Real-Time Scale Selection in Hybrid Multi-scale Representations

  • Tony Lindeberg
  • Lars Bretzner
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2695)


Local scale information extracted from visual data in a bottom-up manner constitutes an important cue for a large number of visual tasks. This article presents a framework for how the computation of such scale descriptors can be performed in real time on a standard computer.

The proposed scale selection framework is expressed within a novel type of multi-scale representation, referred to as hybrid multi-scale representation, which aims at integrating and providing variable trade-offs between the relative advantages of pyramids and scale-space representation, in terms of computational efficiency and computational accuracy. Starting from binomial scale-space kernels of different widths, we describe a family pyramid representations, in which the regular pyramid concept and the regular scale-space representation constitute limiting cases. In particular, the steepness of the pyramid as well as the sampling density in the scale direction can be varied.

It is shown how the definition of γ-normalized derivative operators underlying the automatic scale selection mechanism can be transferred from a regular scale-space to a hybrid pyramid, and two alternative definitions are studied in detail, referred to as variance normalization and l p-normalization. The computational accuracy of these two schemes is evaluated, and it is shown how the choice of sub-sampling rate provides a trade-off between the computational efficiency and the accuracy of the scale descriptors. Experimental evaluations are presented for both synthetic and real data. In a simplified form, this scale selection mechanism has been running for two years, in a real-time computer vision system.


