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A full curvature based algorithm for image registration

JOURNAL OF MATHEMATICAL IMAGING AND vision 2006年第2期24卷 195-208页

作者： Henn, S Univ Dusseldorf Inst Math D-40225 Dusseldorf Germany

Image registration, i.e., finding an optimal displacement field u which minimizes a distance functional D(u) is known to be an ill-posed problem. In this paper a novel variational image registration method is presented, which matches two images acquired from the same or from different medical imaging modalities. The approach proposed here is also independent of the image dimension. The proposed variational penalty against oscillations in the solutions is the standard H-2(ohm) Sobolev semi-inner product for each component of the displacement. We investigate the associated Euler-Lagrange equation of the energy functional. Furthermore, we approach the solution of the underlying system of biharmonic differential equations with higher order boundary conditions as the steady-state solution of a parabolic partial differential equation (PDE). One of the important aspects of this approach is that the kernel of the Euler-Lagrange equation is spanned by all rigid motions. Hence, the presented approach includes a rigid alignment. Experimental results on both synthetic and real images are presented to illustrate the capabilities of the proposed approach.

关键词： image processing image registration variational methods regularization biharmonic differential-equation

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Optic flow from multi-scale dynamic anchor point attributes

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3rd international conference on Image Analysis and Recognition

作者： Janssen, B. J. Florack, L. M. J. Duits, R. ter Haar Romeny, B. M. Eindhoven Univ Technol NL-5600 MB Eindhoven Netherlands

ISBN: (纸本)3540448918

Optic flow describes the apparent motion that is present in an image sequence. We show the feasibility of obtaining optic flow from dynamic properties of a sparse set of multi-scale anchor points. Singular points of a Gaussian scale space image are identified as feasible anchor point candidates and analytical expressions describing their dynamic properties are presented. Advantages of approaching the optic flow estimation problem using these anchor points are that (i) in these points the notorious aperture problem does not manifest itself, (ii) it combines the strengths of variational and multi-scale methods, (iii) optic flow definition becomes independent of image resolution, (iv) computations of the components of the optic flow field are decoupled and that (v) the feature set inducing the optic flow field is very sparse (typically < 1/2% of the number of pixels in a frame). A dense optic flow vector field is obtained through projection into a Sobolev space defined by and consistent with the dynamic constraints in the anchor points. As opposed to classical optic flow estimation schemes the proposed method accounts for an explicit scale component of the vector field, which encodes some dynamic differential flow property.

关键词： Image analysis

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A multigrid platform for real-time motion computation with discontinuity-preserving variational methods

A multigrid platform for real-time motion computation with d...

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5th international conference on scale-space and PDE methods in computer vision

作者： Bruhn, Andres Weickert, Joachim Kohlberger, Timo Schnoerr, Christoph Univ Saarland Math Image Anal Grp Fac Math & Comp Sci D-66041 Saarbrucken Germany Univ Mannheim Dept Math & Comp Sci Comp Vis Graph & Pattern Recognit Grp D-68131 Mannheim Germany

variational methods are among the most accurate techniques for estimating the optic flow. They yield dense flow fields and can be designed such that they preserve discontinuities, estimate large displacements correctly and perform well under noise and varying illumination. However, such adaptations render the minimisation of the underlying energy functional very expensive in terms of computational costs: Typically one or more large linear or nonlinear equation systems have to be solved in order to obtain the desired solution. Consequently, variational methods are considered to be too slow for real-time performance. In our paper we address this problem in two ways: (i) We present a numerical framework based on bidirectional multigrid methods for accelerating a broad class of variational optic flow methods with different constancy and smoothness assumptions. Thereby, our work focuses particularly on regularisation strategies that preserve discontinuities. (ii) We show by the examples of five classical and two recent variational techniques that real-time performance is possible in all cases-even for very complex optic flow models that offer high accuracy. Experiments show that frame rates up to 63 dense flow fields per second for image sequences of size 160 x 120 can be achieved on a standard PC. Compared to classical iterative methods this constitutes a speedup of two to four orders of magnitude.

