Showing papers on "Affine transformation published in 1997"
TL;DR: The basic idea is that instead of matching two images directly, one performs intermediate within-modality registrations to two template images that are already in register, and a least-squares minimization is used to determine the affine transformations that map between the templates and the images.
975 citations
TL;DR: In this article, a robust nonlinear control toolbox includes a number of methods for systems affine in deterministic bounded disturbances, but the problem when the disturbance is unbounded stochastic noise has hardly been considered.
572 citations
TL;DR: It is concluded that such automatic, rapid, robust algorithms significantly increase the likelihood that multimodality registrations will be routinely used to aid clinical diagnoses and post-therapeutic assessment in the near future.
519 citations
17 Jun 1997
TL;DR: The author describes a new method for camera autocalibration and scaled Euclidean structure and motion, from three or more views taken by a moving camera with fixed but unknown intrinsic parameters, based on a general constrained optimization technique-sequential quadratic programming-that may well be useful in other vision problems.
Abstract: The author describes a new method for camera autocalibration and scaled Euclidean structure and motion, from three or more views taken by a moving camera with fixed but unknown intrinsic parameters. The motion constancy of these is used to rectify an initial projective reconstruction. Euclidean scene structure is formulated in terms of the absolute quadric-the singular dual 3D quadric (4/spl times/4 rank 3 matrix) giving the Euclidean dot-product between plane normals. This is equivalent to the traditional absolute conic but simpler to use. It encodes both affine and Euclidean structure, and projects very simply to the dual absolute image conic which encodes camera calibration. Requiring the projection to be constant gives a bilinear constraint between the absolute quadric and image conic, from which both can be recovered nonlinearly from m/spl ges/3 images, or quasi-linearly from m/spl ges/4. Calibration and Euclidean structure follow easily. The nonlinear method is stabler, faster, more accurate and more general than the quasi-linear one. It is based on a general constrained optimization technique-sequential quadratic programming-that may well be useful in other vision problems.
514 citations
TL;DR: This work has developed a rapid and automatic method for performing affine registrations that uses a Bayesian scheme to incorporate prior knowledge of the variability in the shape and size of heads.
493 citations
TL;DR: A simplified model of a pushbroom sensor (the linear Pushbroom model) is introduced, which has the advantage of computational simplicity while at the same time giving very accurate results compared with the full orbiting push broom model.
Abstract: Modeling and analyzing pushbroom sensors commonly used in satellite imagery is difficult and computationally intensive due to the motion of an orbiting satellite with respect to the rotating Earth, and the nonlinearity of the mathematical model involving orbital dynamics. In this paper, a simplified model of a pushbroom sensor (the linear pushbroom model) is introduced. It has the advantage of computational simplicity while at the same time giving very accurate results compared with the full orbiting pushbroom model. Besides remote sensing, the linear pushbroom model is also useful in many other imaging applications. Simple noniterative methods are given for solving the major standard photogrammetric problems for the linear pushbroom model: computation of the model parameters from ground-control points; determination of relative model parameters from image correspondences between two images; and scene reconstruction given image correspondences and ground-control points. The linear pushbroom model leads to theoretical insights that are approximately valid for the full model as well. The epipolar geometry of linear pushbroom cameras is investigated and shown to be totally different from that of a perspective camera. Nevertheless, a matrix analogous to the fundamental matrix of perspective cameras is shown to exist for linear pushbroom sensors. From this it is shown that a scene is determined up to an affine transformation from two views with linear pushbroom cameras.
386 citations
TL;DR: Several classes of planar functions over a finite field are described, including a class whose associated affine planes are not translation planes or dual translation planes, and which cannot be obtained by derivation or lifting.
Abstract: Planar functions were introduced by Dembowski and Ostrom [4] to describe projective planes possessing a collineation group with particular properties. Several classes of planar functions over a finite field are described, including a class whose associated affine planes are not translation planes or dual translation planes. This resolves in the negative a question posed in [4]. These planar functions define at least one such affine plane of order 3 ^e for every e ≥ 4 and their projective closures are of Lenz-Barlotti type II. All previously known planes of type II are obtained by derivation or lifting. At least when e is odd, the planes described here cannot be obtained in this manner.
