Martedě 30-4 ore 11.00 presso LIRA-Lab villa Bonino (piano terra).

**Marcello Demi**, CNR Institute of Clinical
Physiology, Pisa, Italy.

**Title
**The First Absolute Central Moment in Low Level Image
Processing

**Abstract
**The first absolute central moment belongs to the wide class of moments of n
order, which includes variance, skewness and kurtosis. However, the first
absolute central moment has not been analyzed in depth in the past and, in
particular, its properties have never been exploited in image processing. The
first absolute central moment is only used in robust statistics. Here the median
and the first absolute central moment are used to estimate the central value and
the width, respectively, of the distribution since both these measures are
robust against outliers.

However, the first absolute central moment supplies features of the utmost importance in image processing. Due to the absolute value involved, the first absolute central moment can be separated into two components: a positive deviation ep and a negative deviation en. Once ep and en are computed they can be combined. Derivative filters of both the first order and the second order can be obtained as well as mechanisms which are able to compensate the noise effects. Edges can be located and image key points such as corners, lines, line-endings and intersections between different discontinuities can be highlighted.

While the difference ep-en provides a result which is equivalent to that provided by a DoG filter, the sum ep+en provides a result which is analogous to that provided by a GoG filter. Therefore, both a first derivative operator and a second derivative operator can be obtained with the same filtering stage. However, ep and en are themselves two mathematical operators which reveal interesting properties. While en provides a ridge with the peak at the dark border of a gray level discontinuity, ep provides a ridge with the peak at the bright border. Moreover, the ridges provided by these two operators at a discontinuity partially overlap. The profile of the overlapping area is that of a thin ridge and the peak of the ridge locates the discontinuity; the greater the discontinuity, the higher the peak. Consequently, the function Min(positive deviation, |negative deviation|) provides both an edge map Mpn, similar to the zero-crossing map of an equivalent DoG filter, and the strength of each edge point. In addition to the Mpn map a local thresholding procedure also can be achieved by combining two ridge maps obtained when two different sets of low-pass filters are used.

Finally, another property emerges from the analysis of the mass center of the first absolute central moment. If the correct parameters of the operator are chosen, the mass center of the first absolute central moment p’, when computed at a starting point p near an edge, is closer to the edge than p, independently of the distance between p and the edge. Therefore, an iterative localization procedure can be developed by exploiting this property. When given an approximate starting contour the final contour of the structure in interest can be located by computing iteratively the mass center of the first absolute central moment at the points of the starting contour. The procedure is simple and converges in just a few iterations.