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T. Lindberg, "Effective Scale: A Natural Unit for Measuring ScaleSpace Lifetime," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 10, pp. 10681074, October, 1993.  
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@article{ 10.1109/34.254063, author = {T. Lindberg}, title = {Effective Scale: A Natural Unit for Measuring ScaleSpace Lifetime}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {15}, number = {10}, issn = {01628828}, year = {1993}, pages = {10681074}, doi = {http://doi.ieeecomputersociety.org/10.1109/34.254063}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Pattern Analysis and Machine Intelligence TI  Effective Scale: A Natural Unit for Measuring ScaleSpace Lifetime IS  10 SN  01628828 SP1068 EP1074 EPD  10681074 A1  T. Lindberg, PY  1993 KW  effective scale; scalespace lifetime measurement unit; image processing VL  15 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
A manner in which a notion of effective scale can be introduced in a formal way is developed. For continuous signals, a scaling argument directly gives a natural unit for measuring scalespace lifetime in terms of the logarithm of the ordinary scale parameter. That approach is, however, not appropriate for discrete signals since an infinite lifetime would be assigned to structures existing in the original signal. It is shown how such an effective scale parameter can be defined to give consistent results for both discrete and continuous signals. The treatment is based on the assumption that the probability that a local extremum disappears during a shortscale interval should not vary with scale. As a tool for the analysis, estimates are given of how the density of local extrema can be expected to vary with scale in the scalespace representation of different random noise signals both in the continuous and discrete cases.
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