例: コンボリューションと比較によるエッジ検出

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例: コンボリューションと比較によるエッジ検出

この例の使用方法については、画像処理の例についてを参照してください。

kirsch

kirschによるエッジ検出では次の 8 つのカーネルが使用されます。

<region id="ID0EQYMZ" top="120" left="24" width="94.81" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>15</real> </apply> <matrix rows="3" cols="3"> <real>5</real> <real>5</real> <real>5</real> <real>-3</real> <real>0</real> <real>-3</real> <real>-3</real> <real>-3</real> <real>-3</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>	<region id="ID0EDZMZ" top="120" left="144" width="102.873333333333" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>15</real> </apply> <matrix rows="3" cols="3"> <real>5</real> <real>5</real> <real>-3</real> <real>5</real> <real>0</real> <real>-3</real> <real>-3</real> <real>-3</real> <real>-3</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>	<region id="ID0EWZMZ" top="120" left="264" width="102.873333333333" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>15</real> </apply> <matrix rows="3" cols="3"> <real>5</real> <real>-3</real> <real>-3</real> <real>5</real> <real>0</real> <real>-3</real> <real>5</real> <real>-3</real> <real>-3</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>	<region id="ID0EJ1MZ" top="120" left="384" width="102.873333333333" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>15</real> </apply> <matrix rows="3" cols="3"> <real>-3</real> <real>-3</real> <real>-3</real> <real>5</real> <real>0</real> <real>-3</real> <real>5</real> <real>5</real> <real>-3</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>
<region id="ID0E61MZ" top="192" left="24" width="94.81" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>15</real> </apply> <matrix rows="3" cols="3"> <real>-3</real> <real>-3</real> <real>-3</real> <real>-3</real> <real>0</real> <real>-3</real> <real>5</real> <real>5</real> <real>5</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>	<region id="ID0ER2MZ" top="192" left="144" width="102.873333333333" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>15</real> </apply> <matrix rows="3" cols="3"> <real>-3</real> <real>-3</real> <real>-3</real> <real>-3</real> <real>0</real> <real>5</real> <real>-3</real> <real>5</real> <real>5</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>	<region id="ID0ED3MZ" top="192" left="264" width="102.873333333333" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>15</real> </apply> <matrix rows="3" cols="3"> <real>-3</real> <real>-3</real> <real>5</real> <real>-3</real> <real>0</real> <real>5</real> <real>-3</real> <real>-3</real> <real>5</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>	<region id="ID0EV3MZ" top="192" left="384" width="102.873333333333" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>15</real> </apply> <matrix rows="3" cols="3"> <real>-3</real> <real>5</real> <real>5</real> <real>-3</real> <real>0</real> <real>5</real> <real>-3</real> <real>-3</real> <real>-3</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>

(lena.bmp)

(lena_mkir.bmp)

robinson3

robinson3によるエッジ検出では次の 8 つのカーネルが使用されます。

<region id="ID0ELDNZ" top="936" left="24" width="80.7633333333333" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>3</real> </apply> <matrix rows="3" cols="3"> <real>1</real> <real>1</real> <real>1</real> <real>0</real> <real>0</real> <real>0</real> <real>-1</real> <real>-1</real> <real>-1</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>	<region id="ID0E5DNZ" top="936" left="120" width="88.8266666666667" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>3</real> </apply> <matrix rows="3" cols="3"> <real>1</real> <real>1</real> <real>0</real> <real>1</real> <real>0</real> <real>-1</real> <real>0</real> <real>-1</real> <real>-1</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>	<region id="ID0ERENZ" top="936" left="240" width="96.89" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>3</real> </apply> <matrix rows="3" cols="3"> <real>1</real> <real>0</real> <real>-1</real> <real>1</real> <real>0</real> <real>-1</real> <real>1</real> <real>0</real> <real>-1</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>	<region id="ID0EEFNZ" top="936" left="360" width="88.8266666666667" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>3</real> </apply> <matrix rows="3" cols="3"> <real>0</real> <real>-1</real> <real>-1</real> <real>1</real> <real>0</real> <real>-1</real> <real>1</real> <real>1</real> <real>0</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>
<region id="ID0E1FNZ" top="1008" left="24" width="80.7633333333333" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>3</real> </apply> <matrix rows="3" cols="3"> <real>-1</real> <real>-1</real> <real>-1</real> <real>0</real> <real>0</real> <real>0</real> <real>1</real> <real>1</real> <real>1</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>	<region id="ID0EMGNZ" top="1008" left="120" width="88.8266666666667" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>3</real> </apply> <matrix rows="3" cols="3"> <real>-1</real> <real>-1</real> <real>0</real> <real>-1</real> <real>0</real> <real>1</real> <real>0</real> <real>1</real> <real>1</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>	<region id="ID0E5GNZ" top="1008" left="240" width="96.89" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>3</real> </apply> <matrix rows="3" cols="3"> <real>-1</real> <real>0</real> <real>1</real> <real>-1</real> <real>0</real> <real>1</real> <real>-1</real> <real>0</real> <real>1</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>	<region id="ID0EQHNZ" top="1008" left="360" width="88.8266666666667" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>3</real> </apply> <matrix rows="3" cols="3"> <real>0</real> <real>1</real> <real>1</real> <real>-1</real> <real>0</real> <real>1</real> <real>-1</real> <real>-1</real> <real>0</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>

