From 2e5848d05424d5ef47a04d112ceb4d9c465c969b Mon Sep 17 00:00:00 2001 From: =?utf8?q?Bj=C3=B8rn=20Rustad?= Date: Fri, 19 Dec 2014 10:22:58 +0100 Subject: [PATCH] Update pixel perimeter figure --- fig/pixel_perimeter.tex | 54 +++++++++++++++++++++++------------------ 1 file changed, 30 insertions(+), 24 deletions(-) diff --git a/fig/pixel_perimeter.tex b/fig/pixel_perimeter.tex index e63e887..d0904f6 100644 --- 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} -- 2.47.3