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Update filter example

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Martin Thoma 2017-01-12 14:57:41 +01:00
parent b73c601641
commit a2fee03a8a
3 changed files with 172 additions and 17 deletions
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169
tikz/convolution-linear/convolution-linear.tex
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@ -9,19 +9,20 @@
\newcommand{\filtery}{2.2} \newcommand{\filtery}{2.2}
\newcommand{\filteroffset}{1} \newcommand{\filteroffset}{1}
\newcommand{\filterxres}{12}
\newcommand{\imagesize}{7} \newcommand{\imagesize}{7}
\newcommand{\imagex}{0} \newcommand{\imagex}{0}
\newcommand{\imagey}{0} \newcommand{\imagey}{0}
\newcommand{\imageoffset}{2} \newcommand{\imageoffset}{2}
\newcommand{\outx}{13} \newcommand{\outx}{16}
\newcommand{\outy}{0} \newcommand{\outy}{0}
\newcommand{\outoffset}{2} \newcommand{\outoffset}{2}
\newcommand{\percx}{1} \newcommand{\percx}{1}
\newcommand{\percy}{2} \newcommand{\percy}{2}
\begin{tikzpicture} \begin{tikzpicture}
% ,circle,thick,draw=black,fill=black,minimum width=4pt,minimum height=4pt
\tikzstyle{point}=[draw=none,inner sep=0pt] \tikzstyle{point}=[draw=none,inner sep=0pt]
@ -45,7 +46,7 @@
\outy+\percy+1+\percx*\outoffset/\imagesize+1*\outoffset/\imagesize+1+1*\outoffset/\imagesize) {}; \outy+\percy+1+\percx*\outoffset/\imagesize+1*\outoffset/\imagesize+1+1*\outoffset/\imagesize) {};
\node (o4)[point] at (\outx+\percx+1, \node (o4)[point] at (\outx+\percx+1,
\outy+\percy+2+\percx*\outoffset/\imagesize+1*\outoffset/\imagesize) {}; \outy+\percy+2+\percx*\outoffset/\imagesize+1*\outoffset/\imagesize) {};
\draw[fill=black] (o1.center) -- (o2.center) -- (o3.center) -- (o4.center) -- (o1.center); \draw[fill=gray] (o1.center) -- (o2.center) -- (o3.center) -- (o4.center) -- (o1.center);
% draw image % draw image
\foreach \x in {0,...,\imagesize} \foreach \x in {0,...,\imagesize}
@ -61,6 +62,13 @@
\draw (\filterx, \filtery+\x) -- (\filterx+\filtersize, \filtery+\x+\filteroffset); \draw (\filterx, \filtery+\x) -- (\filterx+\filtersize, \filtery+\x+\filteroffset);
} }
% draw filter result
\foreach \x in {0,...,\filtersize}
{
\draw (\filterxres+\x, \filtery+\x*\filteroffset/\filtersize) -- (\filterxres+\x, \filtery+\filtersize+\x*\filteroffset/\filtersize);
\draw (\filterxres, \filtery+\x) -- (\filterxres+\filtersize, \filtery+\x+\filteroffset);
}
% draw out % draw out
\foreach \x in {0,...,\imagesize} \foreach \x in {0,...,\imagesize}
{ {
@ -68,21 +76,148 @@
\draw (\outx, \outy+\x) -- (\outx+\imagesize, \outy+\x+\outoffset); \draw (\outx, \outy+\x) -- (\outx+\imagesize, \outy+\x+\outoffset);
} }
\node at (\imagex + \imagesize/2,\imagey + \imagesize + 2) {$I \in \mathbb{R}^{\imagesize \times \imagesize}$}; \node at (\imagex + \imagesize/2,\imagey + \imagesize + 2) {\Huge $I \in \mathbb{R}^{\imagesize \times \imagesize}$};
\node at (\filterx + \filtersize/2,\filtery + \filtersize + 2) {$F \in \mathbb{R}^{\filtersize \times \filtersize}$}; \node[text width=4cm, align=center] at (\filterx + \filtersize/2,\filtery + \filtersize - 4) {\large Filter kernel\\$F \in \mathbb{R}^{\filtersize \times \filtersize}$};
\node at (\outx + \imagesize/2,\outy + \imagesize + 2) {$I' \in \mathbb{R}^{\imagesize \times \imagesize}$}; \node[text width=4cm, align=center] at (\filterx + 4 + \filtersize/2,\filtery + \filtersize - 4) {\large Result of point-wise multiplication};
\node[draw,circle] (sumsymb) at (\filterx + \filtersize+1,\filtery + \filtersize/2 + \filteroffset-0.5) {$\sum$}; \node at (\outx + \imagesize/2,\outy + \imagesize + 2) {\Huge $I' \in \mathbb{R}^{\imagesize \times \imagesize}$};
\draw[dashed] (1.5, 2.9) -- (10.5, 2.9) -- (sumsymb.center); % Start image (left to right, top to bottom)
\draw[dashed] (1.5, 2.9+\filtersize-1) -- (10.5, 2.9+\filtersize-1) -- (sumsymb.center); \node[draw=none] at (0.5, 6.6) {\large 104};
