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              <c val="#800080">Gaussian Kernel Filtering</c>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">These functions convolve (or deconvolve) an image with a Gaussian kernel with half-width<b><sp /></b><f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">s. Convolution is accomplished</inlineAttr></f><b><sp /></b>by multiplying the Matrix and gaussian in spatial frequency (the Fourier transform domain). Gaussian filtering can result in smoothing, edge detection, or noise reduction, depending upon the chosen half-width. Gaussian filters are important analytically because their transforms are also Gaussian.</p>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">The functions return a matrix containing the convolved image in the image domain.</p>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">This function performs function convolution by multiplication in the transform domain using a Gaussian filter function with half-width determined by <f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">s</inlineAttr></f>. Specifically, the half-width is:</p>
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          <b>funconv</b> performs the same function given a Gaussian for <f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">f(x).</inlineAttr></f> Compare the two:</p>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Remember that displayed precision is not the same as the precision used for the calculation. You can display up to 15 decimals, if you like.</p>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Convolution with a Gaussian is equivalent to low-pass filtering an image. Look at what it does to the sharp edges in the picture.</p>
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          <b>
            <c val="#800000">Function Details</c>
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          <b>
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              <c val="#800000">gaussdeconv(M, s, </c>
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                <c val="#800000">e</c>
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              <c val="#800000">)</c>
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        <phrase>gaussdeconv function</phrase>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">This function performs deconvolution. The argument<b><sp /></b><f family="Symbol" charset="2"><inlineAttr font-weight="normal" line-through="false">e</inlineAttr></f><b><sp /></b>is a small term which is added to all expressions in denominators during all divisions in the routine. Therefore as a starting point you should <i><inlineAttr font-weight="normal">always try a value of 0 for </inlineAttr></i><f family="Symbol" charset="2"><i><inlineAttr font-weight="normal">e</inlineAttr></i></f>; if you use <b>gaussdeconv</b> and receive a divide-by-zero error message, try a small value for <f family="Symbol" charset="2"><inlineAttr font-weight="normal" line-through="false">e</inlineAttr></f>.</p>
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