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197
Flexible smoothing with Bsplines and penalties
 STATISTICAL SCIENCE
, 1996
"... Bsplines are attractive for nonparametric modelling, but choosing the optimal number and positions of knots is a complex task. Equidistant knots can be used, but their small and discrete number allows only limited control over smoothness and fit. We propose to use a relatively large number of knots ..."
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Cited by 395 (6 self)
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Bsplines are attractive for nonparametric modelling, but choosing the optimal number and positions of knots is a complex task. Equidistant knots can be used, but their small and discrete number allows only limited control over smoothness and fit. We propose to use a relatively large number of knots and a difference penalty on coefficients of adjacent Bsplines. We show connections to the familiar spline penalty on the integral of the squared second derivative. A short overview of Bsplines, their construction, and penalized likelihood is presented. We discuss properties of penalized Bsplines and propose various criteria for the choice of an optimal penalty parameter. Nonparametric logistic regression, density estimation and scatterplot smoothing are used as examples. Some details of the computations are presented.
Fitting Smooth Surfaces to Dense Polygon Meshes
 Proceedings of SIGGRAPH 96
, 1996
"... Recent progress in acquiring shape from range data permits the acquisition of seamless millionpolygon meshes from physical models. In this paper, we present an algorithm and system for converting dense irregular polygon meshes of arbitrary topology into tensor product Bspline surface patches with ..."
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Cited by 237 (5 self)
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Recent progress in acquiring shape from range data permits the acquisition of seamless millionpolygon meshes from physical models. In this paper, we present an algorithm and system for converting dense irregular polygon meshes of arbitrary topology into tensor product Bspline surface patches with accompanying displacement maps. This choice of representation yields a coarse but efficient model suitable for animation and a fine but more expensive model suitable for rendering. The first step in our process consists of interactively painting patch boundaries over a rendering of the mesh. In many applications, interactive placement of patch boundaries is considered part of the creative process and is not amenable to automation. The next step is gridded resampling of eachboundedsection of the mesh. Our resampling algorithm lays a grid of springs acrossthe polygonmesh, then iterates between relaxing this grid and subdividing it. This grid provides a parameterization for the mesh section, w...
A survey of freeform object representation and recognition techniques
 Computer Vision and Image Understanding
, 2001
"... Advances in computer speed, memory capacity, and hardware graphics acceleration have made the interactive manipulation and visualization of complex, detailed (and therefore large) threedimensional models feasible. These models are either painstakingly designed through an elaborate CAD process or re ..."
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Cited by 199 (1 self)
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Advances in computer speed, memory capacity, and hardware graphics acceleration have made the interactive manipulation and visualization of complex, detailed (and therefore large) threedimensional models feasible. These models are either painstakingly designed through an elaborate CAD process or reverse engineered from sculpted prototypes using modern scanning technologies and integration methods. The availability of detailed data describing the shape of an object offers the computer vision practitioner new ways to recognize and localize freeform objects. This survey reviews recent literature on both the 3D model building process and techniques used to match and identify freeform objects from imagery. c ○ 2001 Academic Press 1.
A chronology of interpolation: From ancient astronomy to modern signal and image processing
 Proceedings of the IEEE
, 2002
"... This paper presents a chronological overview of the developments in interpolation theory, from the earliest times to the present date. It brings out the connections between the results obtained in different ages, thereby putting the techniques currently used in signal and image processing into histo ..."
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Cited by 101 (0 self)
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This paper presents a chronological overview of the developments in interpolation theory, from the earliest times to the present date. It brings out the connections between the results obtained in different ages, thereby putting the techniques currently used in signal and image processing into historical perspective. A summary of the insights and recommendations that follow from relatively recent theoretical as well as experimental studies concludes the presentation. Keywords—Approximation, convolutionbased interpolation, history, image processing, polynomial interpolation, signal processing, splines. “It is an extremely useful thing to have knowledge of the true origins of memorable discoveries, especially those that have been found not by accident but by dint of meditation. It is not so much that thereby history may attribute to each man his own discoveries and others should be encouraged to earn like commendation, as that the art of making discoveries should be extended by considering noteworthy examples of it. ” 1 I.
JumpDi®usion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing
 Review of Derivatives Research
, 2000
"... Abstract. This paper discusses extensions of the implied diffusion approach of Dupire (1994) to asset processes with Poisson jumps. We show that this extension yields important model improvements, particularly in the dynamics of the implied volatility surface. The paper derives a forward PIDE (Parti ..."
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Cited by 99 (3 self)
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Abstract. This paper discusses extensions of the implied diffusion approach of Dupire (1994) to asset processes with Poisson jumps. We show that this extension yields important model improvements, particularly in the dynamics of the implied volatility surface. The paper derives a forward PIDE (Partial IntegroDifferential Equation) and demonstrates how this equation can be used to fit the model to European option prices. For numerical pricing of general contingent claims, we develop an ADI finite difference method that is shown to be unconditionally stable and, if combined with Fast Fourier Transform methods, computationally efficient. The paper contains several detailed examples from the S&P500 market.
