Uniqueness of the Gaussian kernel for scale-space filtering. (English) Zbl 0574.93054
Scale-space filtering constructs hierarchic symbolic signal descriptions by transforming the signal into a continuum of versions of the original signal convolved with a kernel containing a scale or bandwidth parameter. It is shown that the Gaussian probability density function is the only kernel in a broad class for which first-order maxima and minima, respectively, increase and decrease when the bandwidth of the filter is increased. The consequences of this result are explored when the signal - or its image by a linear differential operator - is analyzed in terms of zero-crossing contours of the transform in scale-space.
MSC:
| 93E11 | Filtering in stochastic control theory |
| 60G35 | Signal detection and filtering (aspects of stochastic processes) |
| 62M20 | Inference from stochastic processes and prediction |
| 93E14 | Data smoothing in stochastic control theory |
| 94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |
