Showing papers on "Affine transformation published in 1999"
TL;DR: The results clearly indicate that the proposed nonrigid registration algorithm is much better able to recover the motion and deformation of the breast than rigid or affine registration algorithms.
Abstract: In this paper the authors present a new approach for the nonrigid registration of contrast-enhanced breast MRI. A hierarchical transformation model of the motion of the breast has been developed. The global motion of the breast is modeled by an affine transformation while the local breast motion is described by a free-form deformation (FFD) based on B-splines. Normalized mutual information is used as a voxel-based similarity measure which is insensitive to intensity changes as a result of the contrast enhancement. Registration is achieved by minimizing a cost function, which represents a combination of the cost associated with the smoothness of the transformation and the cost associated with the image similarity. The algorithm has been applied to the fully automated registration of three-dimensional (3-D) breast MRI in volunteers and patients. In particular, the authors have compared the results of the proposed nonrigid registration algorithm to those obtained using rigid and affine registration techniques. The results clearly indicate that the nonrigid registration algorithm is much better able to recover the motion and deformation of the breast than rigid or affine registration algorithms.
5,490 citations
TL;DR: A methodology is developed to derive algorithms for optimal basis selection by minimizing diversity measures proposed by Wickerhauser (1994) and Donoho (1994), which include the p-norm-like (l/sub (p/spl les/1)/) diversity measures and the Gaussian and Shannon entropies.
Abstract: A methodology is developed to derive algorithms for optimal basis selection by minimizing diversity measures proposed by Wickerhauser (1994) and Donoho (1994). These measures include the p-norm-like (l/sub (p/spl les/1)/) diversity measures and the Gaussian and Shannon entropies. The algorithm development methodology uses a factored representation for the gradient and involves successive relaxation of the Lagrangian necessary condition. This yields algorithms that are intimately related to the affine scaling transformation (AST) based methods commonly employed by the interior point approach to nonlinear optimization. The algorithms minimizing the (l/sub (p/spl les/1)/) diversity measures are equivalent to a previously developed class of algorithms called focal underdetermined system solver (FOCUSS). The general nature of the methodology provides a systematic approach for deriving this class of algorithms and a natural mechanism for extending them. It also facilitates a better understanding of the convergence behavior and a strengthening of the convergence results. The Gaussian entropy minimization algorithm is shown to be equivalent to a well-behaved p=0 norm-like optimization algorithm. Computer experiments demonstrate that the p-norm-like and the Gaussian entropy algorithms perform well, converging to sparse solutions. The Shannon entropy algorithm produces solutions that are concentrated but are shown to not converge to a fully sparse solution.
554 citations
TL;DR: It is shown that mutual information is a continuous function of the affine registration parameters when appropriate interpolation is used and it is derived analytic expressions of its derivatives that allow numerically exact evaluation of its gradient.
455 citations
TL;DR: The design of a residual generator for fault detection and isolation (FDI) in nonlinear systems which are affine in the control signals and in the failure modes is studied.
Abstract: The design of a residual generator for fault detection and isolation (FDI) in nonlinear systems which are affine in the control signals and in the failure modes is studied, First, the problem statement used for linear systems is extended, and a set of sufficient conditions for the existence of a solution is given. Next, circumstances under which high-gain observers for uniformly observable systems can be used in the synthesis of the residual generator are provided.
410 citations
TL;DR: In this paper, the authors present a model that delivers closed-form solutions for bond prices and a concave relationship between the interest rate and the yields, showing that in empirical analyses, their model outperforms the one-factor affine models in both time-series as well as cross-sectional tests.
Abstract: Recent nonparametric estimation studies pioneered by Ait-Sahalia document that the diffusion of the short rate is similar to the parametric function, r[superscript 1.5], estimated by Chan et al., whereas the drift is substantially nonlinear in the short rate. These empirical properties call into question the efficacy of the existing affine term structure models and beg for alternative models which admit the observed behavior. This article presents such a model. Our model delivers closed-form solutions for bond prices and a concave relationship between the interest rate and the yields. We show that in empirical analyses, our model outperforms the one-factor affine models in both time-series as well as cross-sectional tests. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.
