範例：迴旋積分尋邊器

函數 > 圖像處理 > 尋邊器 > 範例：迴旋積分尋邊器

範例：迴旋積分尋邊器

使用 freichen、sobel、prewitt 及 roberts 函數檢測圖像邊緣，方法是在矩陣上依序迴旋各核。邊緣檢測可用於改善取決於邊界之特定特徵類型的圖像可讀性。

如需使用此範例的資訊，請參閱＜關於圖像處理範例＞。

freichen

此函數使用下列兩個核迴旋圖像矩陣：

按一下以複製此運算式

<region id="ID0ECUL3" top="216" left="24" xml:lang="zh_TW" height="64.331" width="163.025998692513" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math xml:lang="zh_TW">
    <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">
      <id xml:lang="zh_TW" label="None">K1</id>
      <apply xml:lang="zh_TW">
        <mult xml:lang="zh_TW" />
        <apply xml:lang="zh_TW">
          <div xml:lang="zh_TW" />
          <real xml:lang="zh_TW">1</real>
          <apply xml:lang="zh_TW">
            <plus xml:lang="zh_TW" />
            <real xml:lang="zh_TW">2</real>
            <apply xml:lang="zh_TW">
              <nthRoot xml:lang="zh_TW" />
              <placeholder xml:lang="zh_TW" />
              <real xml:lang="zh_TW">2</real>
            </apply>
          </apply>
        </apply>
        <matrix rows="3" cols="3" xml:lang="zh_TW">
          <real xml:lang="zh_TW">1</real>
          <apply xml:lang="zh_TW">
            <nthRoot xml:lang="zh_TW" />
            <placeholder xml:lang="zh_TW" />
            <real xml:lang="zh_TW">2</real>
          </apply>
          <real xml:lang="zh_TW">1</real>
          <real xml:lang="zh_TW">0</real>
          <real xml:lang="zh_TW">0</real>
          <real xml:lang="zh_TW">0</real>
          <real xml:lang="zh_TW">-1</real>
          <apply xml:lang="zh_TW">
            <neg xml:lang="zh_TW" />
            <apply xml:lang="zh_TW">
              <nthRoot xml:lang="zh_TW" />
              <placeholder xml:lang="zh_TW" />
              <real xml:lang="zh_TW">2</real>
            </apply>
          </apply>
          <real xml:lang="zh_TW">-1</real>
        </matrix>
      </apply>
    </define>
    <resultFormat xml:lang="zh_TW">
      <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" />
      <matrix size="12,12" offset="0,0" xml:lang="zh_TW" />
    </resultFormat>
  </math>
</region>

按一下以複製此運算式

<region id="ID0EUUL3" top="216" left="216" xml:lang="zh_TW" height="64.331" width="167.220665795008" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math xml:lang="zh_TW">
    <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">
      <id xml:lang="zh_TW" label="None">K2</id>
      <apply xml:lang="zh_TW">
        <mult xml:lang="zh_TW" />
        <apply xml:lang="zh_TW">
          <div xml:lang="zh_TW" />
          <real xml:lang="zh_TW">1</real>
          <apply xml:lang="zh_TW">
            <plus xml:lang="zh_TW" />
            <real xml:lang="zh_TW">2</real>
            <apply xml:lang="zh_TW">
              <nthRoot xml:lang="zh_TW" />
              <placeholder xml:lang="zh_TW" />
              <real xml:lang="zh_TW">2</real>
            </apply>
          </apply>
        </apply>
        <matrix rows="3" cols="3" xml:lang="zh_TW">
          <real xml:lang="zh_TW">-1</real>
          <real xml:lang="zh_TW">0</real>
          <real xml:lang="zh_TW">1</real>
          <apply xml:lang="zh_TW">
            <neg xml:lang="zh_TW" />
            <apply xml:lang="zh_TW">
              <nthRoot xml:lang="zh_TW" />
              <placeholder xml:lang="zh_TW" />
              <real xml:lang="zh_TW">2</real>
            </apply>
          </apply>
          <real xml:lang="zh_TW">0</real>
          <apply xml:lang="zh_TW">
            <nthRoot xml:lang="zh_TW" />
            <placeholder xml:lang="zh_TW" />
            <real xml:lang="zh_TW">2</real>
          </apply>
          <real xml:lang="zh_TW">-1</real>
          <real xml:lang="zh_TW">0</real>
          <real xml:lang="zh_TW">1</real>
        </matrix>
      </apply>
    </define>
    <resultFormat xml:lang="zh_TW">
      <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" />
      <matrix size="12,12" offset="0,0" xml:lang="zh_TW" />
    </resultFormat>
  </math>
</region>

