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<h1>
[Convolutional Neural Networks] week4. Special applications: Face recognition & Neural style transfer
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<time datetime="2017-11-30T00:00:00+01:00"><i class="fa fa-calendar"></i> Thu, 30 Nov 2017</time>
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<span class="label label-default">Series</span>
Part 13 of «Andrew Ng Deep Learning MOOC»
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目录
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<div id="toc"><ul><li><a class="toc-href" href="#i-face-recognition" title="I-Face Recognition">I-Face Recognition</a><ul><li><a class="toc-href" href="#what-is-face-recognition" title="What is face recognition">What is face recognition</a></li><li><a class="toc-href" href="#one-shot-learning" title="One Shot Learning">One Shot Learning</a></li><li><a class="toc-href" href="#siamese-network" title="Siamese Network">Siamese Network</a></li><li><a class="toc-href" href="#triplet-loss" title="Triplet Loss">Triplet Loss</a></li><li><a class="toc-href" href="#face-verification-and-binary-classification" title="Face Verification and Binary Classification">Face Verification and Binary Classification</a></li></ul></li><li><a class="toc-href" href="#ii-neural-style-transfer_1" title="II-Neural Style Transfer">II-Neural Style Transfer</a><ul><li><a class="toc-href" href="#what-is-neural-style-transfer" title="What is neural style transfer?">What is neural style transfer?</a></li><li><a class="toc-href" href="#what-are-deep-convnets-learning" title="What are deep ConvNets learning?">What are deep ConvNets learning?</a></li><li><a class="toc-href" href="#cost-function" title="Cost Function">Cost Function</a></li><li><a class="toc-href" href="#content-cost-function" title="Content Cost Function">Content Cost Function</a></li><li><a class="toc-href" href="#style-cost-function" title="Style Cost Function">Style Cost Function</a></li><li><a class="toc-href" href="#1d-and-3d-generalizations" title="1D and 3D Generalizations">1D and 3D Generalizations</a></li></ul></li></ul></div>
</div>
</div>
<p>This week: two special application of ConvNet. </p>
<h2 id="i-face-recognition">I-Face Recognition</h2>
<h3 id="what-is-face-recognition">What is face recognition</h3>
<p><strong>Face verification & face recognition</strong> </p>
<ul>
<li>verification: input = image and ID → output whether the image and ID are the same. </li>
<li>recognition: database = K persons, input = image → output = ID of the image among the K person or "not recognized". </li>
</ul>
<p>→ the verification system's precision needs to be very high in order to be used in face recognition. </p>
<h3 id="one-shot-learning">One Shot Learning</h3>
<p>"one shot": learn from just <em>one</em> example, and able to recognize the person again.<br/>
A CNN+softmax is not practical, e.g. when new images are added to database, output_dim will change... </p>
<p>⇒ instead, learn a <em>similarity</em> function.<br/>
<code>d(img1, img2)</code> = degree of difference between images. + threshold <code>tau</code> </p>
<h3 id="siamese-network">Siamese Network</h3>
<p><img alt="" class="img-responsive" src="../images/Ng_DLMooc_c4wk4/pasted_image.png"/><br/>
To learn a disimilarity function: <em>Siamese Network</em>. </p>
<p>Use CNN+FC to <strong>encode</strong><em> a pic </em><code>x</code><em> into vector </em><code>f(x)</code><em>.</em><br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c4wk4/pasted_image001.png"/><br/>
⇒ define disimilarity function d(x1, x2) as distance between encoded vectors.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c4wk4/pasted_image002.png"/> </p>
<p>More formally:<br/>
want to learn NN params for the encoding f(x) such that:<br/>
when x1 and x2 are same person, dist(f(x1), f(x2)) is small, otherwise large. </p>
