Abstract
The deep structure of scale-space of a signal refers to tracking the zero-crossings of differential invariants across scales. In classical approaches, feature tracking is performed by neighbor search between consecutive levels of a discrete collection of scales. Such an approach is prone to noise and tracking errors and provides just a coarse representation of the deep structure. We propose a new approach that allows us to construct a virtually continuous scale-space for scalar functions, supporting reliable tracking and a fine representation of the deep structure of their critical points. Our approach is based on a piecewise-linear approximation of the scale-space, in both space and scale dimensions. We present results on terrain data and range images.
Chapter PDF
Similar content being viewed by others
References
Bauer, D., Peikert, R.: Vortex tracking in scale-space. In: Proceedings of the Symposium on Data Visualisation, VISSYM 2002, p. 233. Eurographics Association, Aire-la-Ville (2002)
Correa, C., Ma, K.L.: Size-based transfer functions: A new volume exploration technique. IEEE Trans. Visualization and Computer Graphics 14, 1380–1387 (2008)
de Ferranti, J.: Viewfinder panoramas (2012), http://www.viewfinderpanoramas.org/dem3.html
Gingold, Y.I., Zorin, D.: Controlled-topology filtering. Comput. Aided Des. 39(8), 676–684 (2007)
Gupta, S., Castleman, K., Markey, M., Bovik, A.: Texas 3d face recognition database. In: 2010 IEEE Southwest Symposium on Image Analysis Interpretation (SSIAI), pp. 97–100 (2010)
Kindlmann, G.L., Estepar, R.S.J., Smith, S.M., Westin, C.F.: Sampling and visualizing creases with scale-space particles. IEEE Trans. Visualization and Computer Graphics 15(6), 1415–1424 (2009)
Klein, T., Ertl, T.: Scale-space tracking of critical points in 3d vector fields. In: Topology-based Methods in Visualization, Mathematics and Visualization, pp. 35–50. Springer (2007)
Koenderink, J.J.: The structure of images. Biological Cybernetics 50, 363–370 (1984)
Lindeberg, T.: Scale-Space Theory in Computer Vision. Kluwer Academic Publishers (1994)
Price, K.: Annotated computer vision bibliography, http://www.visionbib.com/bibliography/contents.html
Reininghaus, J., Kotava, N., Guenther, D., Kasten, J., Hagen, H., Hotz, I.: A scale space based persistence measure for critical points in 2d scalar fields. IEEE Trans. Visualization and Computer Graphics 17(12), 2045–2052 (2011)
Witkin, A.P.: Scale-space filtering. In: Proc. 8th Int. Joint Conf. Art. Intell., pp. 1019–1022. Karlsruhe, Germany (1983)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rocca, L., Puppo, E. (2013). A Virtually Continuous Representation of the Deep Structure of Scale-Space. In: Petrosino, A. (eds) Image Analysis and Processing – ICIAP 2013. ICIAP 2013. Lecture Notes in Computer Science, vol 8157. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41184-7_53
Download citation
DOI: https://doi.org/10.1007/978-3-642-41184-7_53
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-41183-0
Online ISBN: 978-3-642-41184-7
eBook Packages: Computer ScienceComputer Science (R0)