1. 讀取圖像。

按一下以複製此運算式

2. 將 freichen 函數套用至圖像。

按一下以複製此運算式

按一下以複製此運算式

3. 比較兩個圖像。

(brain.bmp)

(brain_fre.bmp)

freichen 邊緣檢測器可用於含有各種強度的圖像，以定義圖片的各種邊緣。這些核顯示對相關像素值的感應很高，而無關於其亮度。

sobel

此函數使用下列兩個核迴旋圖像矩陣：

按一下以複製此運算式

<region id="ID0EM4L3" top="936" left="24" xml:lang="zh_TW" height="53.012" width="109.183333333333" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math xml:lang="zh_TW">
    <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">
      <id xml:lang="zh_TW" label="None">K1</id>
      <apply xml:lang="zh_TW">
        <mult xml:lang="zh_TW" />
        <apply xml:lang="zh_TW">
          <div xml:lang="zh_TW" />
          <real xml:lang="zh_TW">1</real>
          <real xml:lang="zh_TW">4</real>
        </apply>
        <matrix rows="3" cols="3" xml:lang="zh_TW">
          <real xml:lang="zh_TW">1</real>
          <real xml:lang="zh_TW">2</real>
          <real xml:lang="zh_TW">1</real>
          <real xml:lang="zh_TW">0</real>
          <real xml:lang="zh_TW">0</real>
          <real xml:lang="zh_TW">0</real>
          <real xml:lang="zh_TW">-1</real>
          <real xml:lang="zh_TW">-2</real>
          <real xml:lang="zh_TW">-1</real>
        </matrix>
      </apply>
    </define>
    <resultFormat xml:lang="zh_TW">
      <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" />
      <matrix size="12,12" offset="0,0" xml:lang="zh_TW" />
    </resultFormat>
  </math>
</region>

按一下以複製此運算式

<region id="ID0E54L3" top="936" left="168" xml:lang="zh_TW" height="53.012" width="125.31" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math xml:lang="zh_TW">
    <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">
      <id xml:lang="zh_TW" label="None">K2</id>
      <apply xml:lang="zh_TW">
        <mult xml:lang="zh_TW" />
        <apply xml:lang="zh_TW">
          <div xml:lang="zh_TW" />
          <real xml:lang="zh_TW">1</real>
          <real xml:lang="zh_TW">4</real>
        </apply>
        <matrix rows="3" cols="3" xml:lang="zh_TW">
          <real xml:lang="zh_TW">-1</real>
          <real xml:lang="zh_TW">0</real>
          <real xml:lang="zh_TW">1</real>
          <real xml:lang="zh_TW">-2</real>
          <real xml:lang="zh_TW">0</real>
          <real xml:lang="zh_TW">2</real>
          <real xml:lang="zh_TW">-1</real>
          <real xml:lang="zh_TW">0</real>
          <real xml:lang="zh_TW">1</real>
        </matrix>
      </apply>
    </define>
    <resultFormat xml:lang="zh_TW">
      <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" />
      <matrix size="12,12" offset="0,0" xml:lang="zh_TW" />
    </resultFormat>
  </math>
</region>

將 sobel 函數套用至輸入圖像。

按一下以複製此運算式

按一下以複製此運算式

(brain_sob.bmp)

sobel 核提供一致的邊緣檢測，但會提供加權給對角像素上的正交像素。

prewitt

此函數使用下列兩個核迴旋圖像矩陣：

按一下以複製此運算式

<region id="ID0EMBM3" top="1584" left="24" xml:lang="zh_TW" height="53.012" width="109.183333333333" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math xml:lang="zh_TW">
    <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">
      <id xml:lang="zh_TW" label="None">K1</id>
      <apply xml:lang="zh_TW">
        <mult xml:lang="zh_TW" />
        <apply xml:lang="zh_TW">
          <div xml:lang="zh_TW" />
          <real xml:lang="zh_TW">1</real>
          <real xml:lang="zh_TW">3</real>
        </apply>
        <matrix rows="3" cols="3" xml:lang="zh_TW">
          <real xml:lang="zh_TW">1</real>
          <real xml:lang="zh_TW">1</real>
          <real xml:lang="zh_TW">1</real>
          <real xml:lang="zh_TW">0</real>
          <real xml:lang="zh_TW">0</real>
          <real xml:lang="zh_TW">0</real>
          <real xml:lang="zh_TW">-1</real>
          <real xml:lang="zh_TW">-1</real>
          <real xml:lang="zh_TW">-1</real>
        </matrix>
      </apply>
    </define>
    <resultFormat xml:lang="zh_TW">
      <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" />
      <matrix size="12,12" offset="0,0" xml:lang="zh_TW" />
    </resultFormat>
  </math>
</region>

