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            <c val="#008080">EDGE FINDERS</c>
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            <b>
              <c val="#800080">Canny Edge Detector</c>
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        <phrase>canny edge detector</phrase>
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          <b>
            <c val="#800000">Function Definition and Syntax</c>
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              <c val="#800000">canny(M, sigma, low, high)</c>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">This function uses Canny's algorithm for detecting edges in an image. The algorithm has several steps involving convolution with a derivative-of-Gaussian kernel, and several thresholding steps. This edge-detection algorithm can be used to find boundaries of objects in an image.</p>
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        <phrase>Canny's algorithm</phrase>
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              <c val="#008080">•</c>
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          </f>
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          <b>M</b>, the image matrix.</p>
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              <c val="#008080">•</c>
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              <sp />
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              <inlineAttr font-style="normal" line-through="false">sigma</inlineAttr>
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          </f>, the standard deviation of the derivative-of-Gaussian kernel. Large values result in coarser edges and small values in finer edges. Value is greater than 0, typically between 0 and 2. It should also be true that: <region region-id="710" left="62.25" top="286.5" width="189.75" height="15.75" align-x="129.75" align-y="297.75" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:apply><ml:lessOrEqual /><ml:apply><ml:mult style="default" /><ml:real>4</ml:real><ml:apply><ml:id xml:space="preserve">ceil</ml:id><ml:id xml:space="preserve">sigma</ml:id></ml:apply></ml:apply><ml:apply><ml:id xml:space="preserve">min</ml:id><ml:sequence><ml:apply><ml:id xml:space="preserve">rows</ml:id><ml:id xml:space="preserve">M</ml:id></ml:apply><ml:apply><ml:id xml:space="preserve">cols</ml:id><ml:id xml:space="preserve">M</ml:id></ml:apply></ml:sequence></ml:apply></ml:apply></math><rendering item-idref="6" /></region></p>
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              <c val="#008080">•</c>
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              <c val="#008080">•</c>
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          <inlineAttr font-style="normal">,</inlineAttr> the upper threshold value for intensity gradients: values are real and <inlineAttr font-style="normal">low</inlineAttr> &lt; <inlineAttr font-style="normal">high.</inlineAttr><sp /></p>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">The function returns a binary image matrix containing the detected edges, where the edge points have value 1 and the background has value 0. The perimeter of the image will have undefined values, since the kernels will not fully overlap the image there.</p>
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          <b>
            <c val="#800000">Function Details</c>
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              <c val="#800000">canny(M, sigma, low, high)</c>
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        <phrase>canny function</phrase>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">This function uses Canny's algorithm for detecting edges in an image, <f family="Times New Roman" charset="0"><b><inlineAttr font-style="normal" line-through="false">M</inlineAttr></b></f><f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">. This algorithm finds locations of edges very accurately and minimizes the appearance of false edges. </inlineAttr></f></p>
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            <inlineAttr font-weight="normal" line-through="false">Canny's edge detection algorithm consists of three stages.</inlineAttr>
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            <f family="Times New Roman" charset="0">1. Convolution of the input image with a derivative-of-Gaussian kernel, where </f>
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            <inlineAttr font-weight="normal" line-through="false"> is the standard deviation of the Gaussian. </inlineAttr>
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          </b> plays the role of a scale parameter for the edges: large values of <f family="Times New Roman" charset="0"><b><inlineAttr font-style="normal" line-through="false">sigma</inlineAttr></b></f> produce coarser scale edges and small values of <inlineAttr font-style="normal" line-through="false"><f family="Times New Roman" charset="0"><b>sigma</b></f></inlineAttr> produce finer scale edges. Larger values of <f family="Times New Roman" charset="0"><b><inlineAttr font-style="normal" line-through="false">sigma</inlineAttr></b></f> also result in greater noise suppression.</p>
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            <f family="Times New Roman" charset="0">2. Nonmaxima suppression along the direction of the intensity gradient for each pixel.</f>
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            <inlineAttr font-weight="normal" line-through="false">3. Hysteresis thresholding using the </inlineAttr>
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              <f family="Times New Roman" charset="0">low</f>
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            <f family="Times New Roman" charset="0"> and </f>
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              <f family="Times New Roman" charset="0">high</f>
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            <f family="Times New Roman" charset="0"> threshold values. </f>
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          <f family="Times New Roman" charset="0">
            <inlineAttr font-weight="normal" line-through="false">In hysteresis thresholding, the magnitudes of the intensity gradients are first thresholded using the lower threshold value. Then, pixels that have gradient magnitudes above the lower threshold, but with connected segments having at least one pixel with gradient magnitude larger than the higher threshold are retained.</inlineAttr>
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        <phrase>hysteresis thresholding</phrase>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Here is an example of Canny's edge detection on an artificial image. </p>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">You can observe the effect of changing the parameter values on the edges in the output image. For example, increasing the value of <f family="Times New Roman" charset="0"><b><inlineAttr font-style="normal" line-through="false">sigma</inlineAttr></b></f> produces coarser edges (better for the noisy horizontal strip), but a loss of detail elsewhere (for example, two edges may start merging into one). Increasing the value of the lower threshold leads to a cleaner edge image because only edges above a certain gradient value are retained. Increasing the value of the upper threshold illustrates the effect of hysteresis thresholding. Larger values of <f family="Times New Roman" charset="0"><b><inlineAttr font-style="normal" line-through="false">high</inlineAttr></b></f> result in the complete disappearance of edges corresponding to objects with no pixel on a connected edge of intensity greater than <f family="Times New Roman" charset="0"><b><inlineAttr font-style="normal" line-through="false">high</inlineAttr></b></f><inlineAttr font-style="normal">.</inlineAttr></p>
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        <phrase>hysteresis thresholding</phrase>
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        <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Application of this algorithm on the brain image, above, shows that it can detect</p>
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        <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Now let's apply the algorithm to a fingerprint image:</p>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Again, the application of this algorithm finds the boundaries of the major contours on the fingerprint image, which can then be input to a pattern-recognition system.</p>
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        <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Finally we show the application of this edge-detection algorithm on the</p>
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