304 citations
TL;DR: The elastic body spline is a physical model of a homogeneous, isotropic three-dimensional (3-D) elastic body that is used to match 3-D magnetic resonance images of the breast that are used in the diagnosis and evaluation of breast cancer.
Abstract: Many image matching schemes are based on mapping coordinate locations, such as the locations of landmarks, in one image to corresponding locations in a second image. A new approach to this mapping (coordinate transformation), called the elastic body spline (EBS), is described. The spline is based on a physical model of a homogeneous, isotropic three-dimensional (3-D) elastic body. The model can approximate the way that some physical objects deform. The EBS as well as the affine transformation, the thin plate spline and the volume spline are used to match 3-D magnetic resonance images (MRI's) of the breast that are used in the diagnosis and evaluation of breast cancer. These coordinate transformations are evaluated with different types of deformations and different numbers of corresponding (paired) coordinate locations. In all but one of the cases considered, using the EBS yields more similar images than the other methods.
303 citations
TL;DR: A general class of methods for deriving 3-D shape cues from a 2-D image data based on the estimation of locally linearized deformations of brightness patterns, which constitutes a common framework for describing several problems in computer vision.
301 citations
TL;DR: A specialisation of the algorithm to recover structure and camera position modulo an affine transformation is described, together with a method to periodically update the affine coordinate frame to prevent drift over time.
Abstract: A structure from motion algorithm is described which recovers structure and camera position, modulo a projective ambiguity. Camera calibration is not required, and camera parameters such as focal length can be altered freely during motion. The structure is updated sequentially over an image sequence, in contrast to schemes which employ a batch process. A specialisation of the algorithm to recover structure and camera position modulo an affine transformation is described, together with a method to periodically update the affine coordinate frame to prevent drift over time. We describe the constraint used to obtain this specialisation.
Structure is recovered from image corners detected and matched automatically and reliably in real image sequences. Results are shown for reference objects and indoor environments, and accuracy of recovered structure is fully evaluated and compared for a number of reconstruction schemes. A specific application of the work is demonstrated—affine structure is used to compute free space maps enabling navigation through unstructured environments and avoidance of obstacles. The path planning involves only affine constructions.
279 citations
TL;DR: In this paper, dual Gramian techniques are used to verify whether a dual pair of affine frames is also a pair of bi-orthogonal Riesz bases, and a general method for a painless derivation of a dual-pair affine frame from an arbitrary MRA is obtained via the mixed extension principle.
Abstract: The fiberization of affine systems via dual Gramian techniques, which was developed in previous papers of the authors, is applied here for the study of affine frames that have an affine dual system. Gramian techniques are also used to verify whether a dual pair of affine frames is also a pair of bi-orthogonal Riesz bases. A general method for a painless derivation of a dual pair of affine frames from an arbitrary MRA is obtained via the mixed extension principle.
PARC1
TL;DR: This paper develops a rasterised approach to the search and a number of techniques that allow it to locate quickly all transformations of the model that satisfy two quality criteria; it can also efficiently locate only the best transformation.
Abstract: The Hausdorff distance is a measure defined between two point sets, here representing a model and an image. The Hausdorff distance is reliable even when the image contains multiple objects, noise, spurious features, and occlusions. In the past, it has been used to search images for instances of a model that has been translated, or translated and scaled, by finding transformations that bring a large number of model features close to image features, and vice versa. In this paper, we apply it to the task of locating an affine transformation of a model in an image; this corresponds to determining the pose of a planar object that has undergone weak-perspective projection. We develop a rasterised approach to the search and a number of techniques that allow us to locate quickly all transformations of the model that satisfy two quality criteria; we can also efficiently locate only the best transformation. We discuss an implementation of this approach, and present some examples of its use.
TL;DR: A technique for estimating affine transforms between nearby image patches which is based on solving a system of linear constraints derived from a differential analysis and yields predictions for both computer vision algorithms and human perception of shape from texture.
