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Fundamental Performance Limits in Image Registration
- IEEE TRANSACTIONS ON IMAGE PROCESSING
, 2003
"... The task of image registration is fundamental in image processing. It often is a critical preprocessing step to many modern image processing and computer vision tasks, and many algorithms and techniques have been proposed to address the registration problem. Often, the performances of these techni ..."
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Cited by 51 (8 self)
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The task of image registration is fundamental in image processing. It often is a critical preprocessing step to many modern image processing and computer vision tasks, and many algorithms and techniques have been proposed to address the registration problem. Often, the performances of these techniques have been presented using a variety of relative measures comparing different estimators, leaving open the critical question of overall optimality. In this paper, we present the fundamental performance limits for the problem of image registration as derived from the Cramer-Rao inequality. We compare experimental performance of several popular methods with respect to this performance bound, and explain the fundamental tradeoff between variance and bias inherent to the problem of image registration. In particular, we derive and explore the bias of the popular gradient-based estimator showing how widely used multiscale methods for improving performance can be explained with this bias expression. Finally, we present experimental simulations showing general rule-of-thumb performance limits for gradient-based image registration techniques.
Stochastic methods for joint registration, restoration, and interpolation of multiple undersampled images
- IEEE Trans. Image Process
, 2006
"... Abstract—Using a stochastic framework, we propose two algorithms for the problem of obtaining a single high-resolution image from multiple noisy, blurred, and undersampled images. The first is based on a Bayesian formulation that is implemented via the expectation maximization algorithm. The second ..."
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Cited by 35 (2 self)
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Abstract—Using a stochastic framework, we propose two algorithms for the problem of obtaining a single high-resolution image from multiple noisy, blurred, and undersampled images. The first is based on a Bayesian formulation that is implemented via the expectation maximization algorithm. The second is based on a maximum a posteriori formulation. In both of our formulations, the registration, noise, and image statistics are treated as unknown parameters. These unknown parameters and the high-resolution image are estimated jointly based on the available observations. We present an efficient implementation of these algorithms in the frequency domain that allows their application to large images. Simulations are presented that test and compare the proposed algorithms.
A subspace identification extension to the phase correlation method
- IEEE Trans. Med. Imaging
, 2003
"... Abstract—The phase correlation method is known to pro-vide straightforward estimation of rigid translational mo-tion between two images. It is often claimed that the origi-nal method is best suited to identify integer pixel displace-ments, which has prompted the development of numerous subpixel disp ..."
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Cited by 27 (0 self)
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Abstract—The phase correlation method is known to pro-vide straightforward estimation of rigid translational mo-tion between two images. It is often claimed that the origi-nal method is best suited to identify integer pixel displace-ments, which has prompted the development of numerous subpixel displacement identification methods. However, the fact that the phase correlation matrix is rank one for a noise-free rigid translation model is often overlooked. This prop-erty leads to the low complexity subspace identification tech-nique presented here. The combination of non-integer pixel displacement identification without interpolation, robust-ness to noise, and limited computational complexity make this approach a very attractive extension of the phase cor-relation method. In addition, this approach is shown to be complementary with other subpixel phase correlation based techniques. Keywords—phase correlation method, SVD, subpixel im-age registration I.
Ziv-zakai bounds on image registration
- IEEE Trans. Signal Proc
"... Abstract—Image registration is a fundamental and important task in image processing. The goal essentially is to estimate the transformation that aligns two images. We focus on the general rigid body transformation case. In this paper, we derive the Ziv–Zakai bounds (ZZB) on image registration by ass ..."
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Cited by 5 (0 self)
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Abstract—Image registration is a fundamental and important task in image processing. The goal essentially is to estimate the transformation that aligns two images. We focus on the general rigid body transformation case. In this paper, we derive the Ziv–Zakai bounds (ZZB) on image registration by assuming an uncertainty model for the rotation and translation errors, and propose to use the ZZB as a benchmark to evaluate the registra-tion ability of an image pair. We also compare the performance of several image registration algorithms with the derived bounds when applied to several datasets. Index Terms—Image registration, parameter estimation, Ziv–Zakai bound. I.
