Optic Flow from Multi-scale Dynamic Anchor Point Attributes

• Published in: Image Analysis and Recognition pp. 767 - 779
• Main Authors: Janssen, B. J., Florack, L. M. J., Duits, R., ter Haar Romeny, B. M.
• Format: Book Chapter Conference Proceeding
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 2006; Springer
• Series: Lecture Notes in Computer Science
• Subjects: Anchor Point; Applied sciences; Artificial intelligence; Computer science; control theory; systems; Exact sciences and technology; Image Sequence; Optic Flow; Pattern recognition. Digital image processing. Computational geometry; Scale Space; Singular Point; Computer vision; Image recognition; Image resolution; Scale space; Image processing; Sobolev space; Singular point; Dynamic properties; Aperture; Image analysis; Gaussian process; Image sequence; Sparse set; Variational calculus; Feasibility; Optical flow
• ISBN: 3540448918; 9783540448914
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/11867586_70

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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$<{{1}\over{2}}\%$\end{document} 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.