\draw[dashed] (1.5+\filtersize-1, 2.9+\filtersize-1+2*\filteroffset/3) -- (10.5+\filtersize-1, 2.9+\filtersize-1+2*\filteroffset/3) -- (sumsymb.center); \node[draw=none] at (1.5, 6.9) {\large 116};
\draw[dashed] (1.5+\filtersize-1, 2.9+2*\filteroffset/3) -- (10.5+\filtersize-1, 2.9+2*\filteroffset/3) -- (sumsymb.center); \node[draw=none] at (2.5, 7.2) {\large 116};
\draw[dashed] (sumsymb.center) -- (15, 4); \node[draw=none] at (3.5, 7.5) {\large 112};
\node[draw=none] at (4.5, 7.8) {\large 58};
\node[draw=none] at (5.5, 8.1) {\large 47};
\node[draw=none] at (6.5, 8.4) {\large 47};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\node[draw,circle,fill=white] at (5.5, 2.9) {$+$}; \node[draw=none] at (0.5, 5.6) {\large 109};
\node[draw,circle,fill=white] at (5.5+\filtersize-1, 2.9+2*\filteroffset/3) {$+$}; \node[draw=none] at (1.5, 5.9) {\large 97};
\node[draw,circle,fill=white] at (5.5+\filtersize-1, 2.9+2*\filteroffset/3+\filtersize-1) {$+$}; \node[draw=none] at (2.5, 6.2) {\large 114};
\node[draw,circle,fill=white] at (5.5, 2.9+\filtersize-1) {$+$}; \node[draw=none] at (3.5, 6.5) {\large 116};
\node[draw,circle,fill=white] at (sumsymb.center) {$\sum$}; \node[draw=none] at (4.5, 6.8) {\large 105};
\node[draw=none] at (5.5, 7.1) {\large 110};
\node[draw=none] at (6.5, 7.4) {\large 45};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\node[draw=none] at (0.5, 4.6) {\large 116};
\node[draw=none] at (1.5, 4.9) {\large 104};
\node[draw=none] at (2.5, 5.2) {\large 111};
\node[draw=none] at (3.5, 5.5) {\large 109};
\node[draw=none] at (4.5, 5.8) {\large 97};
\node[draw=none] at (5.5, 6.1) {\large 46};
\node[draw=none] at (6.5, 6.4) {\large 100};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\node[draw=none] at (0.5, 3.6) {\large 101};
\node[draw=none] at (1.5, 3.9) {\large 47};
\node[draw=none] at (2.5, 4.2) {\large 109};
\node[draw=none] at (3.5, 4.5) {\large 97};
\node[draw=none] at (4.5, 4.8) {\large 115};
\node[draw=none] at (5.5, 5.1) {\large 116};
\node[draw=none] at (6.5, 5.4) {\large 101};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\node[draw=none] at (0.5, 2.6) {\large 114};
\node[draw=none] at (1.5, 2.9) {\large 47};
\node[draw=none] at (2.5, 3.2) {\large 99};
\node[draw=none] at (3.5, 3.5) {\large 97};
\node[draw=none] at (4.5, 3.8) {\large 116};
\node[draw=none] at (5.5, 4.1) {\large 99};
\node[draw=none] at (6.5, 4.4) {\large 97};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\node[draw=none] at (0.5, 1.6) {\large 116};
\node[draw=none] at (1.5, 1.9) {\large 99};
\node[draw=none] at (2.5, 2.2) {\large 97};
\node[draw=none] at (3.5, 2.5) {\large 116};
\node[draw=none] at (4.5, 2.8) {\large 46};
\node[draw=none] at (5.5, 3.1) {\large 112};
\node[draw=none] at (6.5, 3.4) {\large 104};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\node[draw=none] at (0.5, 0.6) {\large 112};
\node[draw=none] at (1.5, 0.9) {\large 63};
\node[draw=none] at (2.5, 1.2) {\large 118};
\node[draw=none] at (3.5, 1.5) {\large 61};
\node[draw=none] at (4.5, 1.8) {\large 49};
\node[draw=none] at (5.5, 2.1) {\large 46};
\node[draw=none] at (6.5, 2.4) {\large 48};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Filter
\node[draw=none] at ( 8.5, 4.8) {\large 9};
\node[draw=none] at ( 9.5, 5.1) {\large -3};
\node[draw=none] at (10.5, 5.4) {\large -1};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\node[draw=none] at ( 8.5, 3.8) {\large -6};
\node[draw=none] at ( 9.5, 4.1) {\large 5};
\node[draw=none] at (10.5, 4.4) {\large 3};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\node[draw=none] at ( 8.5, 2.8) {\large 2};
\node[draw=none] at ( 9.5, 3.1) {\large -8};
\node[draw=none] at (10.5, 3.4) {\large 0};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Result
\node[draw=none] at (12.5, 4.8) {\large 936};
\node[draw=none] at (13.5, 5.1) {\large -333};
\node[draw=none] at (14.5, 5.4) {\large -109};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\node[draw=none] at (12.5, 3.8) {\large -282};
\node[draw=none] at (13.5, 4.1) {\large 545};