按一下以複製此運算式

<region id="ID0E5BM3" top="1584" left="168" xml:lang="zh_TW" height="53.012" width="125.31" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math xml:lang="zh_TW">
    <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">
      <id xml:lang="zh_TW" label="None">K2</id>
      <apply xml:lang="zh_TW">
        <mult xml:lang="zh_TW" />
        <apply xml:lang="zh_TW">
          <div xml:lang="zh_TW" />
          <real xml:lang="zh_TW">1</real>
          <real xml:lang="zh_TW">3</real>
        </apply>
        <matrix rows="3" cols="3" xml:lang="zh_TW">
          <real xml:lang="zh_TW">-1</real>
          <real xml:lang="zh_TW">0</real>
          <real xml:lang="zh_TW">1</real>
          <real xml:lang="zh_TW">-1</real>
          <real xml:lang="zh_TW">0</real>
          <real xml:lang="zh_TW">1</real>
          <real xml:lang="zh_TW">-1</real>
          <real xml:lang="zh_TW">0</real>
          <real xml:lang="zh_TW">1</real>
        </matrix>
      </apply>
    </define>
    <resultFormat xml:lang="zh_TW">
      <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" />
      <matrix size="12,12" offset="0,0" xml:lang="zh_TW" />
    </resultFormat>
  </math>
</region>

將 prewitt 函數套用至輸入圖像。

按一下以複製此運算式

按一下以複製此運算式

(brain_pre.bmp)

prewitt 核將正交與對角像素微分一視同仁。

roberts

此函數使用下列兩個核迴旋圖像矩陣：

按一下以複製此運算式

<region id="ID0EMFM3" top="2160" left="24" xml:lang="zh_TW" height="53.012" width="90.7366666666667" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math xml:lang="zh_TW">
    <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">
      <id xml:lang="zh_TW" label="None">K1</id>
      <matrix rows="3" cols="3" xml:lang="zh_TW">
        <real xml:lang="zh_TW">0</real>
        <real xml:lang="zh_TW">0</real>
        <real xml:lang="zh_TW">0</real>
        <real xml:lang="zh_TW">0</real>
        <real xml:lang="zh_TW">1</real>
        <real xml:lang="zh_TW">0</real>
        <real xml:lang="zh_TW">-1</real>
        <real xml:lang="zh_TW">0</real>
        <real xml:lang="zh_TW">0</real>
      </matrix>
    </define>
    <resultFormat xml:lang="zh_TW">
      <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" />
      <matrix size="12,12" offset="0,0" xml:lang="zh_TW" />
    </resultFormat>
  </math>
</region>

按一下以複製此運算式

<region id="ID0E5FM3" top="2160" left="168" xml:lang="zh_TW" height="53.012" width="90.7366666666667" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math xml:lang="zh_TW">
    <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">
      <id xml:lang="zh_TW" label="None">K2</id>
      <matrix rows="3" cols="3" xml:lang="zh_TW">
        <real xml:lang="zh_TW">-1</real>
        <real xml:lang="zh_TW">0</real>
        <real xml:lang="zh_TW">0</real>
        <real xml:lang="zh_TW">0</real>
        <real xml:lang="zh_TW">1</real>
        <real xml:lang="zh_TW">0</real>
        <real xml:lang="zh_TW">0</real>
        <real xml:lang="zh_TW">0</real>
        <real xml:lang="zh_TW">0</real>
      </matrix>
    </define>
    <resultFormat xml:lang="zh_TW">
      <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" />
      <matrix size="12,12" offset="0,0" xml:lang="zh_TW" />
    </resultFormat>
  </math>
</region>

將 roberts 函數套用至輸入圖像。

按一下以複製此運算式

按一下以複製此運算式

(brain_rob.bmp)

roberts 核僅會考慮對角像素微分，此微分強調邊角更清晰，但可能模糊微小的水平或垂直特徵。