Image Registration Using Log-Polar Mappings for Recovery of Large-Scale Similarity and Projective Transformations
"... Abstract—This paper describes a novel technique to recover large similarity transformations (rotation/scale/translation) and moderate perspective deformations among image pairs. We introduce a hybrid algorithm that features log-polar mappings and nonlinear least squares optimization. The use of log- ..."
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Abstract—This paper describes a novel technique to recover large similarity transformations (rotation/scale/translation) and moderate perspective deformations among image pairs. We introduce a hybrid algorithm that features log-polar mappings and nonlinear least squares optimization. The use of log-polar techniques in the spatial domain is introduced as a preprocessing module to recover large scale changes (e.g., at least four-fold) and arbitrary rotations. Although log-polar techniques are used in the Fourier–Mellin transform to accommodate rotation and scale in the frequency domain, its use in registering images subjected to very large scale changes has not yet been exploited in the spatial domain. In this paper, we demonstrate the superior performance of the log-polar transform in featureless image registration in the spatial domain. We achieve subpixel accuracy through the use of nonlinear least squares optimization. The registration process yields the eight parameters of the perspective transformation that best aligns the two input images. Extensive testing was performed on uncalibrated real images and an array of 10,000 image pairs with known transformations derived from the Corel Stock Photo Library of royalty-free photographic images. Index Terms—Image registration, Levenberg–Marquardt nonlinear least-squares optimization, log-polar transform, perspective transformation, similarity transformation. I.
Dedication
, 1905
"... This document describing the Aegis program, and the Aegis program itself, are ..."
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This document describing the Aegis program, and the Aegis program itself, are
Pseudopolar-Based Estimation of Large Translations, Rotations, and Scalings in Images
"... Abstract—One of the major challenges related to image registration is the estimation of large motions without prior knowledge. This paper presents a Fourier-based approach that estimates large translations, scalings, and rotations. The algorithm uses the pseudopolar (PP) Fourier transform to achieve ..."
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Abstract—One of the major challenges related to image registration is the estimation of large motions without prior knowledge. This paper presents a Fourier-based approach that estimates large translations, scalings, and rotations. The algorithm uses the pseudopolar (PP) Fourier transform to achieve substantial improved approximations of the polar and log-polar Fourier transforms of an image. Thus, rotations and scalings are reduced to translations which are estimated using phase correlation. By utilizing the PP grid, we increase the performance (accuracy, speed, and robustness) of the registration algorithms. Scales up to 4 and arbitrary rotation angles can be robustly recovered, compared to a maximum scaling of 2 recovered by state-of-the-art algorithms. The algorithm only utilizes one-dimensional fast Fourier transform computations whose overall complexity is significantly lower than prior works. Experimental results demonstrate the applicability of the proposed algorithms. Index Terms—Global motion estimation, gradient methods, image alignment, subpixel registration. I.
EÆciency and Accuracy Tradeos in using Projections for Motion Estimation
"... This paper presents an investigation of the use of the Radon (projection) transform in speeding up exist-ing image registration techniques. The ultimate goal is to make these algorithms more computationally sim-ple, while simultaneously realizing acceptably accurate performance. The use of the proje ..."
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This paper presents an investigation of the use of the Radon (projection) transform in speeding up exist-ing image registration techniques. The ultimate goal is to make these algorithms more computationally sim-ple, while simultaneously realizing acceptably accurate performance. The use of the projections in estimating transla-tional motion decomposes a 2-D problem into a pair of 1-D problems, leading to signicant computational savings. Here we present the tradeos of computa-tional eÆciency and accuracy for two current meth-ods. Our experiments show that for most applications, the modications we suggest in using the projections instead of the image directly cost little in performance, yet realize dramatic improvements in computational eÆciency. 1
