CoCalc -- convolution-linear.tex

📚 The CoCalc Library - books, templates and other resources
cocalc-examples / martinthoma-latex-examples / presentations / CNN-Intro / graphics / convolution-linear.tex
¹³²⁹³⁰ views
License: OTHER
1

2
\newcommand{\filtersize}{3}
3
\newcommand{\filterx}{8}
4
\newcommand{\filtery}{2.2}
5
\newcommand{\filteroffset}{1}
6

7
\newcommand{\filterxres}{12}
8

9
\newcommand{\imagesize}{7}
10
\newcommand{\imagex}{0}
11
\newcommand{\imagey}{0}
12
\newcommand{\imageoffset}{2}
13

14
\newcommand{\outx}{16}
15
\newcommand{\outy}{0}
16
\newcommand{\outoffset}{2}
17

18
\newcommand{\percx}{1}
19
\newcommand{\percy}{2}
20
\begin{tikzpicture}[scale=0.6]
21
    \tikzstyle{point}=[draw=none,inner sep=0pt]
22

23

24
    % draw perceptive field
25
    \node (p1)[point] at (\imagex+\percx,
26
                          \imagey+\percy+\percx*\imageoffset/\imagesize) {};
27
    \node (p2)[point] at (\imagex+\percx+\filtersize,
28
                          \imagey+\percy+\percx*\imageoffset/\imagesize+\filtersize*\imageoffset/\imagesize) {};
29
    \node (p3)[point,blue] at (\imagex+\percx+\filtersize,
30
                          \imagey+\percy+\filtersize+\percx*\imageoffset/\imagesize+\filtersize*\imageoffset/\imagesize) {};
31
    \node (p4)[point] at (\imagex+\percx,
32
                          \imagey+\percy+\filtersize+\percx*\imageoffset/\imagesize) {};
33
    \draw[fill=gray] (p1.center) -- (p2.center) -- (p3.center) -- (p4.center) -- (p1.center);
34

35
    % draw output point
36
    \node (o1)[point] at (\outx+\percx+1,
37
                          \outy+\percy+\percx*\outoffset/\imagesize+1+1*\outoffset/\imagesize) {};
38
    \node (o2)[point] at (\outx+\percx+2,
39
                          \outy+\percy+\percx*\outoffset/\imagesize+1*\outoffset/\imagesize+1+1*\outoffset/\imagesize) {};
40
    \node (o3)[point,blue] at (\outx+\percx+2,
41
                          \outy+\percy+1+\percx*\outoffset/\imagesize+1*\outoffset/\imagesize+1+1*\outoffset/\imagesize) {};
42
    \node (o4)[point] at (\outx+\percx+1,
43
                          \outy+\percy+2+\percx*\outoffset/\imagesize+1*\outoffset/\imagesize) {};
44
    \draw[fill=gray] (o1.center) -- (o2.center) -- (o3.center) -- (o4.center) -- (o1.center);
45

46
    % draw image
47
    \foreach \x in {0,...,\imagesize}
48
    {
49
    \draw (\imagex+\x, \imagey+\x*\imageoffset/\imagesize) -- (\imagex+\x, \imagey+\imagesize+\x*\imageoffset/\imagesize);
50
    \draw (\imagex, \imagey+\x) -- (\imagex+\imagesize, \imagey+\x+\imageoffset);
51
    }
52

53
    % draw filter
54
    \foreach \x in {0,...,\filtersize}
55
    {
56
    \draw (\filterx+\x, \filtery+\x*\filteroffset/\filtersize) -- (\filterx+\x, \filtery+\filtersize+\x*\filteroffset/\filtersize);
57
    \draw (\filterx, \filtery+\x) -- (\filterx+\filtersize, \filtery+\x+\filteroffset);
58
    }
59

60
    % draw filter result
61
    \foreach \x in {0,...,\filtersize}
62
    {
63
    \draw (\filterxres+\x, \filtery+\x*\filteroffset/\filtersize) -- (\filterxres+\x, \filtery+\filtersize+\x*\filteroffset/\filtersize);
64
    \draw (\filterxres, \filtery+\x) -- (\filterxres+\filtersize, \filtery+\x+\filteroffset);
65
    }
66

67
    % draw out
68
    \foreach \x in {0,...,\imagesize}
69
    {
70
    \draw (\outx+\x, \outy+\x*\outoffset/\imagesize) -- (\outx+\x, \outy+\imagesize+\x*\outoffset/\imagesize);
71
    \draw (\outx, \outy+\x) -- (\outx+\imagesize, \outy+\x+\outoffset);
72
    }
73

