\n\t\t\t\t\t $\"\"$ \n\t\t\t\t\t\u30dd\u30c1\u30c3\u30d7<\/span>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\n\n\n

\u30a8\u30c3\u30b8\u62bd\u51fa\u306e\u539f\u7406<\/h2>\n\n\n\n
\u30bd\u30fc\u30d9\u30eb\u30d5\u30a3\u30eb\u30bf\u306b\u3064\u3044\u3066\u7406\u89e3\u3059\u308b\u305f\u3081\u306b\u306f\u3001\u30a8\u30c3\u30b8\u62bd\u51fa\u306e\u539f\u7406\u3092\u5b66\u3076\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u3053\u3067\u306f\u3001\u5fae\u5206\u306b\u3088\u3063\u3066\u30a8\u30c3\u30b8\u691c\u51fa\u3059\u308b\u539f\u7406<\/span><\/strong>\u3092\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\u5fae\u5206\u3067\u52fe\u914d\u3092\u6570\u5024\u5316<\/h3>\n\n\n\n
\u753b\u50cf\u51e6\u7406\u3067\u306e\u30a8\u30c3\u30b8\u3068\u306f\u3001\u753b\u50cf\u306e\u660e\u308b\u3044\u90e8\u5206\u3068\u6697\u3044\u90e8\u5206\u304c\u6025\u6fc0\u306b\u5909\u5316\u3059\u308b\u52fe\u914d\u90e8<\/span><\/strong>\u3067\u3059\u3002\u3053\u306e\u52fe\u914d\u90e8\u3092\u62bd\u51fa\u3059\u308b\u306b\u306f\u3001\u753b\u50cf\u306e\u8f1d\u5ea6\u5024\u3092\u5fae\u5206\u3057\u6570\u5024\u5316\u3057\u307e\u3059\u3002\u95a2\u6570\$f(x)\$\u306e\u5fae\u5206\$f'(x)\$\u306f\u4ee5\u4e0b\u5f0f\u3067\u8868\u3055\u308c\u307e\u3059\u3088\u306d\u3002<\/p>\n\n\n\n
$$f'(x)=\\lim_{h \\to 0}\\frac{f(x+h)-f(x)}{h}$$<\/p>\n\n\n\n
\u4e0b\u56f3\u306e\u3088\u3046\u306b\u3001\u8f1d\u5ea6\u5024\u3092\u5fae\u5206\u3057\u305f\u5024\u304c\u5927\u304d\u3044\u90e8\u5206\u304c\u30a8\u30c3\u30b8\u306b\u76f8\u5f53<\/span><\/strong>\u3059\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n
$\"\"$ <\/figure>\n\n\n
\n
\n
$\"\"$ <\/figure>\n<\/div>\n
\n
\u30c7\u30b8\u30bf\u30eb\u753b\u50cf\u306f2\u5909\u6570\u304b\u30641\u753b\u7d20\u3054\u3068\u306e\u5024\u306e\u305f\u3081\u3001\u3069\u3046\u3084\u3063\u305f\u3089\u52fe\u914d\u3092\u6c42\u3081\u3089\u308c\u308b\uff1f<\/p>\n<\/div>\n<\/div>\n
\u504f\u5fae\u5206\u3068\u5fae\u5206\u306e\u96e2\u6563\u5316\u306b\u3088\u3063\u3066\u30c7\u30b8\u30bf\u30eb\u753b\u50cf\u306e\u52fe\u914d\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/div>\n\n\n