358 citations
TL;DR: This paper presents an algorithm for temporal and/or multimodal registration of retinal images based on point correspondence that has been applied to the registration of fluorescein images with green images.
Abstract: Image registration is a real challenge because physicians handle many images. Temporal registration is necessary in order to follow the various steps of a disease, whereas multimodal registration allows us to improve the identification of some lesions or to compare pieces of information gathered from different sources. This paper presents an algorithm for temporal and/or multimodal registration of retinal images based on point correspondence. As an example, the algorithm has been applied to the registration of fluorescein images (obtained after a fluorescein dye injection) with green images (green filter of a color image). The vascular tree is first detected in each type of images and bifurcation points are labeled with surrounding vessel orientations. An angle-based invariant is then computed in order to give a probability for two points to match. Then a Bayesian Hough transform is used to sort the transformations with their respective likelihoods. A precise affine estimate is finally computed for most likely transformations. The best transformation is chosen for registration.
334 citations
TL;DR: In this paper, a unified state-space formulation for parameter estimation of exponential-affine term structure models is proposed, which only requires specifying the conditional mean and variance of the system in an approximate sense.
Abstract: This paper proposes a unified state-space formulation for parameter estimation of exponential-affine term structure models. The proposed method uses an approximate linear Kalman filter which only requires specifying the conditional mean and variance of the system in an approximate sense. The method allows for measurement errors in the observed yields to maturity, and can simultaneously deal with many yields on bonds with different maturities. An empirical analysis of two special cases of this general class of model is carried out: the Gaussian case (Vasicek 1977) and the non-Gaussian case (Cox Ingersoll and Ross 1985 and Chen and Scott 1992). Our test results indicate a strong rejection of these two cases. A Monte Carlo study indicates that the procedure is reliable for moderate sample sizes.
311 citations
TL;DR: An original approach to partitioning of a video document into shots is described, which exploits image motion information, which is generally more intrinsic to the video structure itself, and other possible extensions, such as mosaicing and mobile zone detection are described.
Abstract: This paper describes an original approach to partitioning of a video document into shots. Instead of an interframe similarity measure which is directly intensity based, we exploit image motion information, which is generally more intrinsic to the video structure itself. The proposed scheme aims at detecting all types of transitions between shots using a single technique and the same parameter set, rather than a set of dedicated methods. The proposed shot change detection method is related to the computation, at each time instant, of the dominant image motion represented by a two-dimensional affine model. More precisely, we analyze the temporal evolution of the size of the support associated to the estimated dominant motion. Besides, the computation of the global motion model supplies by-products, such as qualitative camera motion description, which we describe in this paper, and other possible extensions, such as mosaicing and mobile zone detection. Results on videos of various content types are reported and validate the proposed approach.
278 citations
01 Jan 1999
TL;DR: An algorithm to compute correspondence between stereo images or between frames of a motion sequence is proposed by minimizing an energy functional that accounts for slanted surfaces by segmenting the image into a number of non-overlapping regions.
Abstract: Slanted surfaces pose a problem for correspondence algorithms utilizing search because of the greatly increased number of possibilities, when compared with fronto-parallel surfaces. In this paper we propose an algorithm to compute correspondence between stereo images or between frames of a motion sequence by minimizing an energy functional that accounts for slanted surfaces. The energy is minimized in a greedy strategy that alternates between segmenting the image into a number of non-overlapping regions (using the multiway-cut algorithm of Boykov, Veksler, and Zabih) and finding the affine parameters describing the displacement function of each region. A follow-up step enables the algorithm to escape local minima due to oversegmentation. Experiments on real images show the algorithm's ability to find an accurate segmentation and displacement map, as well as discontinuities and creases, from a wide variety of stereo and motion imagery.