(lena_mrob3.bmp)

robinson5

robinson5によるエッジ検出では次の 8 つのカーネルが使用されます。

<region id="ID0EZLNZ" top="1464" left="24" width="80.7633333333333" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>4</real> </apply> <matrix rows="3" cols="3"> <real>1</real> <real>2</real> <real>1</real> <real>0</real> <real>0</real> <real>0</real> <real>-1</real> <real>-2</real> <real>-1</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>	<region id="ID0EMMNZ" top="1464" left="120" width="88.8266666666667" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>4</real> </apply> <matrix rows="3" cols="3"> <real>2</real> <real>1</real> <real>0</real> <real>1</real> <real>0</real> <real>-1</real> <real>0</real> <real>-1</real> <real>-2</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>	<region id="ID0E6MNZ" top="1464" left="240" width="96.89" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>4</real> </apply> <matrix rows="3" cols="3"> <real>1</real> <real>0</real> <real>-1</real> <real>2</real> <real>0</real> <real>-2</real> <real>1</real> <real>0</real> <real>-1</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>	<region id="ID0ESNNZ" top="1464" left="360" width="88.8266666666667" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>4</real> </apply> <matrix rows="3" cols="3"> <real>0</real> <real>-1</real> <real>-2</real> <real>1</real> <real>0</real> <real>-1</real> <real>2</real> <real>1</real> <real>0</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>
<region id="ID0EIONZ" top="1536" left="24" width="80.7633333333333" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>4</real> </apply> <matrix rows="3" cols="3"> <real>-1</real> <real>-2</real> <real>-1</real> <real>0</real> <real>0</real> <real>0</real> <real>1</real> <real>2</real> <real>1</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>	<region id="ID0E1ONZ" top="1536" left="120" width="88.8266666666667" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>4</real> </apply> <matrix rows="3" cols="3"> <real>-2</real> <real>-1</real> <real>0</real> <real>-1</real> <real>0</real> <real>1</real> <real>0</real> <real>1</real> <real>2</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>	<region id="ID0EMPNZ" top="1536" left="240" width="96.89" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>4</real> </apply> <matrix rows="3" cols="3"> <real>-1</real> <real>0</real> <real>1</real> <real>-2</real> <real>0</real> <real>2</real> <real>-1</real> <real>0</real> <real>1</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>	<region id="ID0E5PNZ" top="1536" left="360" width="88.8266666666667" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>4</real> </apply> <matrix rows="3" cols="3"> <real>0</real> <real>1</real> <real>2</real> <real>-1</real> <real>0</real> <real>1</real> <real>-2</real> <real>-1</real> <real>0</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>

(lena_mrob5.bmp)

compgrad

compgradによるエッジ検出では次の 8 つのカーネルが使用されます。

<region id="ID0EHUNZ" top="2112" left="24" width="88.8266666666667" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>5</real> </apply> <matrix rows="3" cols="3"> <real>1</real> <real>1</real> <real>1</real> <real>1</real> <real>-2</real> <real>1</real> <real>-1</real> <real>-1</real> <real>-1</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>	<region id="ID0E1UNZ" top="2112" left="120" width="88.8266666666667" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>5</real> </apply> <matrix rows="3" cols="3"> <real>1</real> <real>1</real> <real>1</real> <real>1</real> <real>-2</real> <real>-1</real> <real>1</real> <real>-1</real> <real>-1</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>	<region id="ID0ENVNZ" top="2112" left="240" width="96.89" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>5</real> </apply> <matrix rows="3" cols="3"> <real>1</real> <real>1</real> <real>-1</real> <real>1</real> <real>-2</real> <real>-1</real> <real>1</real> <real>1</real> <real>-1</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>	<region id="ID0EAWNZ" top="2112" left="360" width="88.8266666666667" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>5</real> </apply> <matrix rows="3" cols="3"> <real>1</real> <real>-1</real> <real>-1</real> <real>1</real> <real>-2</real> <real>-1</real> <real>1</real> <real>1</real> <real>1</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>
<region id="ID0EWWNZ" top="2184" left="24" width="88.8266666666667" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>5</real> </apply> <matrix rows="3" cols="3"> <real>-1</real> <real>-1</real> <real>-1</real> <real>1</real> <real>-2</real> <real>1</real> <real>1</real> <real>1</real> <real>1</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>	<region id="ID0EIXNZ" top="2184" left="120" width="88.8266666666667" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>5</real> </apply> <matrix rows="3" cols="3"> <real>-1</real> <real>-1</real> <real>1</real> <real>-1</real> <real>-2</real> <real>1</real> <real>1</real> <real>1</real> <real>1</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>	<region id="ID0E1XNZ" top="2184" left="240" width="96.89" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>5</real> </apply> <matrix rows="3" cols="3"> <real>-1</real> <real>1</real> <real>1</real> <real>-1</real> <real>-2</real> <real>1</real> <real>-1</real> <real>1</real> <real>1</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>	<region id="ID0EMYNZ" top="2184" left="360" width="88.8266666666667" height="53.012" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <apply xmlns="http://schemas.mathsoft.com/math50"> <mult /> <apply> <div /> <real>1</real> <real>5</real> </apply> <matrix rows="3" cols="3"> <real>1</real> <real>1</real> <real>1</real> <real>-1</real> <real>-2</real> <real>1</real> <real>-1</real> <real>-1</real> <real>1</real> </matrix> </apply> <resultFormat> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>

(lena_comp.bmp)

関連トピック

コンボリューションと比較によるエッジ検出

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