Update pixel perimeter figure

diff --git a/fig/pixel_perimeter.tex b/fig/pixel_perimeter.tex
index e63e887ab891436612c3bb3ed22a7b6d46744713..d0904f63c444265f2eea46654236688f50fe0b01 100644 (file)
--- a/fig/pixel_perimeter.tex
+++ b/fig/pixel_perimeter.tex
@@ -1,37 +1,43 @@
 \centering
 \begin{tikzpicture}[scale=1.2]
-    \foreach \x in {0,...,3} {
-        \foreach \y in {0,...,3} {
+    \foreach \x in {0,...,4} {
+        \foreach \y in {0,...,4} {
             \node[tiny vertex] (\x\y) at (\x, \y) {};
         }
     }
-    \node[tiny vertex,draw] (a) at (1, 2) {};
-    \node[tiny vertex,draw] (b) at (1, 3) {};
-    \node[tiny vertex,draw] (c) at (2, 2) {};
-    \node[tiny vertex,draw] (d) at (2, 3) {};
-    \node[tiny vertex,draw] (e) at (2, 4) {};
-    \node[tiny vertex,draw] (f) at (3, 3) {};
-    \node[tiny vertex,draw] (g) at (3, 1) {};
-    \node[tiny vertex,draw] (h) at (2, 1) {};
-    \node[tiny vertex,draw] (i) at (2, 0) {};
+    \begin{scope}[shift={(0.5,0.5)}]
+        \draw[step=1cm,gray,very thin] (-.5,-.5) grid (3.5,3.5);
+    \end{scope}
 
-    \path[edge,-] (a) -- (b);
-    \path[edge,-] (a) -- (c);
-    \path[edge,-] (a) -- (d);
-    \path[edge,-] (a) -- (e);
-    \path[edge,-] (a) -- (f);
-    \path[edge,-] (a) -- (g);
-    \path[edge,-] (a) -- (h);
-    \path[edge,-] (a) -- (i);
+    \draw[very thick,blue] (1.5,1.5) rectangle (2.5,2.5);
 
-    \path[dash] (1, 2) -- +(35.785:4cm);
-    \path[dash] (1, 2) -- +(54.215:4cm);
+    \path[edge,-] (1,1) -- (3,2);
+    \path[edge,-] (1,1) -- (2,3);
 
-    \draw (1,2) +(35.785:3.1cm) arc (35.785:54.215:3.1cm);
-    \path (1,2) ++(45:3.4cm) node {$\Delta \phi$};
+    \path[edge,-] (2,1) -- (3,3);
+    \path[edge,-] (1,2) -- (3,3);
+
+    \path[edge,-] (2,1) -- (1,3);
+    \path[edge,-] (3,1) -- (2,3);
+
+    \path[edge,-] (3,1) -- (1,2);
+    \path[edge,-] (1,3) -- (3,2);
+
+    \node[tiny vertex,draw] at (1, 1) {};
+    \node[tiny vertex,draw] at (2, 1) {};
+    \node[tiny vertex,draw] at (3, 1) {};
+    \node[tiny vertex,draw] at (1, 2) {};
+    \node[tiny vertex,draw] at (3, 2) {};
+    \node[tiny vertex,draw] at (1, 3) {};
+    \node[tiny vertex,draw] at (2, 3) {};
+    \node[tiny vertex,draw] at (3, 3) {};
 
 \end{tikzpicture}
 \caption{%
-    BOP.
+    A selection of edges contributing to the wrong approximation of the
+    length of a single pixel's perimeter. The edges cross the perimeter
+    twice, but we count zero crossings in our approximation. This leads
+    to residual pixel noise in the restored image, when large
+    neighborhood stencils are used.
 }
 \label{fig:pixel_perimeter}