Principles for Automatic Scale Selection
Tony Lindeberg
Technical report ISRN KTH NA/P98/14SE.
Department of Numerical Analysis and Computing Science,
KTH (Royal Institute of Technology), S100 44 Stockholm, Sweden, August 1998.
In: B. Jähne (et al., eds.),
Handbook on Computer Vision and Applications,, volume 2, pp 239274,
Academic Press, Boston, USA, 1999.
Abstract
An inherent property of objects in the world is that they only exist
as meaningful entities over certain ranges of scale. If one aims at
describing the structure of unknown realworld signals, then a
multiscale representation of data is of crucial importance.
Whereas conventional scalespace theory provides a wellfounded
framework for dealing with image structures at different scales,
this theory does not directly address the problem of how to
select appropriate scales for further analysis.
This article outlines a systematic methodology of how mechanisms
for automatic scale selection can be formulated in the problem
domains of feature detection and image matching (flow estimation),
respectively.
For feature detectors expressed in terms of Gaussian derivatives,
hypotheses about interesting scale levels can be generated from
scales at which normalized measures of feature strength assume
local maxima with respect to scale. It is shown how the notion
of $\gamma$normalized derivatives arises by necessity given
the requirement that the scale selection mechanism should
commute with rescalings of the image pattern. Specifically,
it is worked out in detail how feature detection algorithms
with automatic scale selection can be formulated for the
problems of edge detection, blob detection, junction detection,
ridge detection and frequency estimation. A general property
of this scheme is that the selected scale levels reflect
the size of the image structures.
When estimating image deformations, such as in image matching
and optic flow computations, scale levels with associated
deformation estimates can be selected from the scales at
which normalized measures of uncertainty assume local minima
with respect to scales. It is shown how an integrated scale
selection and flow estimation algorithm has the qualitative
properties of leading to the selection of coarser scales
for larger size image structures and increasing noise level,
whereas it leads to the selection of finer scales
in the neighbourhood of flow field discontinuities.
Keywords:
scale, scalespace, scale selection, normalized derivative,
feature detection, blob detection, corner detection,
frequency estimation, Gaussian derivative, scalespace,
multiscale representation, computer vision
Postscript:
(8.2 Mb)
PDF:
(2.3 Mb)
This article is largely a tutorial summary of selected parts of the
following material:

T. Lindeberg (1996)
"Feature detection with automatic scale selection",
Tech. Rep. ISRN KTH/NA/P96/18SE, KTH, May 1996.
Int. J. of Computer Vision, vol 30, number 2, pp 77116, 1998.
Earlier version in 8th Scand Conf on Image Analysis,
Tromso, Norway, 1993.

T. Lindeberg (1996)
"Edge detection and ridge detection with automatic scale selection",
Tech. Rep. ISRN KTH/NA/P96/18SE, KTH, May 1996.
Int. J. of Computer Vision, vol 30, number 2, pp 117154, 1998.
Shortened version in IEEE Comp. Soc. Conf. on Computer Vision and
Pattern Recognition, CVPR'96, San Francisco, California, 465470, 1996.

T. Lindeberg (1996)
"A scale selection principle for estimating image deformations,
Tech. Rep. ISRN KTH/NA/P96/16SE, KTH, May 1996.
Image and Vision Computing, vol. 16, no. 14, pp. 961977, 1998.
Earlier version in 5th Int Conf on Computer Vision,
Boston, Massachussetts, 1995.

T. Lindeberg (1994)
"ScaleSpace Theory in Computer Vision", (chapter 13),
Kluwer Academic Publishers.
Sample applications of these scale selection principles to various
problems in computer vision can be found in:

A. Almansa and T. Lindeberg
``Enhancement of fingerprint images using shapeadaptated
scalespace operators'',
Technical report ISRN KTH/NA/R99/01SE.
IEEE Transactions on Image Processing,
volume 9, number 12, pp 20272042, 2000
(PostScript 2.7 Mb)
(PDF 1.5 Mb)
.
Earlier versions presented as
Technical report ISRN KTH/NA/P98/03SE
and as
Chapter 3 in J. Sporring, M. Nielsen, L. Florack, and P. Johansen (eds.)
Gaussian ScaleSpace Theory: Proc. PhD School on ScaleSpace Theory
.
(Copenhagen, Denmark, May 1996), Kluwer Academic Publishers/Springer, 1997.

L. Bretzner and T. Lindeberg:
``Feature tracking with automatic selection of spatial scales'',
Computer Vision and Image Understanding.
vol. 71, pp. 385392, Sept. 1998.

L. Bretzner and T. Lindeberg:
``Qualitative multiscale feature hierarchies for object tracking'',
,
Proc. 2nd International Conference on ScaleSpace Theory in Computer Vision,
Corfu, Greece, September 1999.
Springer Lecture Notes in Computer Science. (in press)

J. Garding and T. Lindeberg:
``Direct computation of shape cues using scaleadapted
spatial derivative operators'',
International Journal of Computer Vision,
vol 17(2), pp. 163191, 1996.

T. Lindeberg and J. Garding:
``Shapeadapted smoothing in estimation of 3D depth cues from
affine distortions of local 2D brightness structure'',
in Image and Vision Computing,
vol. 15, pp. 415434, 1997.

T. Lindeberg
``On automatic selection of temporal scales in timecausal scalespace''
.
In: Proc. AFPAC'97: Algebraic Frames for the PerceptionAction Cycle"
(G. Sommer and J. J. Koenderink, eds.),
vol. 1315 of Lecture Notes in Computer Science, (Kiel, Germany), pp.
94113, Springer Verlag, Berlin, Sept. 1997.

T. Lindeberg and M.X. Li
``Segmentation and classification of edges using
minimum description length approximation
and complementary junction cues'',
Proc. 9th Scandinavian Conference on Image Processing,
Uppsala, Sweden,
June 1995, pages 767776.
Extended version in
Computer Vision and Image Understanding,
vol. 67, no. 1, pp. 8898, 1997

K. Wiltschi, T. Lindeberg and A. Pinz
``Classification of carbide distributions using scale selection and
directional distributions'',
Proc. 4th International Conference on Image Processing ICIP'97,
(Santa Barbara, California), vol. II, pp. 122125, Oct. 1997.
Other tutorial summaries on related topics can be found in:

T. Lindeberg,
"Automatic scale selection as a preprocessing stage
to interpreting the visual world",
Invited paper in: D. Chetverikov and T. Sziranyi (eds)
Proc. Fundamental Structural Properties in
Image and Pattern Analysis FSPIPA'99
(Budapest, Hungary),
September 67, 1999. Schriftenreihen der Österreichischen Computer
Gesellschaft, volume 130, pp 923.

T. Lindeberg,
``Scalespace:
A framework for handling image structures at multiple scales'',
Proc. CERN School of Computing,
Egmond aan Zee, The Netherlands, 821 September, 1996.
Responsible for this page:
Tony Lindeberg
