Results 1  10
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48
Splines: A Perfect Fit for Signal/Image Processing
 IEEE SIGNAL PROCESSING MAGAZINE
, 1999
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A Pyramid Approach to SubPixel Registration Based on Intensity
, 1998
"... We present an automatic subpixel registration algorithm that minimizes the mean square intensity difference between a reference and a test data set, which can be either images (2D) or volumes (3D). It uses an explicit spline representation of the images in conjunction with spline processing, and ..."
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Cited by 226 (18 self)
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We present an automatic subpixel registration algorithm that minimizes the mean square intensity difference between a reference and a test data set, which can be either images (2D) or volumes (3D). It uses an explicit spline representation of the images in conjunction with spline processing, and is based on a coarsetofine iterative strategy (pyramid approach). The minimization is performed according to a new variation (ML*) of the MarquardtLevenberg algorithm for nonlinear leastsquare optimization. The geometric deformation model is a global 3D affine transformation that can be optionally restricted to rigidbody motion (rotation and translation), combined with isometric scaling. It also includes an optional adjustment of image contrast differences. We obtain excellent results for the registration of intramodality Positron Emission Tomography (PET) and functional Magnetic Resonance Imaging (fMRI) data. We conclude that the multiresolution refinement strategy is more robust than a comparable singlestage method, being less likely to be trapped into a false local optimum. In addition, our improved version of the MarquardtLevenberg algorithm is faster.
Fast parametric elastic image registration
 IEEE Transactions on Image Processing
, 2003
"... Abstract—We present an algorithm for fast elastic multidimensional intensitybased image registration with a parametric model of the deformation. It is fully automatic in its default mode of operation. In the case of hard realworld problems, it is capable of accepting expert hints in the form of so ..."
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Cited by 102 (8 self)
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Abstract—We present an algorithm for fast elastic multidimensional intensitybased image registration with a parametric model of the deformation. It is fully automatic in its default mode of operation. In the case of hard realworld problems, it is capable of accepting expert hints in the form of soft landmark constraints. Much fewer landmarks are needed and the results are far superior compared to pure landmark registration. Particular attention has been paid to the factors influencing the speed of this algorithm. The Bspline deformation model is shown to be computationally more efficient than other alternatives. The algorithm has been successfully used for several twodimensional (2D) and threedimensional (3D) registration tasks in the medical domain, involving MRI, SPECT, CT, and ultrasound image modalities. We also present experiments in a controlled environment, permitting an exact evaluation of the registration accuracy. Test deformations are generated automatically using a random hierarchical fractional waveletbased generator. Index Terms—Elastic registration, image registration, landmarks, splines. I.
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 102 (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.
Cardinal exponential splines: Part I—Theory and filtering algorithms
 IEEE Trans. Signal Process
, 2005
"... Abstract—Causal exponentials play a fundamental role in classical system theory. Starting from those elementary building blocks, we propose a complete and selfcontained signal processing formulation of exponential splines defined on a uniform grid. We specify the corresponding Bspline basis functi ..."
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Cited by 54 (21 self)
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Abstract—Causal exponentials play a fundamental role in classical system theory. Starting from those elementary building blocks, we propose a complete and selfcontained signal processing formulation of exponential splines defined on a uniform grid. We specify the corresponding Bspline basis functions and investigate their reproduction properties (Green function and exponential polynomials); we also characterize their stability (Riesz bounds). We show that the exponential Bspline framework allows an exact implementation of continuoustime signal processing operators including convolution, differential operators, and modulation, by simple processing in the discrete Bspline domain. We derive efficient filtering algorithms for multiresolution signal extrapolation and approximation, extending earlier results for polynomial splines. Finally, we present a new asymptotic error formula that predicts the magnitude and the thorder decay of the Papproximation error as a function of the knot spacing. Index Terms—Continuoustime signal processing, convolution, differential operators, Green functions, interpolation, modulation, multiresolution approximation, splines. I.
Scalespace derived from Bsplines
 IEEE Trans. Pattern Anal. Machine Intell
, 1998
"... Abstract—It is wellknown that the linear scalespace theory in computer vision is mainly based on the Gaussian kernel. The purpose of the paper is to propose a scalespace theory based on Bspline kernels. Our aim is twofold. On one hand, we present a general framework and show how Bsplines provid ..."
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Cited by 27 (7 self)
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Abstract—It is wellknown that the linear scalespace theory in computer vision is mainly based on the Gaussian kernel. The purpose of the paper is to propose a scalespace theory based on Bspline kernels. Our aim is twofold. On one hand, we present a general framework and show how Bsplines provide a flexible tool to design various scalespace representations: continuous scalespace, dyadic scalespace frame, and compact scalespace representation. In particular, we focus on the design of continuous scalespace and dyadic scalespace frame representation. A general algorithm is presented for fast implementation of continuous scalespace at rational scales. In the dyadic case, efficient frame algorithms are derived using Bspline techniques to analyze the geometry of an image. Moreover, the image can be synthesized from its multiscale local partial derivatives. Also, the relationship between several scalespace approaches is explored. In particular, the evolution of wavelet theory from traditional scalespace filtering can be well understood in terms of Bsplines. On the other hand, the behavior of edge models, the properties of completeness, causality, and other properties in such a scalespace representation are examined in the framework of Bsplines. It is shown that, besides the good properties inherited from the Gaussian kernel, the Bspline derived scalespace exhibits many advantages for modeling visual mechanism with regard to the efficiency, compactness, orientation feature, and parallel structure. Index Terms—Image modeling, Bspline, wavelet, scalespace, scaling theorem, fingerprint theorem.
