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<title>kernelSelection</title>
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<h1 class="mume-header" id="kernel-selection">Kernel selection</h1>
<h2 class="mume-header" id="creating-a-kernel-using-opencv">Creating a kernel using opencv</h2>
<pre data-role="codeBlock" data-info="py" class="language-python"><span class="token keyword">import</span> cv2
ksize <span class="token operator">=</span> <span class="token punctuation">(</span><span class="token number">100</span><span class="token punctuation">,</span><span class="token number">100</span><span class="token punctuation">)</span>
sigma <span class="token operator">=</span> <span class="token number">5</span>
theta <span class="token operator">=</span> <span class="token number">0</span><span class="token operator">*</span><span class="token punctuation">(</span>np<span class="token punctuation">.</span>pi<span class="token operator">/</span><span class="token number">8</span><span class="token punctuation">)</span>
lambd <span class="token operator">=</span> <span class="token number">10</span>
gamma <span class="token operator">=</span> <span class="token number">0</span>
phi <span class="token operator">=</span> <span class="token number">0</span>
kernel <span class="token operator">=</span> cv2<span class="token punctuation">.</span>getGaborKernel<span class="token punctuation">(</span>ksize<span class="token punctuation">,</span>sigma<span class="token punctuation">,</span>theta<span class="token punctuation">,</span>lambd<span class="token punctuation">,</span>gamma<span class="token punctuation">,</span>phi<span class="token punctuation">,</span>ktype <span class="token operator">=</span> cv2<span class="token punctuation">.</span>CV_32F<span class="token punctuation">)</span>
plt<span class="token punctuation">.</span>imshow<span class="token punctuation">(</span>cv2<span class="token punctuation">.</span>cvtColor<span class="token punctuation">(</span>kernel<span class="token punctuation">,</span>cv2<span class="token punctuation">.</span>COLOR_BGR2RGB<span class="token punctuation">)</span><span class="token punctuation">)</span>
</pre><h2 class="mume-header" id="to-apply-a-kernel-on-a-image">To apply a kernel on a image</h2>
<pre data-role="codeBlock" data-info="py" class="language-python">img <span class="token operator">=</span> cv2<span class="token punctuation">.</span>imread<span class="token punctuation">(</span>img_path<span class="token punctuation">,</span><span class="token number">0</span><span class="token punctuation">)</span> <span class="token comment"># 0 is for reading image as grayscale</span>
filtered_img <span class="token operator">=</span> cv2<span class="token punctuation">.</span>filter2D<span class="token punctuation">(</span>img<span class="token punctuation">,</span> cv2<span class="token punctuation">.</span>CV_8UC3<span class="token punctuation">,</span>kernel<span class="token punctuation">)</span>
</pre><h2 class="mume-header" id="sample-kernels">Sample kernels</h2>
<p><strong>100 x 100 kernel</strong><br>
<img src="./img/kernelselectionmd066.png" alt="11x11 kernel" title="11x11 kernel"><br>
<em>Note : The kernel shapes are always in odd numbers even after defining shape explicitly. Hence ksize=(2,2) will return (3,3) size kernel.</em></p>
<h3 class="mume-header" id="changing-sigma">Changing sigma</h3>
<p><img src="./img/kernelselectionmd065.png" alt="changing sigma" title="changing sigma"></p>
<h3 class="mume-header" id="changing-theta">Changing theta</h3>
<p><img src="./img/kernelselectionmd067.png" alt="changing theta" title="changing theta"></p>
<h3 class="mume-header" id="changing-lambda">Changing lambda</h3>
<p><img src="./img/kernelselectionmd068.png" alt="changing lambda" title="changing lambda"></p>
<h3 class="mume-header" id="changing-gamma">Changing gamma</h3>
<p><img src="./img/kernelselectionmd069.png" alt="changing gamma" title="changing gamma"></p>
<h3 class="mume-header" id="changing-phi">Changing phi</h3>
<p><img src="./img/kernelselectionmd070.png" alt="changing phi" title="changing phi"></p>
<h2 class="mume-header" id="applying-kernel-on-handwritten-documents">Applying kernel on handwritten documents</h2>
<p>Applying kernel on a handwritten document image.<br>
<strong>Kernel size = (3,3)</strong></p>
<pre data-role="codeBlock" data-info="py" class="language-python">ksize <span class="token operator">=</span> <span class="token punctuation">(</span><span class="token number">3</span><span class="token punctuation">,</span><span class="token number">3</span><span class="token punctuation">)</span>
sigma <span class="token operator">=</span> <span class="token number">0.01</span>