Abstract: Shape from texture is best analyzed in two stages, analogous to stereopsis and structure from motion: (a) Computing the ’texture distortion‘ from the image, and (b) Interpreting the ’texture distortion‘ to infer the orientation and shape of the surface in the scene. We model the texture distortion for a given point and direction on the image plane as an affine transformation and derive the relationship between the parameters of this transformation and the shape parameters. We have developed a technique for estimating affine transforms between nearby image patches which is based on solving a system of linear constraints derived from a differential analysis. One need not explicitly identify texels or make restrictive assumptions about the nature of the texture such as isotropy. We use non-linear minimization of a least squares error criterion to recover the surface orientation (slant and tilt) and shape (principal curvatures and directions) based on the estimated affine transforms in a number of different directions. A simple linear algorithm based on singular value decomposition of the linear parts of the affine transforms provides the initial guess for the minimization procedure. Experimental results on both planar and curved surfaces under perspective projection demonstrate good estimates for both orientation and shape. A sensitivity analysis yields predictions for both computer vision algorithms and human perception of shape from texture.
01 Jan 1997
TL;DR: In this article, the authors describe Bruhat-T buildings attached to classical groups, both spherical and affine buildings, as well as their relationship to the Bruhat and T.
Abstract: monograph on Bruhat-TIts buildings attached to classical groups. Both spherical and affine buildings.
01 Jan 1997
TL;DR: The algorithm presented subsumes previously proposed program transformation algorithms that are based on unimodular transformations, loop fusion, fission, scaling, reindexing and/or statement reordering.
Abstract: This paper presents the first algorithm to find the optimal affine transform that maximizes the degree of parallelism while minimizing the degree of synchronization in a program with arbitrary loop nestings and affine data accesses. The problem is formulated without the use of imprecise data dependence abstractions such as data dependence vectors. The algorithm presented subsumes previously proposed program transformation algorithms that are based on unimodular transformations, loop fusion, fission, scaling, reindexing and/or statement reordering.
TL;DR: Based on 2-D cluster approach, a fast algorithm for point pattern matching is proposed to effectively solve the problems of optimal matches between two point pattern under geometrical transformation and correctly identify the missing or spurious points of patterns.
TL;DR: A very large family of binary features for two-dimensional shapes determined by inductive learning during the construction of classification trees is introduced, which makes it possible to narrow the search for informative ones at each node of the tree.
Abstract: We introduce a very large family of binary features for two-dimensional shapes. The salient ones for separating particular shapes are determined by inductive learning during the construction of classification trees. There is a feature for every possible geometric arrangement of local topographic codes. The arrangements express coarse constraints on relative angles and distances among the code locations and are nearly invariant to substantial affine and nonlinear deformations. They are also partially ordered, which makes it possible to narrow the search for informative ones at each node of the tree. Different trees correspond to different aspects of shape. They are statistically and weakly dependent due to randomization and are aggregated in a simple way. Adapting the algorithm to a shape family is then fully automatic once training samples are provided. As an illustration, we classified handwritten digits from the NIST database; the error rate was 0.7 percent.
TL;DR: In this paper, a local geometric model in terms of F-and M-theory compactification on Calabi-Yau 4-folds is constructed, which leads to N = 1 Yang-Mills theory in d = 4 and its reduction on a circle to d = 3.
TL;DR: The authors show that general mammographic parenchymal and ductal patterns can be well modeled by a set of parameters of affine transformations and demonstrate that the fractal modeling method is an effective way to enhance microcalcifications.
Abstract: The objective of this research is to model the mammographic parenchymal and ductal patterns and enhance the microcalcifications using a deterministic fractal approach. According to the theory of deterministic fractal geometry, images can be modeled by deterministic fractal objects which are attractors of sets of two-dimensional (2-D) affine transformations. The iterated functions systems and the collage theorem are the mathematical foundations of fractal image modeling. Here, a methodology based on fractal image modeling is developed to analyze and model breast background structures. The authors show that general mammographic parenchymal and ductal patterns can be well modeled by a set of parameters of affine transformations. Therefore, microcalcifications can be enhanced by taking the difference between the original image and the modeled image. The authors' results are compared with those of the partial wavelet reconstruction and morphological operation approaches. The results demonstrate that the fractal modeling method is an effective way to enhance microcalcifications. It may also be able to improve the detection and classification of microcalcifications in a computer-aided diagnosis system.
TL;DR: In this paper, the affine length Raff is introduced, which separates solid-like elastic deformations on larger scales from liquid-like nonaffine deformations at smaller scales.