\u504f\u5fae\u5206<\/h4>\n\n\n\n
2\u5909\u6570\u95a2\u6570\u306e\u5834\u5408\u306f\u3001\u5fae\u5206\u3059\u308b\u5909\u6570\u30921\u3064\u6307\u5b9a\u3057\u3001\u305d\u308c\u4ee5\u5916\u306e\u5909\u6570\u3092\u5b9a\u6570\u3068\u3057\u3066\u5fae\u5206\u3057\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u5fae\u5206\u3092\u504f\u5fae\u5206<\/span><\/strong>\u3068\u3044\u3044\u307e\u3059\u30022\u5909\u6570\u95a2\u6570\u3092\$f(x,y)\$\u3068\u3057\u3001x\u3067\u5fae\u5206\u3057\u305f\u5c0e\u95a2\u6570\u3092\$f_x(x,y)\$\u3001y\u3067\u5fae\u5206\u3057\u305f\u5c0e\u95a2\u6570\u3092\$f_y(x,y)\$\u3068\u3059\u308b\u3068<\/p>\n\n\n\n
$$f_x(x,y) = \\lim_{h \\to 0}\\frac{f(x+h, y)-f(x, y)}{h}$$<\/p>\n\n\n\n
$$f_y(x,y) = \\lim_{h \\to 0}\\frac{f(x, y+h)-f(x, y)}{h}$$<\/p>\n\n\n\n
\$f_x(x,y)\$\u306fx\u65b9\u5411\u3001\$f_y(x,y)\$\u306fy\u65b9\u5411\u306e\u52fe\u914d\u3092\u8868\u3057\u307e\u3059\u3002<\/p>\n\n\n\n
\u5fae\u5206\u306e\u96e2\u6563\u5316<\/h4>\n\n\n\n
\u30c7\u30b8\u30bf\u30eb\u753b\u50cf\u306f\u30011\u753b\u7d20\u3054\u3068\u306e\u96e2\u6563\u5024\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\$h\$\u306f\u6709\u9650\u3067\u3059\u3002\u305d\u3053\u3067\u3001\$h=1\$\u3068\u3057\u3066\u5fae\u5206\u5024\u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n\n\n\n
$$f_x(x,y) = f(x+1, y)-f(x, y)$$<\/p>\n\n\n\n
$$f_y(x,y) = f(x, y+1)-f(x, y)$$<\/p>\n\n\n\n
\u3053\u308c\u306f\u5ea7\u6a19\$(x,y)\$\u3068\u305d\u306e\u524d\u65b9\u5ea7\u6a19\$(x+1,y)\u3001(x,y+1)\$\u306e\u5dee\u5206\u3092\u3068\u3063\u3066\u3044\u307e\u3059\u306e\u3067\u524d\u65b9\u5dee\u5206<\/span><\/strong>\u3068\u547c\u3070\u308c\u307e\u3059\u3002<\/p>\n\n\n\n
\u4e00\u65b9\u3001\$h=-1\$\u306e\u5834\u5408\u306f<\/p>\n\n\n\n
$$f_x(x,y) = f(x, y)-f(x-1, y)$$<\/p>\n\n\n\n
$$f_y(x,y) = f(x, y)-f(x, y-1)$$<\/p>\n\n\n\n
\u3068\u306a\u308a\u3001\u5ea7\u6a19\$(x,y)\$\u3068\u305d\u306e\u524d\u65b9\u5ea7\u6a19\$(x-1,y)\$\u3001\$(x,y-1)\$\u306e\u5dee\u5206\u3092\u3068\u308b\u3053\u3068\u304b\u3089\u5f8c\u65b9\u5dee\u5206<\/span><\/strong>\u3068\u547c\u3070\u308c\u307e\u3059\u3002<\/p>\n\n\n\n