theta <span class="token operator">=</span> <span class="token number">1</span><span class="token operator">*</span><span class="token punctuation">(</span>np<span class="token punctuation">.</span>pi<span class="token operator">/</span><span class="token number">4</span><span class="token punctuation">)</span>
lambd <span class="token operator">=</span> <span class="token number">9</span>
gamma <span class="token operator">=</span> <span class="token number">0</span>
phi <span class="token operator">=</span> <span class="token number">0</span>
</pre><p><img src="./img/kernelselectionmd038.png" alt="kernel 3x3" title="kernel 3x3"><br>
<strong>Kernel size = (5,5)</strong></p>
<pre data-role="codeBlock" data-info="py" class="language-python">ksize <span class="token operator">=</span> <span class="token punctuation">(</span><span class="token number">5</span><span class="token punctuation">,</span><span class="token number">5</span><span class="token punctuation">)</span>
sigma <span class="token operator">=</span> <span class="token number">0.1</span>
theta <span class="token operator">=</span> <span class="token number">1</span><span class="token operator">*</span><span class="token punctuation">(</span>np<span class="token punctuation">.</span>pi<span class="token operator">/</span><span class="token number">4</span><span class="token punctuation">)</span>
lambd <span class="token operator">=</span> <span class="token number">9</span>
gamma <span class="token operator">=</span> <span class="token number">0</span>
phi <span class="token operator">=</span> <span class="token number">0</span>
</pre><p><img src="./img/kernelselectionmd039.png" alt="kernel 5x5" title="kernel 5x5"><br>
<strong>Kernel size = (7,7)</strong></p>
<pre data-role="codeBlock" data-info="py" class="language-python">ksize <span class="token operator">=</span> <span class="token punctuation">(</span><span class="token number">7</span><span class="token punctuation">,</span><span class="token number">7</span><span class="token punctuation">)</span>
sigma <span class="token operator">=</span> <span class="token number">0.1</span>
theta <span class="token operator">=</span> <span class="token number">1</span><span class="token operator">*</span><span class="token punctuation">(</span>np<span class="token punctuation">.</span>pi<span class="token operator">/</span><span class="token number">4</span><span class="token punctuation">)</span>
lambd <span class="token operator">=</span> <span class="token number">9</span>
gamma <span class="token operator">=</span> <span class="token number">0</span>
phi <span class="token operator">=</span> <span class="token number">0</span>
</pre><p><img src="./img/kernelselectionmd040.png" alt="kernel 7x7" title="kernel 7x7"><br>
<strong>Kernel size = (7,7) increasing sigma to 15</strong><br>
increasing sigma further more doesn't improve</p>
<pre data-role="codeBlock" data-info="py" class="language-python">ksize <span class="token operator">=</span> <span class="token punctuation">(</span><span class="token number">7</span><span class="token punctuation">,</span><span class="token number">7</span><span class="token punctuation">)</span>
sigma <span class="token operator">=</span> <span class="token number">15</span>
theta <span class="token operator">=</span> <span class="token number">1</span><span class="token operator">*</span><span class="token punctuation">(</span>np<span class="token punctuation">.</span>pi<span class="token operator">/</span><span class="token number">4</span><span class="token punctuation">)</span>
lambd <span class="token operator">=</span> <span class="token number">9</span>
gamma <span class="token operator">=</span> <span class="token number">0</span>
phi <span class="token operator">=</span> <span class="token number">0</span>
</pre><p><img src="./img/kernelselectionmd041.png" alt="kernel 7x7" title="kernel 7x7"><br>
<strong>Kernel size = (9,9)</strong></p>
<pre data-role="codeBlock" data-info="py" class="language-python">ksize <span class="token operator">=</span> <span class="token punctuation">(</span><span class="token number">9</span><span class="token punctuation">,</span><span class="token number">9</span><span class="token punctuation">)</span>
sigma <span class="token operator">=</span> <span class="token number">5</span>
theta <span class="token operator">=</span> <span class="token number">1</span><span class="token operator">*</span><span class="token punctuation">(</span>np<span class="token punctuation">.</span>pi<span class="token operator">/</span><span class="token number">4</span><span class="token punctuation">)</span>