\node[draw=none] at (14.5, 4.4) {\large 291};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\node[draw=none] at (12.5, 2.8) {\large 94};
\node[draw=none] at (13.5, 3.1) {\large -792};
\node[draw=none] at (14.5, 3.4) {\large 0};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Result image (left to right, top to bottom)
% [[ -4 -254 -498 -662 -849 -642 -187]
\node[draw=none] at (16.5, 6.6) {\large -4};
\node[draw=none] at (17.5, 6.9) {\large -254};
\node[draw=none] at (18.5, 7.2) {\large -498};
\node[draw=none] at (19.5, 7.5) {\large -662};
\node[draw=none] at (20.5, 7.8) {\large -849};
\node[draw=none] at (21.5, 8.1) {\large -642};
\node[draw=none] at (22.5, 8.4) {\large 187};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% [-520 45 240 211 388 215 -861]
\node[draw=none] at (16.5, 5.6) {\large-520};
\node[draw=none] at (17.5, 5.9) {\large 45};
\node[draw=none] at (18.5, 6.2) {\large 240};
\node[draw=none] at (19.5, 6.5) {\large 211};
\node[draw=none] at (20.5, 6.8) {\large 388};
\node[draw=none] at (21.5, 7.1) {\large 215};
\node[draw=none] at (22.5, 7.4) {\large-861};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% [-340 559 -105 185 -138 -180 503]
\node[draw=none] at (16.5, 4.6) {\large -340};
\node[draw=none] at (17.5, 4.9) {\large 559};
\node[draw=none] at (18.5, 5.2) {\large -105};
\node[draw=none] at (19.5, 5.5) {\large 185};
\node[draw=none] at (20.5, 5.8) {\large -138};
\node[draw=none] at (21.5, 6.1) {\large -180};
\node[draw=none] at (22.5, 6.4) {\large 503};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% [-718 429 350 173 251 268 -655]
\node[draw=none] at (16.5, 3.6) {\large -718};
\node[draw=none] at (17.5, 3.9) {\large 429};
\node[draw=none] at (18.5, 4.2) {\large 350};
\node[draw=none] at (19.5, 4.5) {\large 173};
\node[draw=none] at (20.5, 4.8) {\large 251};
\node[draw=none] at (21.5, 5.1) {\large 268};
\node[draw=none] at (22.5, 5.4) {\large -655};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% [-567 -53 -75 80 571 -128 24]
\node[draw=none] at (16.5, 2.6) {\large -567};
\node[draw=none] at (17.5, 2.9) {\large -53};
\node[draw=none] at (18.5, 3.2) {\large -75};
\node[draw=none] at (19.5, 3.5) {\large 80};
\node[draw=none] at (20.5, 3.8) {\large 571};
\node[draw=none] at (21.5, 4.1) {\large -128};
\node[draw=none] at (22.5, 4.4) {\large 24};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% [-408 596 -550 368 26 976 156]
\node[draw=none] at (16.5, 1.6) {\large -408};
\node[draw=none] at (17.5, 1.9) {\large 596};
\node[draw=none] at (18.5, 2.2) {\large -550};
\node[draw=none] at (19.5, 2.5) {\large 368};
\node[draw=none] at (20.5, 2.8) {\large 26};
\node[draw=none] at (21.5, 3.1) {\large 976};
\node[draw=none] at (22.5, 3.4) {\large 156};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% [ 302 647 879 223 811 54 660]]
\node[draw=none] at (16.5, 0.6) {\large 302};
\node[draw=none] at (17.5, 0.9) {\large 647};
\node[draw=none] at (18.5, 1.2) {\large 879};
\node[draw=none] at (19.5, 1.5) {\large 223};
\node[draw=none] at (20.5, 1.8) {\large 811};
\node[draw=none] at (21.5, 2.1) {\large 54};
\node[draw=none] at (22.5, 2.4) {\large 660};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\end{tikzpicture} \end{tikzpicture}
\end{document} \end{document}

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tikz/convolution-linear/filter.py Normal file
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@ -0,0 +1,20 @@
#!/usr/bin/env python
import scipy.signal
import numpy as np
image = [[104, 116, 116, 112, 58, 47, 47],
[109, 97, 114, 116, 105, 110, 45],
[116, 104, 111, 109, 97, 46, 100],
[101, 47, 109, 97, 115, 116, 101],
[114, 47, 99, 97, 116, 99, 97],
[116, 99, 97, 116, 46, 112, 104],
[112, 63, 118, 61, 49, 46, 48]]
filter_kernel = [[9, -3, -1],
[-6, 5, 3],
[2, -8, 0]]
filter_kernel = np.array(filter_kernel)
res = scipy.signal.convolve2d(image, filter_kernel[::-1, ::-1],
mode='same', boundary='fill', fillvalue=0)
print(res)