\u307e\u305f\u3001\u524d\u65b9\u5dee\u5206\u3068\u5f8c\u65b9\u5dee\u5206\u306e\u5e73\u5747\u3092\u6c42\u3081\u308b\u3068<\/p>\n\n\n\n
$$f_x(x,y) = \\frac{f(x+1, y)-f(x-1, y)}{2}$$<\/p>\n\n\n\n
$$f_y(x,y) = \\frac{f(x, y+1)-f(x, y-1)}{2}$$<\/p>\n\n\n\n
\u3068\u306a\u308a\u307e\u3059\u3002\u5ea7\u6a19\$(x+1,y)\$\u3068\u5ea7\u6a19\$(x-1,y)\$\u306e\u5dee\u5206\u3001\u5ea7\u6a19\$(x,y+1)\$\u3068\u5ea7\u6a19\$(x,y-1)\$\u306e\u5dee\u5206\u3092\u3068\u308b\u3053\u3068\u304b\u3089\u4e2d\u5fc3\u5dee\u5206<\/span><\/strong>\u3068\u547c\u3070\u308c\u307e\u3059\u3002<\/p>\n\n\n\n
\u5fae\u5206\u30d5\u30a3\u30eb\u30bf<\/h3>\n\n\n\n
\u7a7a\u9593\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u306b\u304a\u3044\u3066\u7dda\u5f62\u30d5\u30a3\u30eb\u30bf\u306f\u3001\u5165\u529b\u753b\u50cf\u3092\$f(i,j)\$\u3001\u51fa\u529b\u753b\u50cf\u3092\$g(i,j)\$\u3001\u30d5\u30a3\u30eb\u30bf\u4fc2\u6570\u3092\$h(m,n)\$\u3068\u3059\u308b\u3068\u304d\u3001\u4ee5\u4e0b\u5f0f\u3067\u8868\u3055\u308c\u307e\u3057\u305f\u3002<\/p>\n\n\n\n
$$g(i,j)=\\sum_{n=-W}^{W}\\sum_{m=-W}^{W}f(i+m,j+n)h(m,n)$$<\/p>\n\n\n\n
<\/div>\n\n\n\n
\n
https:\/\/craft-gogo.com\/gauss-fillter\/<\/p>\n<\/div>\n\n\n\n
\u5fae\u5206\u3092\u3053\u306e\u5f62\u5f0f\u3067\u8868\u3059\u3068\u5fae\u5206\u30d5\u30a3\u30eb\u30bf\u306f\u4ee5\u4e0b\u8868\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n
<\/td> x\u65b9\u5411<\/td> y\u65b9\u5411<\/td><\/tr>
\u524d\u65b9\u5dee\u5206<\/td> \\begin{pmatrix}
0 & 0 & 0 \\\\
0 & -1 & 1 \\\\
0 & 0 & 0
\\end{pmatrix}<\/td> \\begin{pmatrix}
0 & 0 & 0 \\\\
0 & -1 & 0 \\\\
0 & 1 & 0
\\end{pmatrix}<\/td><\/tr>
\u5f8c\u65b9\u5dee\u5206<\/td> \\begin{pmatrix}
0 & 0 & 0 \\\\
-1 & 1 & 0 \\\\
0 & 0 & 0
\\end{pmatrix}<\/td> \\begin{pmatrix}
0 & -1 & 0 \\\\
0 & 1 & 0 \\\\
0 & 0 & 0
\\end{pmatrix}<\/td><\/tr>
\u4e2d\u5fc3\u5dee\u5206<\/td> \\begin{pmatrix}
0 & 0 & 0 \\\\
-1\/2 & 0 & 1\/2 \\\\
0 & 0 & 0
\\end{pmatrix}<\/td> \\begin{pmatrix}
0 & -1\/2 & 0 \\\\
0 & 0 & 0 \\\\
0 & 1\/2 & 0
\\end{pmatrix}<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\u30bd\u30fc\u30d9\u30eb\u30d5\u30a3\u30eb\u30bf\u3068\u306f<\/h2>\n\n\n\n