lambd <span class="token operator">=</span> <span class="token number">9</span>
gamma <span class="token operator">=</span> <span class="token number">0</span>
phi <span class="token operator">=</span> <span class="token number">0</span>
</pre><p><img src="./img/kernelselectionmd042.png" alt="kernel 9x9" title="kernel 9x9"><br>
<strong>Kernel size = (9,9) increasing sigma to 8</strong></p>
<pre data-role="codeBlock" data-info="py" class="language-python">ksize <span class="token operator">=</span> <span class="token punctuation">(</span><span class="token number">9</span><span class="token punctuation">,</span><span class="token number">9</span><span class="token punctuation">)</span>
sigma <span class="token operator">=</span> <span class="token number">8</span>
theta <span class="token operator">=</span> <span class="token number">1</span><span class="token operator">*</span><span class="token punctuation">(</span>np<span class="token punctuation">.</span>pi<span class="token operator">/</span><span class="token number">4</span><span class="token punctuation">)</span>
lambd <span class="token operator">=</span> <span class="token number">9</span>
gamma <span class="token operator">=</span> <span class="token number">0</span>
phi <span class="token operator">=</span> <span class="token number">0</span>
</pre><p><img src="./img/kernelselectionmd043.png" alt="kernel 9x9" title="kernel 9x9"><br>
<strong>Kernel size = (11,11)</strong></p>
<pre data-role="codeBlock" data-info="py" class="language-python">ksize <span class="token operator">=</span> <span class="token punctuation">(</span><span class="token number">11</span><span class="token punctuation">,</span><span class="token number">11</span><span class="token punctuation">)</span>
sigma <span class="token operator">=</span> <span class="token number">5</span>
theta <span class="token operator">=</span> <span class="token number">1</span><span class="token operator">*</span><span class="token punctuation">(</span>np<span class="token punctuation">.</span>pi<span class="token operator">/</span><span class="token number">4</span><span class="token punctuation">)</span>
lambd <span class="token operator">=</span> <span class="token number">9</span>
gamma <span class="token operator">=</span> <span class="token number">0</span>
phi <span class="token operator">=</span> <span class="token number">0</span>
</pre><p><img src="./img/kernelselectionmd044.png" alt="kernel 11x11" title="kernel 11x11"><br>
<strong>Kernel size = (11,11) sigma 7</strong></p>
<pre data-role="codeBlock" data-info="py" class="language-python">ksize <span class="token operator">=</span> <span class="token punctuation">(</span><span class="token number">11</span><span class="token punctuation">,</span><span class="token number">11</span><span class="token punctuation">)</span>
sigma <span class="token operator">=</span> <span class="token number">7</span>
theta <span class="token operator">=</span> <span class="token number">1</span><span class="token operator">*</span><span class="token punctuation">(</span>np<span class="token punctuation">.</span>pi<span class="token operator">/</span><span class="token number">4</span><span class="token punctuation">)</span>
lambd <span class="token operator">=</span> <span class="token number">9</span>
gamma <span class="token operator">=</span> <span class="token number">0</span>
phi <span class="token operator">=</span> <span class="token number">0</span>
</pre><p><img src="./img/kernelselectionmd045.png" alt="kernel 11x11" title="kernel 11x11"><br>
<strong>Kernel size = (11,11) sigma 9</strong></p>
<pre data-role="codeBlock" data-info="py" class="language-python">ksize <span class="token operator">=</span> <span class="token punctuation">(</span><span class="token number">11</span><span class="token punctuation">,</span><span class="token number">11</span><span class="token punctuation">)</span>
sigma <span class="token operator">=</span> <span class="token number">9</span>
theta <span class="token operator">=</span> <span class="token number">1</span><span class="token operator">*</span><span class="token punctuation">(</span>np<span class="token punctuation">.</span>pi<span class="token operator">/</span><span class="token number">4</span><span class="token punctuation">)</span>
lambd <span class="token operator">=</span> <span class="token number">9</span>
gamma <span class="token operator">=</span> <span class="token number">0</span>
phi <span class="token operator">=</span> <span class="token number">0</span>
</pre><p><img src="./img/kernelselectionmd046.png" alt="kernel 11x11" title="kernel 11x11"><br>
Features are not very clear.<br>
<strong>Kernel size = (13,13)</strong></p>