Interest Point Scale Level Scale Descriptor Scale Selection Blob Detection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Almansa, A. & Lindeberg, T. (2000), ‘Fingerprint enhancement by shape adaptation of scale-space operators with automatic scale-selection’, IEEE Transactions on Image Processing 9(12), 2027–2042.zbMATHCrossRefMathSciNetGoogle Scholar
  2. Bretzner, L., Laptev, I. & Lindeberg, T. (2002), Hand-gesture recognition using multiscale colour features, hierarchical features and particle filtering, Face and Gesture’02, 63–74.Google Scholar
  3. Bretzner, L. & Lindeberg, T. (1998), ‘Feature tracking with automatic selection of spatial scales’, Computer Vision and Image Understanding 71(3), 385–392.CrossRefGoogle Scholar
  4. Burt, P. J. & Adelson, E. H. (1983), ‘The Laplacian pyramid as a compact image code’, IEEE Trans. Comm. 9:4, 532–540.CrossRefGoogle Scholar
  5. Chomat, O., de Verdiere, V., Hall, D. & Crowley, J. (2000), Local scale selection for Gaussian based description techniques, ECCV’00, Springer LNCS 1842, 117–133.Google Scholar
  6. Comaniciu, D., Ramesh, V. & Meer, P. (2001), The variable bandwidth mean shift and data-driven scale selection, ICCV’01, 438–445.Google Scholar
  7. Crowley, J. L. & Parker, A. C. (1984), ‘A representation for shape based on peaks and ridges in the Difference of Low-Pass Transform’, IEEE-PAMI 6(2), 156–170.Google Scholar
  8. Eberly, D., Gardner, R., Morse, B., Pizer, S. & Scharlach, C. (1994), ‘Ridges for image analysis’, J. Math. Im. Vis. 4(4), 353–373.CrossRefGoogle Scholar
  9. Elder, J. H. & Zucker, S. W. (1996), Local scale control for edge detection and blur estimation, in ‘ECCV’96’, 57–69..Google Scholar
  10. Florack, L. M. J. (1997), Image Structure, Kluwer, Netherlands.Google Scholar
  11. Frangi, A. F., Niessen, W. J., Hoogeveen, R. M., van Walsum, T. & Viergever, M. A. (1999), Quantitation of vessel morphology from 3D MRI, ‘MICCAI, 358–367.Google Scholar
  12. Hadjidemetriou, E., Grossberg, M. D. & Nayar, S. K. (2002), Resolution selection using generalized entropies of multiresolution histograms, ECCV’02, Springer LNCS 2350, 220–235.Google Scholar
  13. Hall, D., de Verdiere, V. & Crowley, J. (2000), Object recognition using coloured receptive fields, ECCV’00, Springer LNCS 1842, 164–177.Google Scholar
  14. Jägersand, M. (1995), Saliency maps and attention selection in scale and spatial coordinates: An information theoretic approach, ICCV’95, 195–202.Google Scholar
  15. Jähne, B. (1995), Digital Image Processing, Springer-Verlag.Google Scholar
  16. Kadir, T. & Brady, M. (2001), ‘Saliency, scale and image description’, IJCV 45, 83–105.zbMATHCrossRefGoogle Scholar
  17. Koenderink, J. J. (1984), ‘The structure of images’, Biol. Cyb. 50, 363–370.zbMATHCrossRefMathSciNetGoogle Scholar
  18. Koller, T. M., Gerig, G., Szèkely, G. & Dettwiler, D. (1995), Multiscale detection of curvilinear structures in 2-D and 3-D image data, ICCV’95, 864–869.Google Scholar
  19. Laptev, I. & Lindeberg, T. (2001), Tracking of multi-state hand models using particle filtering and a hierarchy of multi-scale image features, Scale-Space’01, Springer LNCS 2106, 63–74.Google Scholar
  20. Lindeberg, T. (1993a), ‘Detecting salient blob-like image structures and their scales with a scale-space primal sketch: A method for focus-of-attention’, IJCV 11(3), 283–318.CrossRefGoogle Scholar
  21. Lindeberg, T. (1993b), On scale selection for differential operators, SCIA’93, 857–866.Google Scholar
  22. Lindeberg, T. (1994), Scale-Space Theory in Computer Vision, Kluwer, Netherlands.Google Scholar
  23. Lindeberg, T. (1998a), ‘Edge detection and ridge detection with automatic scale selection’, IJCV 30(2), 117–154.CrossRefGoogle Scholar
  24. Lindeberg, T. (1998b), ‘Feature detection with automatic scale selection’, IJCV 30(2), 77–116.Google Scholar
  25. Lindeberg, T. (1998c), ‘A scale selection principle for estimating image deformations’, Image and Vision Computing 16(14), 961–977.CrossRefGoogle Scholar
  26. Lindeberg, T. & Bretzner, L (2003), Real-time scale selection in hybrid multi-scale representations, Technical report, KTH, Stockholm, Sweden.Google Scholar
  27. Lorenz, C., Carlsen, I.-C., Buzug, T. M., Fassnacht, C. & Weese, J. (1997), Multiscale line segmentation with automatic estimation of width contrast and tangential direction in 2D and 3D medical images, CVRMed-MRCAS’97, Springer LNCS 1205, 233–242.CrossRefGoogle Scholar
  28. Lowe, D. (1999), Object recognition from local scale-invariant features, ICCV’99, 1150–1157.Google Scholar
  29. Majer, P. (2001), The influence of the γ-parameter on feature detection with automatic scale selection, Scale-Space’01, Springer LNCS 2106, 245–254.Google Scholar
  30. Mikolajczyk, K. & Schmid, C. (2002), An affine invariant interest point detector, ECCV’02, Springer LNCS 2350, 128–142.Google Scholar
  31. Nielsen, M. & Lillholm, M. (2001), What do features tell about images, Scale-Space’01, Springer LNCS 2106, 39–50.Google Scholar
  32. Niessen, W. & Maas, R. (1996), Optic flow and stereo, in J. Sporring et al (eds) Gaussian Scale-Space Theory, Kluwer.Google Scholar
  33. Pedersen, K. S. & Nielsen, M. (2000), ‘The Hausdorff dimension and scale-space normalisation of natural images’, J. Visual Com. and Im. Repr. 11(2), 266–277.CrossRefGoogle Scholar
  34. Pedersen, K. S. & Nielsen, M. (2001), Computing optic flow by scale-space integration of normal flow, Scale-Space’01, Springer LNCS 2106, 14–25.Google Scholar
  35. Pizer, S. M., Burbeck, C. A., Coggins, J. M., Fritsch, D. S. & Morse, B. S. (1994), ‘Object shape before boundary shape: Scale-space medial axis’, J. Math. Im. Vis. 4, 303–313.CrossRefGoogle Scholar
  36. Sato, Y., Nakajima, S., Shiraga, N., Atsumi, H., Yoshida, S., Koller, T., Gerig, G. & Kikinis, R. (1998), ‘3D multi-scale line filter for segmentation and visualization of curvilinear structures in medical images’, Medical Image Analysis 2(2), 143–168.CrossRefGoogle Scholar
  37. Simoncelli, E. P. & Freeman, W. T. (1995), The steerable pyramid: A flexible architecture for multi-scale derivative computation, ICIP’95, 444–447.Google Scholar
  38. Sporring, J. & Weickert, J. A. (1999), ‘Information measures in scale-spaces’, IEEE-IT 45(3), 1051–1058.zbMATHCrossRefMathSciNetGoogle Scholar
  39. Staal, J., Kalitzin, S., ter Haar Romeny, B. & Viergever, M. (1999), Detection of critical structures in scale-space, Scale-Space’99, Springer LNCS 1682, 105–116.Google Scholar
  40. Witkin, A. P. (1983), Scale-space filtering, 8th IJCAI, pp. 1019–1022.Google Scholar
  41. Yacoob, Y. & Davis, L. S. (1997), Estimating image motion using temporal multi-scale models of flow and acceleration. In: Motion-Based Recognition, Kluwer.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Tony Lindeberg
    • 1
  • Lars Bretzner
    • 1
  1. 1.Computational Vision and Active Perception Laboratory (CVAP), Department of Numerical Analysis and Computer ScienceKTHStockholmSweden

Personalised recommendations