Original formulation. next up previous
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Original formulation.

When Witkin [] introduced the term scale-space, he was concerned with one-dimensional signals and observed that new local extrema cannot be created in this family. Since differentiation commutes with convolution,
this non-creation property applies also to any tex2html_wrap_inline915-order spatial derivative computed from the scale-space representation. Figure 2(b) illustrates this property, by showing zero-crossings of the second derivative of the smoothed signal at different scales. Note that the trajectories of zero-crossings in scale-space form paths across scales that are never closed from below. This property does, however, not extend to dimensions higher than one.

Tony Lindeberg
Tue Jul 1 14:57:47 MET DST 1997