<pre data-role="codeBlock" data-info="py" class="language-python">ksize <span class="token operator">=</span> <span class="token punctuation">(</span><span class="token number">13</span><span class="token punctuation">,</span><span class="token number">13</span><span class="token punctuation">)</span>
sigma <span class="token operator">=</span> <span class="token number">7</span>
theta <span class="token operator">=</span> <span class="token number">1</span><span class="token operator">*</span><span class="token punctuation">(</span>np<span class="token punctuation">.</span>pi<span class="token operator">/</span><span class="token number">4</span><span class="token punctuation">)</span>
lambd <span class="token operator">=</span> <span class="token number">9</span>
gamma <span class="token operator">=</span> <span class="token number">0</span>
phi <span class="token operator">=</span> <span class="token number">0</span>
</pre><p><img src="./img/kernelselectionmd047.png" alt="kernel 13x13" title="kernel 13x13"><br>
Features are not clear. sigma should be less.<br>
<strong>Kernel size = (13,13) sigma 5</strong></p>
<pre data-role="codeBlock" data-info="py" class="language-python">ksize <span class="token operator">=</span> <span class="token punctuation">(</span><span class="token number">13</span><span class="token punctuation">,</span><span class="token number">13</span><span class="token punctuation">)</span>
sigma <span class="token operator">=</span> <span class="token number">5</span>
theta <span class="token operator">=</span> <span class="token number">1</span><span class="token operator">*</span><span class="token punctuation">(</span>np<span class="token punctuation">.</span>pi<span class="token operator">/</span><span class="token number">4</span><span class="token punctuation">)</span>
lambd <span class="token operator">=</span> <span class="token number">9</span>
gamma <span class="token operator">=</span> <span class="token number">0</span>
phi <span class="token operator">=</span> <span class="token number">0</span>
</pre><p><img src="./img/kernelselectionmd048.png" alt="kernel 13x13" title="kernel 13x13"><br>
<strong>Kernel size = (13,13) sigma 5 angle 90</strong></p>
<pre data-role="codeBlock" data-info="py" class="language-python">ksize <span class="token operator">=</span> <span class="token punctuation">(</span><span class="token number">13</span><span class="token punctuation">,</span><span class="token number">13</span><span class="token punctuation">)</span>
sigma <span class="token operator">=</span> <span class="token number">5</span>
theta <span class="token operator">=</span> <span class="token number">1</span><span class="token operator">*</span><span class="token punctuation">(</span>np<span class="token punctuation">.</span>pi<span class="token operator">/</span><span class="token number">4</span><span class="token punctuation">)</span>
lambd <span class="token operator">=</span> <span class="token number">9</span>
gamma <span class="token operator">=</span> <span class="token number">0</span>
phi <span class="token operator">=</span> <span class="token number">0</span>
</pre><p><img src="./img/kernelselectionmd049.png" alt="kernel 13x13" title="kernel 13x13"><br>
Not good. Need to change lambda<br>
<strong>Kernel size = (13,13) sigma 5 angle 90 lambda=14</strong></p>
<pre data-role="codeBlock" data-info="py" class="language-python">ksize <span class="token operator">=</span> <span class="token punctuation">(</span><span class="token number">13</span><span class="token punctuation">,</span><span class="token number">13</span><span class="token punctuation">)</span>
sigma <span class="token operator">=</span> <span class="token number">5</span>
theta <span class="token operator">=</span> <span class="token number">1</span><span class="token operator">*</span><span class="token punctuation">(</span>np<span class="token punctuation">.</span>pi<span class="token operator">/</span><span class="token number">4</span><span class="token punctuation">)</span>
lambd <span class="token operator">=</span> <span class="token number">14</span>
gamma <span class="token operator">=</span> <span class="token number">0</span>
phi <span class="token operator">=</span> <span class="token number">0</span>
</pre><p><img src="./img/kernelselectionmd050.png" alt="kernel 13x13" title="kernel 13x13"><br>
Not good. Need to change lambda<br>
<strong>Kernel size = (13,13) sigma 5 angle 0 lambda=14</strong></p>
<pre data-role="codeBlock" data-info="py" class="language-python">ksize <span class="token operator">=</span> <span class="token punctuation">(</span><span class="token number">13</span><span class="token punctuation">,</span><span class="token number">13</span><span class="token punctuation">)</span>
