Guessing Tangents in Normal Flows

Given a flow field parallel to isophote normals, a normal flow field, we seek a unobservable tangential field as the minimum of a general energy functional of the total field. We generalize existing methods to any linear, differential operator order on the combined field while keeping the projection onto the isophote normal constant. We discuss invariant flow fields, present a novel iterative solution based on Euler-Lagrange equations, prove continuous convergence, and give synthetic examples for common energy functionals. Possible uses are: estimating physical flow in image sequences, estimating human growth processes, and co-warping textures in animation sequences.

[1]  Hans-Hellmut Nagel,et al.  An Investigation of Smoothness Constraints for the Estimation of Displacement Vector Fields from Image Sequences , 1983, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[2]  Andrew Blake,et al.  Visual Reconstruction , 1987, Deep Learning for EEG-Based Brain–Computer Interfaces.

[3]  Gunilla Borgefors.  Theory and applications of image analysis II : selected papers from the 9th Scandinavian Conference on Image Analysis , 1995 .

[4]  Gary E. Christensen,et al.  Large-deformation image registration using fluid landmarks , 2000, 4th IEEE Southwest Symposium on Image Analysis and Interpretation.

[5]  Berthold K. P. Horn,et al.  Determining Optical Flow , 1981, Other Conferences.

[6]  Jan J. Koenderink,et al.  Local structure of movement parallax of the plane , 1976 .

[7]  E. Adelson,et al.  Slow and Smooth: A Bayesian theory for the combination of local motion signals in human vision , 1998 .

[8]  Bo Markussen,et al.  Large deformation diffeomorphisms with application to optic flow , 2007, Comput. Vis. Image Underst..

[9]  Bo Markussen,et al.  Second Order Structure of Scale-Space Measurements , 2008, Journal of Mathematical Imaging and Vision.

[10]  David J. Fleet,et al.  Performance of optical flow techniques , 1994, International Journal of Computer Vision.

[11]  Ronald Fedkiw,et al.  Level set methods and dynamic implicit surfaces , 2002, Applied mathematical sciences.

[12]  Michael Kerckhove,et al.  Scale-Space and Morphology in Computer Vision , 2001, Lecture Notes in Computer Science 2106.

[13]  Bo Markussen,et al.  From Bayes to PDEs in Image Warping , 2006, Handbook of Mathematical Models in Computer Vision.

[14]  T. H. Gronwall.  Note on the Derivatives with Respect to a Parameter of the Solutions of a System of Differential Equations , 1919 .

[15]  Mads Nielsen,et al.  Computing Optic Flow by Scale-Space Integration of Normal Flow , 2001, Scale-Space.

[16]  Hans-Hellmut Nagel,et al.  Extending the 'Oriented Smoothness Constraint' into the Temporal Domain and the Estimation of Derivatives of Optical Flow , 1990, ECCV.

[17]  Jon Sporring,et al.  Direct estimation of first order optic flow , 1996 .

[18]  James A. Sethian,et al.  Level Set Methods and Fast Marching Methods , 1999 .

[19]  Mads Nielsen,et al.  Feature displacement interpolation , 1998, Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269).

[20]  David E. Breen,et al.  3D Metamorphosis Between Different Types of Geometric Models , 2001, Comput. Graph. Forum.

[21]  Joachim Weickert,et al.  Lucas/Kanade Meets Horn/Schunck: Combining Local and Global Optic Flow Methods , 2005, International Journal of Computer Vision.

[22]  Jens Arnspang,et al.  Optic Acceleration , 1988, [1988 Proceedings] Second International Conference on Computer Vision.

[23]  Marko Subasic,et al.  Level Set Methods and Fast Marching Methods , 2003 .

[24]  Thomas Brox,et al.  High Accuracy Optical Flow Estimation Based on a Theory for Warping , 2004, ECCV.

[25]  Joachim Weickert,et al.  A Theoretical Framework for Convex Regularizers in PDE-Based Computation of Image Motion , 2001, International Journal of Computer Vision.

[26]  K. Morton,et al.  Numerical Solution of Partial Differential Equations , 1995 .

[27]  Michael I. Miller,et al.  Landmark matching via large deformation diffeomorphisms , 2000, IEEE Trans. Image Process..

[28]  David E. Breen,et al.  A level-set approach for the metamorphosis of solid models , 1999, SIGGRAPH '99.

[29]  K. Morton,et al.  Numerical Solution of Partial Differential Equations: Introduction , 2005 .