272 citations
TL;DR: An implementation of the Gilbert-Johnson-Keerthi algorithm for comput ing the distance between convex objects, that has improved performance, robustness, and versatility over earlier implementations is presented.
Abstract: This paper presents an implementation of the Gilbert-Johnson-Keerthi algorithm for comput ing the distance between convex objects, that has improved performance, robustness, and versatility over earlier implementations. The algorithm presented here is especially suitable for use in collision detection of objects modeled using various types of geometric primitives, such as boxes, cones, and spheres, and their images under affine transformation.
255 citations
22 Jan 1999
TL;DR: A new watermarking scheme for digital images that allows watermark recovery even if the image has been subjected to generalized geometrical transforms is proposed.
Abstract: In this paper we propose a new watermarking scheme for digital images that allows watermark recovery even if the image has been subjected to generalized geometrical transforms. The watermark is given by a binary number and every watermark bit is represented by a 2D function. The functions are weighted, using a mask that is proportional to the luminance, and then modulated onto the blue component of the image. To recover an embedded bit, the embedded watermark is estimated using a prediction filter. The sign of the correlation between the estimated watermark and the original function determine the embedded several times at horizontally and vertically shifted locations. In the watermark recovery process we first compute a prediction of the embedded watermark. Then the autocorrelation function is computed for this prediction. The multiple embedding of the watermark result in additional autocorrelation peaks. By comparing the configuration of the extracted peaks with their expected configuration we can determine the affine distortion applied to the image. The distortion can then be inverted and the watermark recovered in a standard way.
01 Mar 1999
TL;DR: The registration of 26 pairs of fluoroscein angiography and indocyanine green chorioangiography images with the corresponding red-free retinal images, showed the superiority of combining genetic algorithms with the affine and bilinear transformation models.
Abstract: Retinal image registration is commonly required in order to combine the complementary information in different retinal modalities. In this paper, a new automatic scheme to register retinal images is presented and is currently tested in a clinical environment. The scheme considers the suitability and efficiency of different image transformation models and function optimization techniques, following an initial preprocessing stage. Three different transformation models-affine, bilinear and projective-as well as three optimization techniques-downhill simplex method, simulated annealing and genetic algorithms-are investigated and compared in terms of accuracy and efficiency. The registration of 26 pairs of fluoroscein angiography and indocyanine green chorioangiography images with the corresponding red-free retinal images, showed the superiority of combining genetic algorithms with the affine and bilinear transformation models. A comparative study of the proposed automatic registration scheme against the manual method, commonly used in clinical practice, is finally presented showing the advantage of the proposed automatic scheme in terms of accuracy and consistency.
01 May 1999
TL;DR: An algorithm is presented that maximizes parallelism while minimizing communication in programs with arbitrary loop nestings and affine data accesses and can find the optimal affine partition that maximized the degree of parallelism with the minimum degree of synchronizations.
Abstract: An affine partitioning Framework unifies many useful program transforms such as unimodular transformations (interchange, reversal, skewing), loop fusion, fission, scaling, reindexing, and statement reordering. This paper presents an algorithm, based on this unified framework, that maximizes parallelism while minimizing communication in programs with arbitrary loop nestings and affine data accesses. Our algorithm can find the optimal affine partition that maximizes the degree of parallelism with the minimum degree of synchronizations. In addition, it uses a greedy algorithm to minimize communication between loops heuristically by aligning the computation partitions for different loops, trading off excess degrees of parallelism, and choosing pipelined parallelism over doall paralleIism if it can significantly reduce the communication. The algorithm is optimal in maximizing the degrees of parallelism that require (1) no communication, (2) near-neighbor communication and a constant number of synchronizations, and (3) near-neighbor communication and O(n) synchronizations where n is the number of iterations in a loop.
TL;DR: A stratified approach is proposed, which goes from projective through affine to metric, which allows retrieval of the affine calibration for constant intrinsic parameters and is also suited for use in conjunction with scene knowledge.