sigma <span class="token operator">=</span> <span class="token number">5</span>
theta <span class="token operator">=</span> <span class="token number">0</span><span class="token operator">*</span><span class="token punctuation">(</span>np<span class="token punctuation">.</span>pi<span class="token operator">/</span><span class="token number">4</span><span class="token punctuation">)</span>
lambd <span class="token operator">=</span> <span class="token number">14</span>
gamma <span class="token operator">=</span> <span class="token number">0</span>
phi <span class="token operator">=</span> <span class="token number">0</span>
</pre><p><img src="./img/kernelselectionmd051.png" alt="kernel 13x13" title="kernel 13x13"></p>
<p>Applying this kernel to other images.<br>
<strong>Kernel size = (13,13) img 2</strong></p>
<pre data-role="codeBlock" data-info="py" class="language-python">ksize <span class="token operator">=</span> <span class="token punctuation">(</span><span class="token number">13</span><span class="token punctuation">,</span><span class="token number">13</span><span class="token punctuation">)</span>
sigma <span class="token operator">=</span> <span class="token number">5</span>
theta <span class="token operator">=</span> <span class="token number">0</span><span class="token operator">*</span><span class="token punctuation">(</span>np<span class="token punctuation">.</span>pi<span class="token operator">/</span><span class="token number">4</span><span class="token punctuation">)</span>
lambd <span class="token operator">=</span> <span class="token number">14</span>
gamma <span class="token operator">=</span> <span class="token number">0</span>
phi <span class="token operator">=</span> <span class="token number">0</span>
</pre><p><img src="./img/kernelselectionmd052.png" alt="kernel 13x13" title="kernel 13x13"><br>
increasing sigma value.<br>
<strong>Kernel size = (13,13) img 2 sigma 10</strong></p>
<pre data-role="codeBlock" data-info="py" class="language-python">ksize <span class="token operator">=</span> <span class="token punctuation">(</span><span class="token number">13</span><span class="token punctuation">,</span><span class="token number">13</span><span class="token punctuation">)</span>
sigma <span class="token operator">=</span> <span class="token number">10</span>
theta <span class="token operator">=</span> <span class="token number">0</span><span class="token operator">*</span><span class="token punctuation">(</span>np<span class="token punctuation">.</span>pi<span class="token operator">/</span><span class="token number">4</span><span class="token punctuation">)</span>
lambd <span class="token operator">=</span> <span class="token number">14</span>
gamma <span class="token operator">=</span> <span class="token number">0</span>
phi <span class="token operator">=</span> <span class="token number">0</span>
</pre><p><img src="./img/kernelselectionmd053.png" alt="kernel 13x13" title="kernel 13x13"><br>
same kernel on previous image<br>
<strong>Kernel size = (13,13) img 1 sigma 10</strong></p>
<pre data-role="codeBlock" data-info="py" class="language-python">ksize <span class="token operator">=</span> <span class="token punctuation">(</span><span class="token number">13</span><span class="token punctuation">,</span><span class="token number">13</span><span class="token punctuation">)</span>
sigma <span class="token operator">=</span> <span class="token number">10</span>
theta <span class="token operator">=</span> <span class="token number">0</span><span class="token operator">*</span><span class="token punctuation">(</span>np<span class="token punctuation">.</span>pi<span class="token operator">/</span><span class="token number">4</span><span class="token punctuation">)</span>
lambd <span class="token operator">=</span> <span class="token number">14</span>
gamma <span class="token operator">=</span> <span class="token number">0</span>
phi <span class="token operator">=</span> <span class="token number">0</span>
</pre><p><img src="./img/kernelselectionmd054.png" alt="kernel 13x13" title="kernel 13x13"><br>
<strong>Kernel size = (13,13) img 3</strong></p>
<pre data-role="codeBlock" data-info="py" class="language-python">ksize <span class="token operator">=</span> <span class="token punctuation">(</span><span class="token number">13</span><span class="token punctuation">,</span><span class="token number">13</span><span class="token punctuation">)</span>
sigma <span class="token operator">=</span> <span class="token number">10</span>