Separable Nonlinear Least Squares: the Variable Projection Method and its Applications
 Institute of Physics, Inverse Problems
, 2002
"... this paper nonlinear data fitting problems which have as their underlying model a linear combination of nonlinear functions. More generally, one can also consider that there are two sets of unknown parameters, where one set is dependent on the other and can be explicitly eliminated. Models of this t ..."
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Cited by 95 (2 self)
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this paper nonlinear data fitting problems which have as their underlying model a linear combination of nonlinear functions. More generally, one can also consider that there are two sets of unknown parameters, where one set is dependent on the other and can be explicitly eliminated. Models of this type are very common and we will show a variety of applications in different fields. Inasmuch as many inverse problems can be viewed as nonlinear data fitting problems, this material will be of interest to a wide crosssection of researchers and practitioners in parameter, material or system identification, signal analysis, the analysis of spectral data, medical and biological imaging, neural networks, robotics, telecommunications and model order reduction, to name a few
An Algorithmic Overview of Surface Registration . . .
 MEDICAL IMAGE ANALYSIS
, 2000
"... This paper presents a literature survey of automatic 3D surface registration techniques emphasizing the mathematical and algorithmic underpinnings of the subject. The relevance of surface registration to medical imaging is that there is much useful anatomical information in the form of collected ..."
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Cited by 91 (1 self)
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This paper presents a literature survey of automatic 3D surface registration techniques emphasizing the mathematical and algorithmic underpinnings of the subject. The relevance of surface registration to medical imaging is that there is much useful anatomical information in the form of collected surface points which originate from complimentary modalities and which must be reconciled. Surface registration
Dynamic Bayesian Network and Nonparametric Regression for Nonlinear Modeling of Gene Networks from Time Series Gene Expression Data
 Biosystems
, 2003
"... Abstract. We propose a dynamic Bayesian network and nonparametric regression model for constructing a gene network from time series microarray gene expression data. The proposed method can overcome a shortcoming of the Bayesian network model in the sense of the construction of cyclic regulations. Th ..."
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Cited by 77 (12 self)
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Abstract. We propose a dynamic Bayesian network and nonparametric regression model for constructing a gene network from time series microarray gene expression data. The proposed method can overcome a shortcoming of the Bayesian network model in the sense of the construction of cyclic regulations. The proposed method can analyze the microarray data as continuous data and can capture even nonlinear relations among genes. It can be expected that this model will give a deeper insight into the complicated biological systems. We also derive a new criterion for evaluating an estimated network from Bayes approach. We demonstrate the effectiveness of our method by analyzing Saccharomyces cerevisiae gene expression data. 1
Fitting Scattered Data on SphereLike Surfaces Using Spherical Splines
 J. Comput. Appl. Math
"... . Spaces of polynomial splines defined on planar triangulations are very useful tools for fitting scattered data in the plane. Recently, [4, 5], using homogeneous polynomials, we have developed analogous spline spaces defined on triangulations on the sphere and on spherelike surfaces. Using these s ..."
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Cited by 58 (11 self)
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. Spaces of polynomial splines defined on planar triangulations are very useful tools for fitting scattered data in the plane. Recently, [4, 5], using homogeneous polynomials, we have developed analogous spline spaces defined on triangulations on the sphere and on spherelike surfaces. Using these spaces, it is possible to construct analogs of many of the classical interpolation and fitting methods. Here we examine some of the more interesting ones in detail. For interpolation, we discuss macroelement methods and minimal energy splines, and for fitting, we consider discrete least squares and penalized least squares. 1. Introduction Let S be the unit sphere or a spherelike surface (see Sect. 2 below) in IR 3 . In addition, suppose that we are given a set of scattered points located on S, along with real numbers associated with each of these points. The problem of interest in this paper is to find a function defined on S which either interpolates or approximates these data. This pr...
An adaptive spatial fuzzy clustering algorithm for 3DMR image segmentation
 IEEE Trans. on Medical Imaging
, 2003
"... Abstract—An adaptive spatial fuzzy cmeans clustering algorithm is presented in this paper for the segmentation of threedimensional (3D) magnetic resonance (MR) images. The input images may be corrupted by noise and intensity nonuniformity (INU) artifact. The proposed algorithm takes into accou ..."
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Cited by 43 (6 self)
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Abstract—An adaptive spatial fuzzy cmeans clustering algorithm is presented in this paper for the segmentation of threedimensional (3D) magnetic resonance (MR) images. The input images may be corrupted by noise and intensity nonuniformity (INU) artifact. The proposed algorithm takes into account the spatial continuity constraints by using a dissimilarity index that allows spatial interactions between image voxels. The local spatial continuity constraint reduces the noise effect and the classification ambiguity. The INU artifact is formulated as a multiplicative bias field affecting the true MR imaging signal. By modeling the log bias field as a stack of smoothingspline surfaces, with continuity enforced across slices, the computation of the 3D bias field reduces to that of finding thespline coefficients, which can be obtained using a computationally efficient twostage algorithm. The efficacy of the proposed algorithm is demonstrated by extensive segmentation experiments using both simulated and real MR images and by comparison with other published algorithms. Index Terms—Adaptive spatial fuzzy clustering, intensity nonuniformity correction, MR image segmentation, spatial continuity constraint, spline approximation. I.