\u753b\u50cf\u306b\u30ce\u30a4\u30ba\u304c\u6df7\u5165\u3057\u3066\u3044\u308b\u3068\u3001\u30ce\u30a4\u30ba\u3092\u30a8\u30c3\u30b8\u3068\u8aa4\u691c\u51fa\u3057\u3066\u3057\u307e\u3044\u307e\u3059\u3002<\/p>\n\n\n\n
$\"\"$ <\/figure>\n\n\n\n
\u305d\u3053\u3067\u767b\u5834\u3059\u308b\u306e\u304c\u3001\u30ce\u30a4\u30ba\u3092\u9664\u53bb\u3057\u3064\u3064\u30a8\u30c3\u30b8\u62bd\u51fa\u3059\u308b\u30bd\u30fc\u30d9\u30eb\u30d5\u30a3\u30eb\u30bf<\/span><\/strong>\u3067\u3059\u3002<\/p>\n\n\n\n
\u305d\u3053\u3067\u767b\u5834\u3059\u308b\u306e\u304c\u30bd\u30fc\u30d9\u30eb\u30d5\u30a3\u30eb\u30bf<\/span><\/strong>\u3067\u3059\u3002\u30bd\u30fc\u30d9\u30eb\u30d5\u30a3\u30eb\u30bf\u3068\u306f\u3001\u524d\u7bc0\u3067\u8aac\u660e\u3057\u305f\u4e2d\u592e\u5dee\u5206\u3057\u305f\u306e\u3061\u3001\u4e2d\u592e\u306b\u91cd\u307f\u4ed8\u3051\u3057\u305f\u5e73\u6ed1\u5316\u3092\u884c\u3063\u305f\u30d5\u30a3\u30eb\u30bf<\/span><\/strong>\u3067\u3059\u3002<\/p>\n\n\n\n
\u30d5\u30a3\u30eb\u30bf\u4fc2\u6570<\/h3>\n\n\n\n
\u4e0b\u8a18\u8868\u306f\u3001x\u65b9\u5411\u3001y\u65b9\u5411\u306e\u4e2d\u592e\u5dee\u5206\u3001\u91cd\u307f\u4ed8\u304d\u5e73\u6ed1\u5316\u3001\u30bd\u30fc\u30d9\u30eb\u30d5\u30a3\u30eb\u30bf\u306e\u30d5\u30a3\u30eb\u30bf\u4fc2\u6570\u3067\u3059\u3002<\/p>\n\n\n\n
<\/td> \u4e2d\u592e\u5dee\u5206: \$h_1(x,y)\$<\/td> \u91cd\u307f\u4ed8\u304d\u5e73\u6ed1\u5316: \$h_2(x,y)\$ <\/td> \u30bd\u30fc\u30d9\u30eb\u30d5\u30a3\u30eb\u30bf: \$h_2(x,y)\\cdot h_1(x,y)\$<\/td><\/tr>
x\u65b9\u5411<\/td> \$\\begin{pmatrix}
0 & 0 & 0 \\\\
-\\frac{1}{2} & 0 & \\frac{1}{2} \\\\
0 & 0 & 0
\\end{pmatrix}\$<\/td> \$\\begin{pmatrix}
0 & \\frac{1}{4} & 0 \\\\
0 & \\frac{2}{4} & 0 \\\\
0 & \\frac{1}{4} & 0
\\end{pmatrix}\$<\/td> \$\\frac{1}{8}\\begin{pmatrix}
-1 & 0 & 1 \\\\
-2 & 0 & 2 \\\\
-1 & 0 & 1
\\end{pmatrix}\$<\/td><\/tr>
y\u65b9\u5411<\/td> \$\\begin{pmatrix}
0 & -\\frac{1}{2} & 0 \\\\
0 & 0 & 0 \\\\
0 & \\frac{1}{2} & 0
\\end{pmatrix}\$<\/td> \$\\begin{pmatrix}
0 & 0 & 0 \\\\
\\frac{1}{4} & \\frac{2}{4} & \\frac{1}{4} \\\\
0 & 0 & 0
\\end{pmatrix}\$<\/td> \$\\frac{1}{8}\\begin{pmatrix}