Abstract: We demonstrate that the origin of the nonlinear elasticity of polymer networks rests in their nonaffine deformations. We introduce the affine length Raff, which separates the solid-like elastic deformations on larger scales from liquid-like nonaffine deformations on smaller scales. This affine length grows with elongation λ as Raff ∼ λ3/2 and decreases upon compression as Raff ∼ λ1/2. The behavior of networks on scales up to Raff is that of stretched or compressed individual chains (we call them affine strands). The affine strands are stretched in the elongation direction and confined and folded in the effective tubes in the compression direction. The fluctuations of affine strands determine the diameters of the confining tubes a, which change nonaffinely with the network deformation a ∼ λ1/2. Our model gives a unified picture of deformations of both phantom and entangled networks and leads to a stress−strain relation that is in excellent agreement with experiments.
TL;DR: This paper considers the problem of minimizing the rank of a positive semidefinite matrix, subject to the constraint that an affine transformation of it is also positive semidfinite, and employs ideas from the ordered linear complementarity theory and the notion of the least element in a vector lattice.
Abstract: We consider the problem of minimizing the rank of a positive semidefinite matrix, subject to the constraint that an affine transformation of it is also positive semidefinite. Our method for solving this problem employs ideas from the ordered linear complementarity theory and the notion of the least element in a vector lattice. This problem is of importance in many contexts, for example in feedback synthesis problems, and such an example is also provided.
TL;DR: In this paper, a conjecture on the irreducibility of the tensor products of quantized affine representations of affine algebras is presented, which is proved in certain cases.
Abstract: We present a conjecture on the irreducibility of the tensor products of fundamental representations of quantized affine algebras. This conjecture implies in particular that the irreducibility of the tensor products of fundamental representations is completely described by the poles of the R-matrices. The conjecture is proved in certain cases.
TL;DR: A linear algorithm for recovering 3D affine shape and motion from line correspondences with uncalibrated affine cameras with the introduction of a one-dimensional projective camera is presented.
Abstract: This paper presents a linear algorithm for recovering 3D affine shape and motion from line correspondences with uncalibrated affine cameras. The algorithm requires a minimum of seven line correspondences over three views. The key idea is the introduction of a one-dimensional projective camera. This converts 3D affine reconstruction of "line directions" into 2D projective reconstruction of "points". In addition, a line-based factorization method is also proposed to handle redundant views. Experimental results both on simulated and real image sequences validate the robustness and the accuracy of the algorithm.
01 Mar 1997
TL;DR: In this paper, the authors consider the problem of minimizing the rank of a positive semidefinite matrix, subject to the constraint that an affine transformation of the matrix is also positive semi-definite.
Abstract: We consider the problem of minimizing the rank of a positive semidefinite matrix, subject to the constraint that an affine transformation of it is also positive semidefinite.
30 Apr 1997
TL;DR: This work presents a z-buffered image-space-based rendering technique that allows navigation in complex static environments and correctly simulates the kinetic depth effect (parallax), occlusion, and can resolve the missing visibility information by combining z- buffered environment maps from multiple viewpoints.
Abstract: We present a z-buffered image-space-based rendering technique that allows navigation in complex static environments. The rendering speed is relatively insensitive to the complexity of the scene as the rendering is performed a priori, and the scene is converted into a bounded complexity representation in the image space. Realtime performance is attained by using hardware texture mapping to implement the image-space warping and hardware affine transformations to compute the viewpoint–dependent warping function. Our proposed method correctly simulates the kinetic depth effect (parallax), occlusion, and can resolve the missing visibility information by combining z-buffered environment maps from multiple viewpoints. CR
01 Jan 1997
TL;DR: In this paper, a nonnegative vector β is defined to be a valid toll vector, if the set of tolled user equilibrium solutions is a subset of the untolled system optimal solutions.
Abstract: This paper concerns tolling methodologies for traffic networks which ensure that the resultant equilibrium flows are system optimal. A nonnegative vector β is defined to be a valid toll vector, if the set of tolled user equilibrium solutions is a subset of the set of untolled system optimal solutions. The problem of characterizing the toll set τ, which is the set of all valid toll vectors, is studied. Descriptions and characterizations of τ are given for the cases when either the cost map is strictly monotonic or is affine monotonic. In the latter case, the cost map is of the form Qυ + c, where Q is a not necessarily symmetric matrix and Q + Q T is positive semidefinite. The results are illustrated with several examples.
