correspondence [15,97]. This idea is an extension of earlier work using Fourier descriptors to parameterize closed contours in two dimensions [88,71]. Similar approaches have been proposed that use wavelet-based shape representations [81].…”

Section: Computationally-derived Shape Modelsmentioning

confidence: 99%

Shape Modeling and Analysis with Entropy-Based Particle Systems

Cates

Fletcher

Styner

et al. 2007

Lecture Notes in Computer Science

137

224

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Many important fields of basic research in medicine and biology routinely employ tools for the statistical analysis of collections of similar shapes. Biologists, for example, have long relied on homologous, anatomical landmarks as shape models to characterize the growth and development of species. Increasingly, however, researchers are exploring the use of more detailed models that are derived computationally from three-dimensional images and surface descriptions. While computationally-derived models of shape are promising new tools for biomedical research, they also present some significant engineering challenges, which existing modeling methods have only begun to address.In this dissertation, I propose a new computational framework for statistical shape modeling that significantly advances the state-of-the-art by overcoming many of the limitations of existing methods. The framework uses a particle-system representation of shape, with a fast correspondence-point optimization based on information content. The optimization balances the simplicity of the model (compactness) with the accuracy of the shape representations by using two commensurate entropy metrics and no free parameters. The idea is to maximize both the geometric accuracy and the statistical simplicity of the shape model, in accordance with the principle of parsimony in model selection. The nonparametric representation allows the method to be applied to a larger class of problems than existing methods, including nonspherical surfaces, open surfaces, and sets of multiple surfaces.The relative simplicity of the surface representation and the low number of free parameters results in a framework that is easy to use and can operate directly on image segmentations. In collaboration with scientists from several important areas of biomedicine, I have demonstrated that the proposed method is indeed an e↵ective tool for scientific research.The specific research contributions of this dissertation are as follows. First, I describe a mathematical framework and a robust numerical algorithm for computing optimized correspondence-point shape models using an entropy-based optimization and particle-system technology. Second, I develop a series of extensions of the framework to more general classes of shape analysis problems, including the analysis of multiple-object complexes, the generalization to correspondence based on generic functions of position, an extension to handle surfaces with open boundaries, and shape modeling with simple regression. Third, I describe the application of statistical hypothesis testing, regression analysis, and multiple-analysis of covariance to the proposed shape models. I also introduce new techniques for visualization and interpretation of these statistics. Finally, in cooperation with biomedical researchers, I present validation of the above research contributions by their successful application to real-world research problems.

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Section: Computationally-derived Shape Modelsmentioning

confidence: 99%

Shape Modeling and Analysis with Entropy-Based Particle Systems

Cates

Fletcher

Styner

et al. 2007

Lecture Notes in Computer Science

137

224

View full text Add to dashboard Cite

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“…In recent years, EFDs have been popularized and studied widely for the parametric representation of 2D closed curves [13], [14] with further extensions on 3D geometries [15]. The major ease brought by EFDs is the ability to represent the closed curve with a finite set of parameters which are obtained via an ordered combination of sinusoidal frequencies.…”

Section: Trajectory Curve Fittingmentioning

confidence: 99%

Contouring Controller for Precise Motion Control Systems

2013

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Original scientific paperThis paper discusses the trajectory generation algorithm, contour error construction method and finally the contour controller design. In the trajectory generation algorithm combination of elliptical Fourier descriptors (EFD) and time based spline approximation (TBSA) is used to generate position, velocity and acceleration references. Contour error is constructed using transformation of trajectory tracking errors. Transformation is computationally efficient and requires only reference velocity information. Contour controller is designed using sliding mode control. Experiments are performed on planar linear motion stage and significant contour error reduction is observed. Konturni regulator za precizne slijedne sustave. Učlanku se raspravlja o algoritmu za generiranje trajektorija, metodi za konstrukciju pogreške konture te o sintezi konturnog regulatora. U algoritum za generiranje trajektorija, korištena je kombinacija eliptičnih Fourierovih odrednika (EFD) i vremenske aproksimacije splajnovima (TBSA) za odre ivanje referentnih vrijednosti položaja, brzine i ubrzanja. Pogreška konture je konstruirana korištenjem transformirane pogreške slije enja trajektorije. Transformacija je računski efikasna i potrebna joj je samo informacija o referentnoj brzini. Konturni regulator je projektiran koristeći upravljanje u kliznim režimima. Provedeni su eksperimenti na linearnom slijednom sustavu i primijećena su znatna smanjenja pogreške konture.Ključne riječi: konturni regulator, precizni slijedni sustavi, vremenska interpolacija splajnovima, upravljanje u kliznim režimima, eliptični Fourierovi odrednici, upravljanje akceleracijom

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“…We develop the curve (s) as an orthogonal Fourier expansion as presented in Ref. [33]. In this representation, derivatives are easily computed.…”

Section: Implementation and Examplesmentioning

confidence: 99%

Invariant characterisation of the Hough transform for pose estimation of arbitrary shapes

Aguado

Montiel

Nixon

2002

Pattern Recognition

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In this paper, we develop a new formulation and methodology for including invariance in a general form of the Hough transform. Essentially, the transformations that control a shape's appearance are extracted using invariance, for arbitrary shapes with a continuous description. We ÿrst develop a formal deÿnition of the Hough transform mapping for arbitrary shapes and general transformations. We then include an invariant characterisation of shapes and develop and apply our new technique to extract shapes under similarity and a ne transformations. Our formulation and implementation is based directly on parametric curves and so avoids the use of indexed look-up tables. This confers the attributes of a continuous shape description avoiding discretisation problems inherent in earlier formulations. To obtain an invariant characterisation, each point in the model is related to a collection of other points deÿning a geometric arrangement. This characterisation does not require the computation of properties for lines or other primitives that compose the model, but is based solely on the local geometry of the points on shapes. The transformation is obtained by solving for the parameters of the curve according to an arrangement of points deÿned for a point in the image and a corresponding arrangement of points for a point in the model with the same invariant properties. The location parameters can be gathered in a 2D accumulator space independent of the transformation and of a shape's complexity. Experimental results show that the new technique is capable of extracting arbitrary shapes under occlusion and when the image contains signiÿcant noise. ?

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Elliptic Fourier features of a closed contour

Cited by 1,545 publications

References 6 publications

Shape Modeling and Analysis with Entropy-Based Particle Systems

Shape Modeling and Analysis with Entropy-Based Particle Systems

Contouring Controller for Precise Motion Control Systems

Invariant characterisation of the Hough transform for pose estimation of arbitrary shapes

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