74
    \node at (\imagex + \imagesize/2,\imagey + \imagesize + 2) {\Huge $I \in \mathbb{R}^{\imagesize \times \imagesize}$};
75
     \node[text width=4cm, align=center] at (\filterx + \filtersize/2,\filtery + \filtersize - 4) {\large Filter kernel\\$F \in \mathbb{R}^{\filtersize \times \filtersize}$};
76
    \node[text width=4cm, align=center] at (\filterx + 4 + \filtersize/2,\filtery + \filtersize - 4) {\large Result of point-wise multiplication};
77
    \node at (\outx + \imagesize/2,\outy + \imagesize + 2) {\Huge $I' \in \mathbb{R}^{\imagesize \times \imagesize}$};
78

79
    % Start image (left to right, top to bottom)
80
    \node[draw=none] at (0.5, 6.6) {\large 104};
81
    \node[draw=none] at (1.5, 6.9) {\large 116};
82
    \node[draw=none] at (2.5, 7.2) {\large 116};
83
    \node[draw=none] at (3.5, 7.5) {\large 112};
84
    \node[draw=none] at (4.5, 7.8) {\large  58};
85
    \node[draw=none] at (5.5, 8.1) {\large  47};
86
    \node[draw=none] at (6.5, 8.4) {\large  47};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
87

88
    \node[draw=none] at (0.5, 5.6) {\large 109};
89
    \node[draw=none] at (1.5, 5.9) {\large  97};
90
    \node[draw=none] at (2.5, 6.2) {\large 114};
91
    \node[draw=none] at (3.5, 6.5) {\large 116};
92
    \node[draw=none] at (4.5, 6.8) {\large 105};
93
    \node[draw=none] at (5.5, 7.1) {\large 110};
94
    \node[draw=none] at (6.5, 7.4) {\large  45};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
95

96
    \node[draw=none] at (0.5, 4.6) {\large 116};
97
    \node[draw=none] at (1.5, 4.9) {\large 104};
98
    \node[draw=none] at (2.5, 5.2) {\large 111};
99
    \node[draw=none] at (3.5, 5.5) {\large 109};
100
    \node[draw=none] at (4.5, 5.8) {\large  97};
101
    \node[draw=none] at (5.5, 6.1) {\large  46};
102
    \node[draw=none] at (6.5, 6.4) {\large 100};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
103

104
    \node[draw=none] at (0.5, 3.6) {\large 101};
105
    \node[draw=none] at (1.5, 3.9) {\large  47};
106
    \node[draw=none] at (2.5, 4.2) {\large 109};
107
    \node[draw=none] at (3.5, 4.5) {\large  97};
108
    \node[draw=none] at (4.5, 4.8) {\large 115};
109
    \node[draw=none] at (5.5, 5.1) {\large 116};
110
    \node[draw=none] at (6.5, 5.4) {\large 101};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
111

112
    \node[draw=none] at (0.5, 2.6) {\large 114};
113
    \node[draw=none] at (1.5, 2.9) {\large  47};
114
    \node[draw=none] at (2.5, 3.2) {\large  99};
115
    \node[draw=none] at (3.5, 3.5) {\large  97};
116
    \node[draw=none] at (4.5, 3.8) {\large 116};
117
    \node[draw=none] at (5.5, 4.1) {\large  99};
118
    \node[draw=none] at (6.5, 4.4) {\large  97};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
119

120
    \node[draw=none] at (0.5, 1.6) {\large 116};
121
    \node[draw=none] at (1.5, 1.9) {\large  99};
122
    \node[draw=none] at (2.5, 2.2) {\large  97};
123
    \node[draw=none] at (3.5, 2.5) {\large 116};
124
    \node[draw=none] at (4.5, 2.8) {\large  46};
125
    \node[draw=none] at (5.5, 3.1) {\large 112};
126
    \node[draw=none] at (6.5, 3.4) {\large 104};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
127

128
    \node[draw=none] at (0.5, 0.6) {\large 112};
129
    \node[draw=none] at (1.5, 0.9) {\large  63};
130
    \node[draw=none] at (2.5, 1.2) {\large 118};
131
    \node[draw=none] at (3.5, 1.5) {\large  61};
132
    \node[draw=none] at (4.5, 1.8) {\large  49};
133
    \node[draw=none] at (5.5, 2.1) {\large  46};
134
    \node[draw=none] at (6.5, 2.4) {\large  48};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
135

136

137
    % Filter
138
    \node[draw=none] at ( 8.5, 4.8) {\large  9};
139
    \node[draw=none] at ( 9.5, 5.1) {\large -3};
140
    \node[draw=none] at (10.5, 5.4) {\large -1};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
141
    \node[draw=none] at ( 8.5, 3.8) {\large -6};
142
    \node[draw=none] at ( 9.5, 4.1) {\large  5};
143
    \node[draw=none] at (10.5, 4.4) {\large  3};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
144
    \node[draw=none] at ( 8.5, 2.8) {\large  2};
145
    \node[draw=none] at ( 9.5, 3.1) {\large -8};
146
    \node[draw=none] at (10.5, 3.4) {\large  0};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
147

