<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\section{Conclusion and perspectives}

\label{sec:conclusion}

In this paper we introduced a new edge detector based on a local analysis of
the image gradient and on the use of blurred segments to vehiculate an
estimation of the edge thickness.
It relies on directional scans of the image around maximal values of the
gradient magnitude, that have previously been presented in a former paper.
Despite of good performances obtained compared to existing detection methods
found in the literature, the former approach suffers of two major drawbacks.
It does not estimate the edge thickness so that many outliers are inserted
into the blurred segment and the provided estmation of the edge orientation 
is biased.
Then the scan direction is derived from a bounded blurred segment, that
inevitably restricts its value to a finite set, so that long edges may be
not completely detected.
We solved these limitations through two new concepts:
first the adaptive directional scans continuously that adjust the scan strip
to the detected blurred segment direction;
then the control of the assigned width based on the observation of the
blurred segment thickenning in the early stage of its expansion.

Expected gains in execution time linked to the suppression of a useless
repetition of the fine tracking stage were confirmed by the experimental
campaign both in supervised and unsupervised contexts.
The residual weakness is the high sensitivity to the initial conditions
despite of the valuable enhancement brought by the duplication of the
initial detection.
Disturbing gradient perturbations in the early stage of the edge expansion,
possibly due to the presence of close edges, can deeply affect the output
blurred segment.
In supervised context, the user can easily select a favourable area where
the awaited edge is dominant.
But this default remains quite sensible in unsupervised context.

In future works, we intend to provide some protection against this drawback
by scoring the detection result on the base of a characterization of the
initial context.
Then experimental validation of the consistency of the estimated width and
orientation values on real situations are planned in different application
fields.
In particular, straight edges are rich visual features for 3D scene
reconstruction from 2D images.
The preimage of the detected blurred segments,
i.e. the space of geometric entities which numerization matches this
blurred segment, may be used to compute some confidence level in the 3D
interpretations delivered, as a promising extension of former works
on discrete epipolar geometry \cite{NatsumiAl08}.

%\section*{Acknowledgements}
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