TL;DR: Simulation results show that the proposed video coding technique using the two-stage MC significantly outperforms H.263 under identical conditions, especially for sequences with fast camera motion.
Abstract: This paper describes a high-efficiency video coding method based on ITU-T H.263. To improve the coding efficiency of H.263, a two-stage motion compensation (MC) method is proposed, consisting of global MC (GMC) for predicting camera motion and local MC (LMC) for macroblock prediction. First, global motion such as panning, tilting, and zooming is estimated, and the global-motion-compensated image is produced for use as a reference in LMC. Next, LMC is performed both for the global-motion-compensated reference image and for the image without GMC. LMC employs an affine motion model in the context of H.263's overlapped block motion compensation. Using the overlapped block affine MC, rotation and scaling of small objects can be predicted, in addition to translational motion. In the proposed method, GMC is adaptively turned on/off for each macroblock since GMC cannot be used for prediction in all regions in a frame. In addition, either an affine or a translational motion model is adaptively selected in LMC for each macroblock. Simulation results show that the proposed video coding technique using the two-stage MC significantly outperforms H.263 under identical conditions, especially for sequences with fast camera motion. The performance improvements in peak-to-peak SNR (PSNR) are about 3 dB over the original H.263, which does not use the two-stage MC.
TL;DR: A method is proposed to decrease the effect of operator variability in the visual or quantitative interpretation of scintigraphic myocardial perfusion studies by adaptation of the iterative closest point algorithm.
Abstract: Single photon emission computed tomography (SPECT) imaging with /sup 201/Tl or /sup 99m/Tc agent is used to assess the location or the extent of myocardial infarction or ischemia. A method is proposed to decrease the effect of operator variability in the visual or quantitative interpretation of scintigraphic myocardial perfusion studies. To effect this, the patient's myocardial images (target cases) are registered automatically over a template image, utilizing a nonrigid transformation. The intermediate steps are: 1) Extraction of feature points in both stress and rest three-dimensional (3-D) images. The images are resampled in a polar geometry to detect edge points, which in turn are filtered by the use of a priori constraints. The remaining feature points are assumed to be points on the edges of the left ventricular myocardium. 2) Registration of stress and rest images with a global affine transformation. The matching method is an adaptation of the iterative closest point algorithm. 3) Registration and morphological matching of both stress and rest images on a template using a nonrigid local spline transformation following a global affine transformation. 4) Resampling of both stress and rest images in the geometry of the template. Optimization of the method was performed on a database of 40 pairs of stress and rest images selected to obtain a wide variation of images and abnormalities. Further testing was performed on 250 cases selected from the same database on the basis of the availability of angiographic results and patient stratification.
TL;DR: This paper presents the simplest affine invariant flow for (convex) surfaces in three-dimensional space, which, like the affine-invariant curve shortening flow, will be of fundamental importance in the processing of three- dimensional images.
Abstract: The study of geometric flows for smoothing, multiscale representation, and analysis of two- and three-dimensional objects has received much attention in the past few years. In this paper, we first survey the geometric smoothing of curves and surfaces via geometric heat-type flows, which are invariant under the groups of Euclidean and affine motions. Second, using the general theory of differential invariants, we determine the general formula for a geometric hypersurface evolution which is invariant under a prescribed symmetry group. As an application, we present the simplest affine invariant flow for (convex) surfaces in three-dimensional space, which, like the affine-invariant curve shortening flow, will be of fundamental importance in the processing of three-dimensional images.
17 Jun 1997
TL;DR: A stratified approach is proposed which gradually retrieves the metric calibration of the camera setup using a constraint which can be formulated between any two arbitrary images of the sequence.
Abstract: Camera calibration is essential to many computer vision applications. In practice this often requires cumbersome calibration procedures to be carried out regularly. In the last few years a lot of work has been done on self-calibration of cameras, ranging from weak calibration to metric calibration. It has been shown that a metric calibration of the camera setup (up to scale) was possible based on the rigidity of the scene only. In this paper a stratified approach is proposed which gradually retrieves the metric calibration of the camera setup. Starting from an uncalibrated image sequence the projective calibration is retrieved first. In projective space the plane at infinity is then identified yielding the affine calibration. This is achieved using a constraint which can be formulated between any two arbitrary images of the sequence. Once the affine calibration is known the upgrade to metric is easily obtained through linear equations.