theta <span class="token operator">=</span> <span class="token number">0</span><span class="token operator">*</span><span class="token punctuation">(</span>np<span class="token punctuation">.</span>pi<span class="token operator">/</span><span class="token number">4</span><span class="token punctuation">)</span>
lambd <span class="token operator">=</span> <span class="token number">14</span>
gamma <span class="token operator">=</span> <span class="token number">0</span>
phi <span class="token operator">=</span> <span class="token number">0</span>
</pre><p><img src="./img/kernelselectionmd055.png" alt="kernel 13x13" title="kernel 13x13"><br>
<strong>Kernel size = (13,13) img 3 angle 45</strong></p>
<pre data-role="codeBlock" data-info="py" class="language-python">ksize <span class="token operator">=</span> <span class="token punctuation">(</span><span class="token number">13</span><span class="token punctuation">,</span><span class="token number">13</span><span class="token punctuation">)</span>
sigma <span class="token operator">=</span> <span class="token number">10</span>
theta <span class="token operator">=</span> <span class="token number">1</span><span class="token operator">*</span><span class="token punctuation">(</span>np<span class="token punctuation">.</span>pi<span class="token operator">/</span><span class="token number">4</span><span class="token punctuation">)</span>
lambd <span class="token operator">=</span> <span class="token number">14</span>
gamma <span class="token operator">=</span> <span class="token number">0</span>
phi <span class="token operator">=</span> <span class="token number">0</span>
</pre><p><img src="./img/kernelselectionmd056.png" alt="kernel 13x13" title="kernel 13x13"><br>
Image have different grayscale level hence its better to binarize image first so that the same value of sigma works for all. Here we need to vary value of sigma based upon the darkness of handwriting.</p>
<h3 class="mume-header" id="on-black-and-white-images">On black and white images</h3>
<p>The images are converted into black and white.<br>
<strong>Kernel size = (13,13)</strong></p>
<pre data-role="codeBlock" data-info="py" class="language-python">ksize <span class="token operator">=</span> <span class="token punctuation">(</span><span class="token number">13</span><span class="token punctuation">,</span><span class="token number">13</span><span class="token punctuation">)</span>
sigma <span class="token operator">=</span> <span class="token number">10</span>
theta <span class="token operator">=</span> <span class="token number">2</span><span class="token operator">*</span><span class="token punctuation">(</span>np<span class="token punctuation">.</span>pi<span class="token operator">/</span><span class="token number">8</span><span class="token punctuation">)</span>
lambd <span class="token operator">=</span> <span class="token number">15</span>
gamma <span class="token operator">=</span> <span class="token number">0</span>
phi <span class="token operator">=</span> <span class="token number">0</span>
</pre><p><img src="./img/kernelselectionmd057.png" alt="kernel 13x13" title="kernel 13x13"><br>
<img src="./img/kernelselectionmd058.png" alt="kernel 13x13" title="kernel 13x13"><br>
<img src="./img/kernelselectionmd059.png" alt="kernel 13x13" title="kernel 13x13"><br>
This image has darker and bold strokes hence filtered image will have more black pixel.<br>
<img src="./img/kernelselectionmd060.png" alt="kernel 13x13" title="kernel 13x13"><br>
<img src="./img/kernelselectionmd061.png" alt="kernel 13x13" title="kernel 13x13"><br>
Filtering out horizontal and vertical strokes.<br>
<img src="./img/kernelselectionmd062.png" alt="kernel 13x13" title="kernel 13x13"><br>
<img src="./img/kernelselectionmd063.png" alt="kernel 13x13" title="kernel 13x13"><br>
<img src="./img/kernelselectionmd064.png" alt="kernel 13x13" title="kernel 13x13"><br>
Filtering out horizontal,45 degree and vertical strokes.</p>
<h2 class="mume-header" id="final-output">Final output</h2>
<blockquote>
<p>Input image<br>
<img src="./img/2bw.png" alt="input image" title="input image"></p>
</blockquote>
<blockquote>
<p>Output image<br>
<img src="./img/2bw1.png" alt="output image" title="output image"><br>
<img src="./img/2bw2.png" alt="output image" title="output image"><br>
<img src="./img/2bw3.png" alt="output image" title="output image"><br>
<img src="./img/2bw4.png" alt="output image" title="output image"><br>
<img src="./img/2bw5.png" alt="output image" title="output image"><br>
<img src="./img/2bw6.png" alt="output image" title="output image"><br>
<img src="./img/2bw7.png" alt="output image" title="output image"><br>
<img src="./img/2bw8.png" alt="output image" title="output image"></p>
</blockquote>
</div>
</body></html>