MOGHADDAMZADEH and BOURBAKIS algorithm

MOGHADDAMZADEH and BOURBAKIS Algorithm

Contrast between two pixels is given by the amplitude of the difference between two color vectors v and w:

$\begin{displaymath}\mbox{Contrast}_{v, w}= \sqrt{(R_v- R_w)^2+ (V_v- V_w)^2+ (B_v- B_w)^2}\end{displaymath}$

Fuzzy concept is expressed by means of a ``membership of a fuzzy subset'' function, expressed by:

$\begin{displaymath}\mu_C=\left\{\begin {array}{ll}0 & \mbox{if contrast} \le......Contrast- a_1}{a_2- a_1} & \mbox{otherwise}\end{array}\right.\end{displaymath}$

This function is applied to two values of contrasts:

the absolute contrast, which is contrast between the pixel being analysed and the average value of the area being expanded;
the relative contrast, which is contrast between the pixel being analysed and its following in the direction of propagation.

The values of thresholds a₁ and a₂, differ for each type of contrast. To avoid favouring a contrast in particular, the two values are amalgamated by an average operator which gives a criterion of homogeneity: if it is lower than a given threshold, the pixel considered is amalgamated in the area.

The approaches presented above are particularly adapted to a local processing starting from a ``seed'' point. For a more global processing, ``Split and merge'' technique is used:

the image is first ``split'' in small and very homogeneous areas,
then the small areas are aggregated with the neighbours to form more significant and relatively homogeneous areas.

This processing has certain similarities to a process of classification. The preliminary phase of ``splitting'' makes it possible to limit the number of aggregations and also to better tolerate small disparities, because the aggregation is done starting from average values. The order in which are considered the areas for the aggregation influences the final result.

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