Abstract: In computer vision and especially for 3D reconstruction, one of the key issues is the retrieval of the calibration parameters of the camera. These are needed to obtain metric information about the scene from the camera. Often these parameters are obtained through cumbersome calibration procedures. There is a way to avoid explicit calibration of the camera. Self-calibration is based on finding the set of calibration parameters which satisfy some constraints (e.g., constant calibration parameters). Several techniques have been proposed but it often proved difficult to reach a metric calibration at once. Therefore, in the paper, a stratified approach is proposed, which goes from projective through affine to metric. The key concept to achieve this is the modulus constraint. It allows retrieval of the affine calibration for constant intrinsic parameters. It is also suited for use in conjunction with scene knowledge. In addition, if the affine calibration is known, it can also be used to cope with a changing focal length.
TL;DR: The presented results indicate that the proposed technique is a very accurate and robust approach for long-term global motion estimation, which can be used for applications such as MPEG-4 sprite coding or MPEG-7 motion description, and the efficiency of globalmotion estimation can be significantly increased if a higher order motion model is applied.
Abstract: We present a new technique for long-term global motion estimation of image objects. The estimated motion parameters describe the continuous and time-consistent motion over the whole sequence relatively to a fixed reference coordinate system. The proposed method is suitable for the estimation of affine motion parameters as well as for higher order motion models like the parabolic model-combining the advantages of feature matching and optical flow techniques. A hierarchical strategy is applied for the estimation, first translation, affine motion, and finally higher order motion parameters, which is robust and computationally efficient. A closed-loop prediction scheme is applied to avoid the problem of error accumulation in long-term motion estimation. The presented results indicate that the proposed technique is a very accurate and robust approach for long-term global motion estimation, which can be used for applications such as MPEG-4 sprite coding or MPEG-7 motion description. We also show that the efficiency of global motion estimation can be significantly increased if a higher order motion model is applied, and we present a new sprite coding scheme for on-line applications. We further demonstrate that the proposed estimator serves as a powerful tool for segmentation of video sequences.
TL;DR: This paper presents two algorithmic approaches to the point matching problem, in an attempt to reduce its computational complexity, while still providing a guarantee of the quality of the final match.
TL;DR: In this article, it was shown that every upper semicontinuous and equi-affine invariant valuation on the space of d-dimensional convex bodies is a linear combination of affine surface area, volume, and the Euler characteristic.
01 Jan 1999
TL;DR: Experimental results show that motion patterns in hand gestures can be extracted and recognized with high recognition rate using motion trajectories using a time-delay neural network.
Abstract: We present an algorithm for extracting and classifying two-dimensional motion in an image sequence based on motion trajectories. First, a multiscale segmentation is performed to generate homogeneous regions in each frame. Regions between consecutive frames are then matched to obtain 2-view correspondences. Affine transformations are computed from each pair of corresponding regions to define pixel matches. Pixels matches over consecutive images pairs are concatenated to obtain pixel-level motion trajectories across the image sequence. Motion patterns are learned from the extracted trajectories using a time-delay neural network. We apply the proposed method to recognize 40 hand gestures of American Sign Language. Experimental results show that motion patterns in hand gestures can be extracted and recognized with high recognition rate using motion trajectories.
29 Sep 1999
TL;DR: This paper presents an approach for embedding a digital watermark into an image using the Fourier transform, and details a new algorithm for the accurate and efficient recovery of the template in an image which has undergone a general affine transformation.
Abstract: Digital watermarks have been proposed as a method for discouraging illicit copying and distribution of copyrighted material. This paper describes a method for the secure and robust copyright protection of digital images. We present an approach for embedding a digital watermark into an image using the Fourier transform. To this watermark is added a template in the Fourier transform domain to render the method robust against general linear transformations. We detail a new algorithm for the accurate and efficient recovery of the template in an image which has undergone a general affine transformation. Furthermore we demonstrate how the template can be used as a tool for asserting the presence of a watermark. We also systematically evaluate the algorithm and present results which demonstrate the robustness of the method against some common image processing operations such as compression, rotation, scaling and aspect ratio changes.