关键词： partial differential equations variational methods optic flow multigrid methods

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The effect of presmoothing image sequences on the computation of optical flow

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3rd international conference on Image Analysis and Recognition

作者： Condell, J. V. Scotney, B. W. Morrow, P. J. Univ Ulster Coleraine BT52 1SA Londonderry North Ireland

ISBN: (纸本)3540448918

The computation of optical flow has been proposed as a preprocessing step for many high-level vision algorithms. One of the main approaches to the optical flow problem is the gradient-based approach which differentiates the image intensity to compute the optical flow. Often motion vectors computed using various approaches are not reliable. Spatial smoothing of the image sequence is advisable in order to improve velocity estimates in the presence of noise. That is, the application of some kind of linear operation to the images in the sequence before solving for the flow. The pre-processing typically takes the form of some type of spatial Gaussian smoothing or scale specific band-pass filtering of the input images. The main objectives of such filtering have been to lessen the effects of noise, to isolate image structure of interest and to attenuate temporal aliasing and quantization effects in the input images. This paper investigates the effect of presmoothing on this computation of optical flow. The well known method of Horn and Schnuck as well as our own finite element method are implemented and tested for improvements due to presmoothing. Discussions are provided on the effects of presmoothing for a variety of image sequences. In our experiments, smoothing is carried out on a selection of well known sequences in both time and space. Improvements are shown using presmoothing.

关键词： finite volume methods inverse finite element methods motion tracking optical flow spatial smoothing temporal smoothing

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Nonlinear inverse scale space methods for image restoration

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3rd international Workshop on variational, Geometric, and Level Set methods in computer vision

作者： Burger, M Osher, S Xu, JJ Gilboa, G Johannes Kepler Univ Linz Ind Math Inst A-4040 Linz Austria Univ Calif Los Angeles Dept Math Los Angeles CA 90095 USA

ISBN: (纸本)3540293485

In this paper we generalize the iterated refinement method, introduced by the authors in [8], to a time-continuous inverse scale-space formulation. The iterated refinement procedure yields a sequence of convex variational problems, evolving toward the noisy image. The inverse scale space method arises as a limit for a penalization parameter tending to zero, while the number of iteration steps tends to infinity. For the limiting flow, similar properties as for the iterated refinement procedure hold. Specifically, when a discrepancy principle is used as the stopping criterion, the error between the reconstruction and the noise-free image decreases until termination, even if only the noisy image is available and a bound on the variance of the noise is known. The inverse flow is computed directly for one-dimensional signals, yielding high quality restorations. In higher spatial dimensions, we introduce a relaxation technique using two evolution equations. These equations allow accurate, efficient and straightforward implementation.

关键词： Image reconstruction

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variational, Geometric, and Level Set methods in computer vision - Third international Workshop, VLSM 2005, Proceedings

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3rd international Workshop on variational, Geometric, and Level Set methods in computer vision, VLSM 2005

ISBN: (纸本)3540293485

The proceedings contain 30 papers. The topics discussed include: a study of non-smooth convex flow decomposition;nonlinear inverse scale space methods for image restoration;towards PDE-based image compression;color image deblurring with impulsive noise;using an oriented PDE to repair image textures;from inpainting to active contours;entropy controlled Gauss-Markov random measure field models for early vision;global minimization of the active contour model with TV-inpainting and two-phase denoising;trimap segmentation for fast and user-friendly alpha matting;a variational approach for object contour tracking;a gradient descent procedure for variational dynamic surface problems with constraints;regularization of mappings between implicit manifolds of arbitrary dimension and codimension;and lens distortion calibration using level sets.

关键词： computer vision

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Skeletons of 3D shapes 1

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5th international conference on scale-space and PDE methods in computer vision

作者： Shah, J Northeastern Univ Dept Math Boston MA 02115 USA

ISBN: (数字)9783540320128

ISBN: (纸本)3540255478

A new method for determining skeletons of 3D shapes is described. It is a combination of the approach based on the "grass-fire" technique and Zhu's approach based on first finding portions of the shape where its width is approximately constant. The method specifically does not require presmoothing of the shape and is robust in the presence of noise. In an appendix, a method based on variational calculus is formulated for determining pruned, smoothed shape skeletons by minimizing A functional.

