示例：噪声的增加和测量

函数 > 图像处理 > 图像操作 > 示例：噪声的增加和测量

示例：噪声的增加和测量

addnoise

使用 addnoise 函数对概率为 p/2 的 M 中的每个元素以量值 n (其中 n 为任意实数) 进行噪声的增减。

有关使用此示例的信息，请参考关于图像处理示例。

1. 将 5 × 5 矩阵的所有元素值定义为 127。

2. 向矩阵 M 添加噪声，将 +/-50 加到 M 中一半的元素上。

3. 使用 READ_IMAGE 函数读入图像、将 addnoise 应用到图像，然后使用 WRITEBMP 将其写入到文件。

(camera.bmp)

(noisy_camera.bmp)

函数 addnoise 将生成的像素值范围裁减至 0–255。

4. 将 imhist 函数应用于两个图像，然后比较柱状图之间的差异，以从数学上理解噪声的效果。

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0 和 255 处较大的差异峰值表明利用 addnoise 函数进行了裁减。

使用其他方法添加噪声

您可以通过构建数学表达式的方式生成其他类型的噪声。

1. 要生成高斯噪声，可使用下列表达式：

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  <math resultRef="67">
    <define xmlns="http://schemas.mathsoft.com/math50">
      <function>
        <id label="None" xml:space="preserve">gnoise</id>
        <boundVars>
          <id label="None" xml:space="preserve">A</id>
          <id label="None" xml:space="preserve">σ</id>
        </boundVars>
      </function>
      <apply>
        <plus />
        <id label="Variable" xml:space="preserve" label-is-contextual="true">A</id>
        <apply>
          <mult />
          <apply>
            <mult />
            <id label="Variable" xml:space="preserve" label-is-contextual="true">σ</id>
            <apply>
              <nthRoot />
              <placeholder />
              <apply>
                <mult />
                <real>-2</real>
                <apply>
                  <id label="Function" xml:space="preserve" label-is-contextual="true">ln</id>
                  <apply>
                    <id label="Function" xml:space="preserve" label-is-contextual="true">rnd</id>
                    <real>1</real>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
          <apply>
            <id label="Function" xml:space="preserve" label-is-contextual="true">cos</id>
            <apply>
              <mult />
              <apply>
                <mult />
                <real>2</real>
                <id label="Constant" xml:space="preserve" label-is-contextual="true">π</id>
              </apply>
              <apply>
                <id label="Function" xml:space="preserve" label-is-contextual="true">rnd</id>
                <real>1</real>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </define>
    <resultFormat>
      <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
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gnoise 不是内置函数。A 为噪声的均值，而 σ 为标准差。

与 addnoise 函数不同，高斯法并不将生成的像素值范围裁减至 0–255。

2. 使用 gnoise 生成噪声矩阵。

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    <define xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <indexer />
        <id label="None" xml:space="preserve">noise2</id>
        <sequence>
          <id label="None" xml:space="preserve">i</id>
          <id label="None" xml:space="preserve">j</id>
        </sequence>
      </apply>
      <apply>
        <id label="Variable" xml:space="preserve" label-is-contextual="true">gnoise</id>
        <sequence>
          <id label="Variable" xml:space="preserve" label-is-contextual="true">A</id>
          <id label="Variable" xml:space="preserve" label-is-contextual="true">σ</id>
        </sequence>
      </apply>
    </define>
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      <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
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3. 绘制噪声的柱状图。

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            <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
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                <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">k_range</id>
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        <yAxis rank="1" legend-position="PlotBoundaryLeft" start="0" end="2750">
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            <gridFrequency>12</gridFrequency>
            <gridLabels display="true" />
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            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat>
            <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
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                <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">Zhis</id>
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        </yAxis>
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柱状图显示大多数信号值落入前 30 个柱中。

4. 插入新图像 M2 (原始图像加上噪声)。

(noisy_camera2.bmp)