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TL;DR: In this article, a 1-parametric deformation of the convolution product from spherical perverse sheaves on a reductive group to affine Grassmannian was proposed. But this deformation was not applied to the affine flag variety.
Abstract: Let $G$ be a reductive group, let $Gr=G((t))/G[[t]]$ be the corresponding affine Grassmannian and let $Fl=G((t))/I$ be the affine flag variety. We construct, following an idea of Belinson, a 1-parametric deformation of the product $Gr\times G/B$ to $Fl$. We use this construction to produce perverse sheaves on $Fl$ which are central with respect to the convolution product from spherical perverse sheaves on $Gr$.
TL;DR: A set of local absolute affine invariants derived from the convex hull of scattered feature points extracted from the image are presented, which are very well suited to handle the occlusion and/or appearance of new objects.
Abstract: This paper is concerned with the problem of feature point registration and scene recognition from images under weak perspective transformations which are well approximated by affine transformations and under possible occlusion and/or appearance of new objects. It presents a set of local absolute affine invariants derived from the convex hull of scattered feature points (e.g., fiducial or marking points, corner points, inflection points, etc.) extracted from the image. The affine invariants are constructed from the areas of the triangles formed by connecting three vertices among a set of four consecutive vertices (quadruplets) of the convex hull, and hence do make direct use of the area invariance property associated with the affine transformation. Because they are locally constructed, they are very well suited to handle the occlusion and/or appearance of new objects. These invariants are used to establish the correspondences between the convex hull vertices of a test image with a reference image in order to undo the affine transformation between them. A point matching approach for recognition follows this. The time complexity for registering L feature points on the test image with N feature points of the reference image is of order O(N/spl times/L). The method has been tested on real indoor and outdoor images and performs well.
TL;DR: Nonrigid registration significantly reduces the effects of movement artifact in subtracted contrast-enhanced breast MRI, which may enable better visualization of small tumors and those within a glandular breast.
Abstract: PURPOSE: A new nonrigid registration method, designed to reduce the effect of movement artifact in subtraction images from breast MR, is compared with existing rigid and affine registration methods. METHOD: Nonrigid registration was compared with rigid and affine registration methods and unregistered images using 54 gadolinium-enhanced 3D breast MR data sets. Twenty-seven data sets had been previously reported normal, and 27 contained a histologically proven carcinoma. The comparison was based on visual assessment and ranking by two radiologists. RESULTS: When analyzed by two radiologists independently, all three registration methods gave better-quality subtraction images than unregistered images (p < 0.01), but nonrigid registration gave significantly better results than the rigid and affine registration methods (p < 0.01). There was no significant difference between rigid and affine registration methods. CONCLUSION: Nonrigid registration significantly reduces the effects of movement artifact in subtracted contrast-enhanced breast MRI. This may enable better visualization of small tumors and those within a glandular breast
TL;DR: A novel recursive method for estimating structure and motion from image sequences that relies on subspace and factorization methods and is derived from both ordinary coordinate representations and camera matrices and from a so-called depth and shape analysis.
01 Sep 1999
TL;DR: An algebraic representation is developed which unifies the three types of measurement and, amongst other advantages, permits a first order error propagation analysis to be performed, associating an uncertainty with each measurement.
Abstract: We describe how 3D affine measurements may be computed from a single perspective view of a scene given only minimal geometric information determined from the image. This minimal information is typically the vanishing line of a reference plane and a vanishing point for a direction not parallel to the plane. It is shown that affine scene structure may then be determined from the image, without knowledge of the camera's internal calibration (e.g. focal length), nor of the explicit relation between camera and world (pose). In particular we show how to: compute the distance between planes parallel to the reference plane (up to a common scale factor); compute area and length ratios on any plane parallel to the reference plane; determine the camera's (viewer's) location. Simple geometric derivations are given for these results. We also develop an algebraic representation which unifies the three types of measurement and, amongst other advantages, permits a first order error propagation analysis to be performed, associating an uncertainty with each measurement. We demonstrate the technique for a variety of applications, including height measurements in forensic images and 3D graphical modelling from single images.
