diff --git a/Article/notions.tex b/Article/notions.tex
index 0830d85c8bbeb0a07d34bdb196df96f2fefadeb6..f2e631180848faf9ee7a0320a02ba2bfee95dbe3 100755
--- a/Article/notions.tex
+++ b/Article/notions.tex
@@ -29,7 +29,7 @@ $\mathcal{L}$ of arithmetical width $w(\mathcal{L}) = \varepsilon$.
 \end{definition}
 
 A linear-time algorithm to recognize a blurred segment of assigned width
-$\varepsilon$ \cite{DebledAl05} is used in the work.
+$\varepsilon$ \cite{DebledAl05} is used in this work.
 It is based on an incremental growth of the convex hull of the blurred
 segment when adding each point $P_i$ successively.
 The minimal width $\mu$ of the blurred segment $\mathcal{B}$ is the
@@ -56,7 +56,7 @@ and $\mathcal{B}_i = \mathcal{B}_{i-1}$.}
 \end{figure}
 
 Associated to this primitive, the following definition of a directional scan
-based on digital straight lines is used in this work.
+ is an important point the proposed method.
 
 \subsection{Directional scan}
 
@@ -163,6 +163,6 @@ $\mathcal{N}_i^{C,\vec{D},w}$:
 \mathcal{D}^{C,\vec{D},w}
 = \mathcal{L}(Y_D,~ -X_D,~ c_3 - w / 2,~ w) \\
 \mathcal{N}_i^{C,\vec{D},w} = \mathcal{L}(X_D,~ Y_D,~
-               c_4 - w / 2 + i\cdot w,~ \nu_{\vec{D}}
+               c_4 - w / 2 + i\cdot w,~ \nu_{\vec{D}})
 \end{array} \right.
 \end{equation}