Exact Feature Extraction using Finite Rate of Innovation Principles with an Application to Image Superresolution
 IEEE TRANSACTIONS ON IMAGE PROCESSING
, 2008
"... The accurate registration of multiview images is of central importance in many advanced image processing applications. Image superresolution, for example, is a typical application where the quality of the superresolved image is degrading as registration errors increase. Popular registration method ..."
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Cited by 25 (9 self)
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The accurate registration of multiview images is of central importance in many advanced image processing applications. Image superresolution, for example, is a typical application where the quality of the superresolved image is degrading as registration errors increase. Popular registration methods are often based on features extracted from the acquired images. The accuracy of the registration is in this case directly related to the number of extracted features and to the precision at which the features are located: images are best registered when many features are found with a good precision. However, in lowresolution images, only a few features can be extracted and often with a poor precision. By taking a sampling perspective, we propose in this paper new methods for extracting features in low resolution images in order to develop efficient registration techniques. We consider in particular the sampling theory of signals with finite rate of innovation [10] and show that some features of interest for registration can be retrieved perfectly in this framework, thus allowing an exact registration. We also demonstrate through simulations that the sampling model which enables the use of finite rate of innovation principles is wellsuited for modeling the acquisition of images by a camera. Simulations of image registration and image superresolution of artificially sampled images are first presented, analyzed and compared to traditional techniques. We finally present favorable experimental results of superresolution of real images acquired by a digital camera available on the market.
Ten Good Reasons For Using Spline Wavelets
 Proc. SPIE vol. 3169, Wavelet Applications in Signal and Image Processing V
, 1997
"... The purpose of this note is to highlight some of the unique properties of spline wavelets. These wavelets can be classified in four categories: othogonal (BattleLemari), semiorthogonal (e.g., Bspline), shiftorthogonal, and biorthogonal (CohenDaubechiesFeauveau) . Unlike most other wavelet bases ..."
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Cited by 23 (5 self)
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The purpose of this note is to highlight some of the unique properties of spline wavelets. These wavelets can be classified in four categories: othogonal (BattleLemari), semiorthogonal (e.g., Bspline), shiftorthogonal, and biorthogonal (CohenDaubechiesFeauveau) . Unlike most other wavelet bases, splines have explicit formulae in both the time and frequency domain, which greatly facilitates their manipulation. They allow for a progressive transition between the two extreme cases of a multiresolution: Haar's piecewise constant representation (spline of degree zero) versus Shannon's bandlimited model (which corresponds to a spline of infinite order). Spline wavelets are extremely regular and usually symmetric or antisymmetric. They can be designed to have compact support and to achieve optimal timefrequency localization (Bspline wavelets). The underlying scaling functions are the Bsplines, which are the shortest and most regular scaling functions of order L. Finally, splines have the best approximation properties among all known wavelets of a given order L. In other words, they are the best for approximating smooth functions.
Discretization of the Radon Transform and of its Inverse by Spline Convolutions
, 2002
"... We present an explicit formula for Bspline convolution kernels; these are defined as the convolution of several Bsplines of variable widths hi and degrees rzl. We apply our results to derive splineconvolutionbased algorithms for two closely related problems: the computation of the Radon transfor ..."
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Cited by 18 (7 self)
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We present an explicit formula for Bspline convolution kernels; these are defined as the convolution of several Bsplines of variable widths hi and degrees rzl. We apply our results to derive splineconvolutionbased algorithms for two closely related problems: the computation of the Radon transform and of its inverse. First, we present an efficient discrete implementation of the Radon transform that is optimal in the leastsquares sense. We then consider the reverse problem and introduce a new splineconvolution version of the filtered backprojection algorithm for tomographic reconstruction. In both cases, our explicit kernel formula allows for the use of highdegree splines; these offer better approximation performance than the conventional lowerdegree formulations (e.g., piecewise constant or piecewise linear models). We present multiple experiments to validate our approach and to find the parameters that give the best tradeoff between image quality and computational complexity. In particular, we find that it can be computationally more efficient to increase the approximation degree than to increase the sampling rate.
HighQuality Image Resizing Using Oblique Projection Operators
 IEEE TRANS. IMAGE PROCESSING
, 1998
"... The standard interpolation approach to image resizing is to fit the original picture with a continuous model and resample the function at the desired rate. However, one can obtain more accurate results if one applies a filter prior to sampling, a fact well known from sampling theory. The optimal sol ..."
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Cited by 18 (2 self)
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The standard interpolation approach to image resizing is to fit the original picture with a continuous model and resample the function at the desired rate. However, one can obtain more accurate results if one applies a filter prior to sampling, a fact well known from sampling theory. The optimal solution corresponds to an orthogonal projection onto the underlying continuous signal space. Unfortunately, the optimal projection prefilter is difficult to implement when sinc or high order spline functions are used. In this paper, we propose to resize the image using an oblique rather than an orthogonal projection operator in order to make use of faster, simpler, and more general algorithms. We show that we can achieve almost the same result as with the orthogonal projection provided that we use the same approximation space. The main advantage is that it becomes perfectly feasible to use higher order models (e.g, splines of degree n 3). We develop the theoretical background and present a si...