关键词： Three dimensional

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Discrete representation of top points via scale space tessellation

Discrete representation of top points via scale space tessel...

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5th international conference on scale space and PDE methods in computer vision, scale-space 2005

作者： Platel, B. Demirci, M. Fatih Shokoufandeh, A. Florack, L.M.J. Kanters, F.M.W. Ter Haar Romeny, B.M. Dickinson, S.J. Eindhoven University of Technology P.O. Box 513 5600 MB Eindhoven Netherlands Drexel University 3141 Chestnut Street Philadelphia PA 19104 United States University of Toronto 6 King's College Rd. Toronto Ont. M5S 3G4 Canada

In previous work, singular points (or top points) in the scale space representation of generic images have proven valuable for image matching. In this paper, we propose a construction that encodes the scale space description of top points in the form of a directed acyclic graph. This representation allows us to utilize graph matching algorithms for comparing images represented in terms of top point configurations instead of using solely the top points and their features in a point matching algorithm, as was done previously. The nodes of the graph represent the critical paths together with their top points. The edge set will capture the neighborhood distribution of vertices in scale space, and is constructed through a Delaunay triangulation scheme. We also will present a many-to-many matching algorithm for comparing such graph-based representations. This algorithm is based on a metric-tree representation of labelled graphs and their low-distortion embeddings into normed vector spaces via spherical encoding. This is a two-step transformation that reduces the matching problem to that of computing a distribution-based distance measure between two such embeddings. To evaluate the quality of our representation, two sets of experiments are considered. First, the stability of this representation under Gaussian noise of increasing magnitude is examined. In the second set of experiments, a series of recognition experiments is run on a small face database. © Springer-Verlag Berlin Heidelberg 2005.

关键词： Image processing

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Feature-based image analysis

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international JOURNAL OF computer vision 2003年第2-3期52卷 73-95页

作者： Lillholm, M Nielsen, M Griffin, LD IT Univ Copenhagen Copenhagen NV Denmark Kings Coll London London WC2R 2LS England

According to Marr's paradigm of computational vision the first process is an extraction of relevant features. The goal of this paper is to quantify and characterize the information carried by features using image-structure measured at feature-points to reconstruct images. In this way, we indirectly evaluate the concept of feature-based image analysis. The main conclusions are that (i) a reasonably low number of features characterize the image to such a high degree, that visually appealing reconstructions are possible, (ii) different feature-types complement each other and all carry important information. The strategy is to define metamery classes of images and examine the information content of a canonical least informative representative of this class. Algorithms for identifying these are given. Finally, feature detectors localizing the most informative points relative to different complexity measures derived from models of natural image statistics, are given.

关键词： features stochastic complexity statistics of natural images least commitment scale-space image reconstruction variational methods

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A distance measure and a feature likelihood map concept for scale-invariant model matching

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international JOURNAL OF computer vision 2003年第2-3期52卷 97-120页

作者： Laptev, I Lindeberg, T Royal Inst Technol Computat Vis & Act Percept Lab Dept Numer Anal & Comp Sci SE-10044 Stockholm Sweden

This paper presents two approaches for evaluating multi-scale feature-based object models. Within the first approach, a scale-invariant distance measure is proposed for comparing two image representations in terms of multi-scale features. Based on this measure, the maximisation of the likelihood of parameterised feature models allows for simultaneous model selection and parameter estimation. The idea of the second approach is to avoid an explicit feature extraction step and to evaluate models using a function defined directly from the image data. For this purpose, we propose the concept of a feature likelihood map, which is a function normalised to the interval [0, 1], and that approximates the likelihood of image features at all points in scale-space. To illustrate the applicability of both methods, we consider the area of hand gesture analysis and show how the proposed evaluation schemes can be integrated within a particle filtering approach for performing simultaneous tracking and recognition of hand models under variations in the position, orientation, size and posture of the hand. The experiments demonstrate the feasibility of the approach, and that real time performance can be obtained by pyramid implementations of the proposed concepts.

关键词： matching scale-space image features tracking recognition multi-scale representations

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