-1 & -2 & 1 \\\\
0 & 0 & 0 \\\\
-1 & 2 & 1
\\end{pmatrix}\$<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\u4e2d\u592e\u5dee\u5206\u3092\$h_1(x,y)\$\u3001\u91cd\u307f\u4ed8\u304d\u5e73\u6ed1\u5316\u3092\$h_2(x,y)\$\u3068\u3059\u308b\u3068\u304d\u3001\u4e2d\u592e\u5dee\u5206\u3068\u91cd\u307f\u4ed8\u304d\u5e73\u6ed1\u5316\u3092\u9806\u306b\u65bd\u3057\u305f\u30bd\u30fc\u30d9\u30eb\u30d5\u30a3\u30eb\u30bf\u306f\u3001\$h_2(x,y)\\cdot h_1(x,y)\$\u3067\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n
\u30d6\u30ea\u30e5\u30fc\u30a6\u30a3\u30c3\u30c8\u30d5\u30a3\u30eb\u30bf\u3068\u306e\u9055\u3044<\/h3>\n\n\n\n
\u30bd\u30fc\u30d9\u30eb\u30d5\u30a3\u30eb\u30bf\u3068\u540c\u69d8\u306a\u30d5\u30a3\u30eb\u30bf\u306b\u30d6\u30ea\u30e5\u30fc\u30a6\u30a3\u30c3\u30c8\u30d5\u30a3\u30eb\u30bf(Prewitt filter)<\/strong>\u3068\u3044\u3046\u3082\u306e\u304c\u3042\u308a\u307e\u3059\u306e\u3067\u7d39\u4ecb\u3057\u3066\u304a\u304d\u307e\u3059\u3002<\/p>\n\n\n\n
<\/td> \u4e2d\u592e\u5dee\u5206: \$h_1(x,y)\$<\/td> \u5e73\u6ed1\u5316: \$h_2(x,y)\$ <\/td> \u30d6\u30ea\u30e5\u30fc\u30a6\u30a3\u30c3\u30c8\u30d5\u30a3\u30eb\u30bf: \$h_2(x,y)\\cdot h_1(x,y)\$<\/td><\/tr>
x\u65b9\u5411<\/td> \$\\begin{pmatrix}
0 & 0 & 0 \\\\
-\\frac{1}{2} & 0 & \\frac{1}{2} \\\\
0 & 0 & 0
\\end{pmatrix}\$<\/td> \$\\begin{pmatrix}
0 & \\frac{1}{3} & 0 \\\\
0 & \\frac{1}{3} & 0 \\\\
0 & \\frac{1}{3} & 0
\\end{pmatrix}\$<\/td> \$\\frac{1}{6}\\begin{pmatrix}
-1 & 0 & 1 \\\\
-1 & 0 & 1 \\\\
-1 & 0 & 1
\\end{pmatrix}\$<\/td><\/tr>
y\u65b9\u5411<\/td> \$\\begin{pmatrix}
0 & -\\frac{1}{2} & 0 \\\\
0 & 0 & 0 \\\\
0 & \\frac{1}{2} & 0
\\end{pmatrix}\$<\/td> \$\\begin{pmatrix}
0 & 0 & 0 \\\\
\\frac{1}{3} & \\frac{1}{3} & \\frac{1}{3} \\\\
0 & 0 & 0
\\end{pmatrix}\$<\/td> \$\\frac{1}{6}\\begin{pmatrix}
-1 & -1 & 1 \\\\
0 & 0 & 0 \\\\
-1 & 1 & 1
\\end{pmatrix}\$<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\u3053\u3061\u3089\u306f\u4e2d\u592e\u5dee\u5206\u3068\u91cd\u307f\u306a\u3057<\/strong>\u306e\u5e73\u6ed1\u5316\u3092\u9806\u306b\u65bd\u3057\u305f\u30d5\u30a3\u30eb\u30bf\u3067\u3059\u3002<\/p>\n\n\n\n