<h3 id="triplet-loss">Triplet Loss</h3>
<p><img alt="" class="img-responsive" src="../images/Ng_DLMooc_c4wk4/pasted_image005.png"/><br/>
triplet: (<em>anchor, positive, negative)</em>.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c4wk4/pasted_image004.png"/><br/>
want f(A) similar to f(P) and different from f(N):<br/>
i.e. want <code>d(A, P) - d(A, N) <= 0</code><br/>
⇒ to avoid NN from learning a trival output (i.e. all encodings are identical, d(A, P)=d(A, N)=0), <em>add margin </em><code>alpha</code>.<br/>
want <code>d(A, P) - d(A, N) + alpha<= 0</code> </p>
<p><img alt="" class="img-responsive" src="../images/Ng_DLMooc_c4wk4/pasted_image006.png"/> </p>
<p><strong>Loss function definition</strong>:<br/>
similar to hinge loss: <code>L = max(0, d(A,P)-d(A,N) + alpha)</code> </p>
<p><img alt="" class="img-responsive" src="../images/Ng_DLMooc_c4wk4/pasted_image007.png"/><br/>
→ Generate triplets from dataset, and feed to the NN.<br/>
note: here we do need >1 pics of the same person (Anchor and Positive). </p>
<p><strong>Choosing triplets A, P, N</strong><br/>
If A,P,N are <em>randomly</em> chosen, the constraint is easily satisfied → NN won't learn much.<br/>
→ <em>choose A,P,N that are "hard" to train on. </em>Computation efficiency of learning is improved.<br/>
(<em>details presented in the FaceNet paper</em>) </p>
<p>in practice: better download pretrained model. </p>
<h3 id="face-verification-and-binary-classification">Face Verification and Binary Classification</h3>
<p><img alt="" class="img-responsive" src="../images/Ng_DLMooc_c4wk4/pasted_image.png"/><br/>
Triplet loss is one way of doing face verification.<br/>
another way that works as well: treat as a binary classification problem. </p>
<p>Given input image x1 and x2 → feed f(x1) and f(x2) to a logistic regression unit.<br/>
→ feed the <em>difference in encodings</em> and feed to logistic regression.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c4wk4/pasted_image009.png"/> </p>
<p>computation trick: precompute encodings of imgs in database at inference time. </p>
<h2 id="ii-neural-style-transfer_1">II-Neural Style Transfer</h2>
<h3 id="what-is-neural-style-transfer">What is neural style transfer?</h3>
<p>content image <code>C</code>+ style image <code>S</code> → generated image <code>G</code><br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c4wk4/pasted_image010.png"/> </p>
<h3 id="what-are-deep-convnets-learning">What are deep ConvNets learning?</h3>
<p><img alt="" class="img-responsive" src="../images/Ng_DLMooc_c4wk4/pasted_image011.png"/><br/>
<strong>visualize hidden units of different layers</strong><br/>
Pick <em>one unit</em> in 1st layer → find the <em>nine image patches that maximize the unit's activation</em>. </p>
<p>In deeper layers: units can see larger image patches → gather nine argmax image patchs as before.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c4wk4/pasted_image012.png"/> </p>
<p>deeper layers can detect higher level shapes:<br/>
layer 3:<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c4wk4/pasted_image013.png"/><br/>
layer 4:<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c4wk4/pasted_image014.png"/> </p>
<h3 id="cost-function">Cost Function</h3>
<p><img alt="" class="img-responsive" src="../images/Ng_DLMooc_c4wk4/pasted_image015.png"/><br/>
Define a cost function <em>for the generated image</em>.<br/>
<code>J(G)</code> measure how good is an image, contains two parts: </p>
<ul>
<li><code>J_content(C, G)</code>: how similar is G to C </li>
<li><code>J_style(S, G)</code>: how similar is G to S. </li>
</ul>
<p><img alt="" class="img-responsive" src="../images/Ng_DLMooc_c4wk4/pasted_image016.png"/><br/>
<strong>Find generated image G</strong><br/>
(similar to embedding?) </p>
<ul>
<li>initialize G randomly </li>
<li>Use gradient-descent to minimized J(G) </li>
</ul>