TL;DR: In this article, the authors consider the construction of Markov chain approximations for an important class of deterministic control problems, which are affine in the dynamics and with quadratic running cost.
Abstract: We consider the construction of Markov chain approximations for an important class of deterministic control problems. The emphasis is on the construction of schemes that can be easily implemented and which possess a number of highly desirable qualitative properties. The class of problems covered is that for which the control is affine in the dynamics and with quadratic running cost. This class covers a number of interesting areas of application, including problems that arise in large deviations, risk-sensitive and robust control, robust filtering, and certain problems in computer vision. Examples are given as well as a proof of convergence.
01 Jan 1999
TL;DR: Imposing chirality constraints to limit the search for the plane at infinity to a 3-dimensional cubic region of parameter space is imposed and it is shown that this dense search allows one to avoid areas of local minima effectively and find global minima of the cost function.
Abstract: This paper considers the problem of self-calibration of a camera from an image sequence in the case where the camera's internal parameters (most notably focal length) may change The problem of camera self-calibration from a sequence of images has proven to be a difficult one in practice, due to the need ultimately to resort to non-linear methods, which have often proven to be unreliable In a stratified approach to self-calibration, a projective reconstruction is obtained first and this is successively refined first to an affine and then to a Euclidean (or metric) reconstruction It has been observed that the difficult step is to obtain the affine reconstruction, or equivalently to locate the plane at infinity in the projective coordinate frame The problem is inherently non-linear and requires iterative methods that risk not finding the optimal solution The present paper overcomes this difficulty by imposing chirality constraints to limit the search for the plane at infinity to a 3-dimensional cubic region of parameter space It is then possible to carry out a dense search over this cube in reasonable time For each hypothesised placement of the plane at infinity, the calibration problem is reduced to one of calibration of a nontranslating camera, for which fast non-iterative algorithms exist A cost function based on the result of the trial calibration is used to determine the best placement of the plane at infinity Because of the simplicity of each trial, speeds of over 10,000 trials per second are achieved on a 256 MHz processor It is shown that this dense search allows one to avoid areas of local minima effectively and find global minima of the cost function
TL;DR: In this paper, the exact solutions of this theory are reviewed and discussed in the context of metric-affine gravity theory, and the exact solution of the problem is discussed in detail.
Abstract: In continuing our series on metric–affine gravity (see Gronwald, Int. J. Mod. Phys.D6, 263 (1997) for Part I), we review the exact solutions of this theory.
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TL;DR: The canonical bases of the higher level q-deformed Fock space modules of the affine Lie algebra sl(n)^ were defined in this article and the transition matrices between the canonical bases and the natural bases of Fock spaces were expressed in terms of affine Kazhdan-Lusztig polynomials.
Abstract: We define canonical bases of the higher-level q-deformed Fock space modules of the affine Lie algebra sl(n)^. This generalizes the result of Leclerc and Thibon for the case of level 1. We express the transition matrices between the canonical bases and the natural bases of the Fock spaces in terms of affine Kazhdan-Lusztig polynomials.
01 Jan 1999
TL;DR: The subgroups of GL(n,R) that act irreducibly on R^n and that can occur as the holonomy of a torsion-free affine connection on an n-manifold are classified in this paper.
Abstract: The subgroups of GL(n,R) that act irreducibly on R^n and that can occur as the holonomy of a torsion-free affine connection on an n-manifold are classified, thus completing the work on this subject begun by M. Berger in the 1950s. The methods employed include representation theory, the theory of hermitian symmetric spaces, twistor theory, and Poisson geometry. The latter theory is especially important for the construction and classification of those torsion-free connections whose holonomy falls into one of the so-called `exotic' cases, i.e., those that were not included in Berger's original lists. Some remarks involving an interpretation of some of the examples in terms of supersymmetric constructions are also included.