148

149
    % Result
150
    \node[draw=none] at (12.5, 4.8) {\large  936};
151
    \node[draw=none] at (13.5, 5.1) {\large -333};
152
    \node[draw=none] at (14.5, 5.4) {\large -109};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
153
    \node[draw=none] at (12.5, 3.8) {\large -282};
154
    \node[draw=none] at (13.5, 4.1) {\large  545};
155
    \node[draw=none] at (14.5, 4.4) {\large  291};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
156
    \node[draw=none] at (12.5, 2.8) {\large   94};
157
    \node[draw=none] at (13.5, 3.1) {\large -792};
158
    \node[draw=none] at (14.5, 3.4) {\large  0};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
159

160
    % Result image (left to right, top to bottom)
161
    % [[  -4 -254 -498 -662 -849 -642 -187]
162
    \node[draw=none] at (16.5, 6.6) {\large -4};
163
    \node[draw=none] at (17.5, 6.9) {\large -254};
164
    \node[draw=none] at (18.5, 7.2) {\large -498};
165
    \node[draw=none] at (19.5, 7.5) {\large -662};
166
    \node[draw=none] at (20.5, 7.8) {\large -849};
167
    \node[draw=none] at (21.5, 8.1) {\large -642};
168
    \node[draw=none] at (22.5, 8.4) {\large 187};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
169
    %  [-520   45  240  211  388  215 -861]
170
    \node[draw=none] at (16.5, 5.6) {\large-520};
171
    \node[draw=none] at (17.5, 5.9) {\large  45};
172
    \node[draw=none] at (18.5, 6.2) {\large 240};
173
    \node[draw=none] at (19.5, 6.5) {\large 211};
174
    \node[draw=none] at (20.5, 6.8) {\large 388};
175
    \node[draw=none] at (21.5, 7.1) {\large 215};
176
    \node[draw=none] at (22.5, 7.4) {\large-861};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
177
    %  [-340  559 -105  185 -138 -180  503]
178
    \node[draw=none] at (16.5, 4.6) {\large -340};
179
    \node[draw=none] at (17.5, 4.9) {\large  559};
180
    \node[draw=none] at (18.5, 5.2) {\large -105};
181
    \node[draw=none] at (19.5, 5.5) {\large  185};
182
    \node[draw=none] at (20.5, 5.8) {\large -138};
183
    \node[draw=none] at (21.5, 6.1) {\large -180};
184
    \node[draw=none] at (22.5, 6.4) {\large  503};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
185
    %  [-718  429  350  173  251  268 -655]
186
    \node[draw=none] at (16.5, 3.6) {\large -718};
187
    \node[draw=none] at (17.5, 3.9) {\large  429};
188
    \node[draw=none] at (18.5, 4.2) {\large  350};
189
    \node[draw=none] at (19.5, 4.5) {\large  173};
190
    \node[draw=none] at (20.5, 4.8) {\large  251};
191
    \node[draw=none] at (21.5, 5.1) {\large  268};
192
    \node[draw=none] at (22.5, 5.4) {\large -655};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
193
    %  [-567  -53  -75   80  571 -128   24]
194
    \node[draw=none] at (16.5, 2.6) {\large -567};
195
    \node[draw=none] at (17.5, 2.9) {\large  -53};
196
    \node[draw=none] at (18.5, 3.2) {\large  -75};
197
    \node[draw=none] at (19.5, 3.5) {\large   80};
198
    \node[draw=none] at (20.5, 3.8) {\large  571};
199
    \node[draw=none] at (21.5, 4.1) {\large -128};
200
    \node[draw=none] at (22.5, 4.4) {\large   24};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
201
    %  [-408  596 -550  368   26  976  156]
202
    \node[draw=none] at (16.5, 1.6) {\large -408};
203
    \node[draw=none] at (17.5, 1.9) {\large  596};
204
    \node[draw=none] at (18.5, 2.2) {\large -550};
205
    \node[draw=none] at (19.5, 2.5) {\large  368};
206
    \node[draw=none] at (20.5, 2.8) {\large   26};
207
    \node[draw=none] at (21.5, 3.1) {\large  976};
208
    \node[draw=none] at (22.5, 3.4) {\large  156};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
209
    %  [ 302  647  879  223  811   54  660]]
210
    \node[draw=none] at (16.5, 0.6) {\large 302};
211
    \node[draw=none] at (17.5, 0.9) {\large 647};
212
    \node[draw=none] at (18.5, 1.2) {\large 879};
213
    \node[draw=none] at (19.5, 1.5) {\large 223};
214
    \node[draw=none] at (20.5, 1.8) {\large 811};
215
    \node[draw=none] at (21.5, 2.1) {\large  54};
216
    \node[draw=none] at (22.5, 2.4) {\large 660};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
217
\end{tikzpicture}
218

219
Product

Resources

Company