<p><img alt="" class="img-responsive" src="../images/Ng_DLMooc_c4wk4/pasted_image017.png"/> </p>
<h3 id="content-cost-function">Content Cost Function</h3>
<p><code>J_content(C, G)</code> </p>
<p><em>Given a pre-trained CNN</em>, use <em>hidden layer l</em> to compute J_content. The depth of <em>l</em> controls the level of details focuses on. </p>
<p>Define J_content(C, G) = difference (e.g. L2-norm) between the activation of layer l of image C and image G.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c4wk4/pasted_image019.png"/> </p>
<h3 id="style-cost-function">Style Cost Function</h3>
<p>Use layer <code>l</code> to measure "style".<br/>
→ <strong>style</strong> defined as <em>correlation between activations across channels</em>.<br/>
e.g. <code>n_C=5</code> channels of slices <code>n_W * n_H</code>.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c4wk4/pasted_image020.png"/><br/>
correlation between 2 channel ~= <em>which high-level features tend to occur / not occur together in an image.</em> </p>
<p><strong>style matrix</strong><br/>
notation: </p>
<ul>
<li><code>a_ijk</code> = (scalar)activation at hight=<code>i</code>, width=<code>j</code>, channel=<code>k</code> </li>
<li>"Style matrix) <code>G[l]</code>, (G for "Gram matrix") shape = <code>n_C * n_C</code>, measures <em>how correlated any two channels are. </em>(i.e. G[l] measures the degree to which the activations of different feature detectors in layer l vary (or correlate) together with each other.) </li>
<li><code>G_kk</code>' = correlation between kth and k'th channel. </li>
</ul>
<p>:= sum_over_i_j( a_ijk * a_ijk') </p>
<p><img alt="" class="img-responsive" src="../images/Ng_DLMooc_c4wk4/pasted_image021.png"/><br/>
mathematically, this "correlation" is unnormalized cross-covariance (without substracting the mean). </p>
<p>Compute <code>G</code> for both the style image and generated image.<br/>
→ J_style(Gen_img, Sty_img) = difference (Frobenius norm) between G(gen) and G(sty)<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c4wk4/pasted_image022.png"/><br/>
In practice, take J_style for multiple layers:<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c4wk4/pasted_image023.png"/> </p>
<h3 id="1d-and-3d-generalizations">1D and 3D Generalizations</h3>
<p>images: 2D data.<br/>
→ <em>generalize convolution to 1D and 3D data.</em> </p>
<p><strong>1D data</strong><br/>
e.g. EKG data (heart voltage).<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c4wk4/pasted_image024.png"/> </p>
<p>(note: most 1D data use RNN...) </p>
<p><strong>3D data</strong><br/>
have height width and depth,<br/>
e.g. C.T. data; movie date (frame by frame)<br/>
→ generalized from 2D<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c4wk4/pasted_image025.png"/> </p>
</div>
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<div id="toc"><ul><li><a class="toc-href" href="#i-face-recognition" title="I-Face Recognition">I-Face Recognition</a><ul><li><a class="toc-href" href="#what-is-face-recognition" title="What is face recognition">What is face recognition</a></li><li><a class="toc-href" href="#one-shot-learning" title="One Shot Learning">One Shot Learning</a></li><li><a class="toc-href" href="#siamese-network" title="Siamese Network">Siamese Network</a></li><li><a class="toc-href" href="#triplet-loss" title="Triplet Loss">Triplet Loss</a></li><li><a class="toc-href" href="#face-verification-and-binary-classification" title="Face Verification and Binary Classification">Face Verification and Binary Classification</a></li></ul></li><li><a class="toc-href" href="#ii-neural-style-transfer_1" title="II-Neural Style Transfer">II-Neural Style Transfer</a><ul><li><a class="toc-href" href="#what-is-neural-style-transfer" title="What is neural style transfer?">What is neural style transfer?</a></li><li><a class="toc-href" href="#what-are-deep-convnets-learning" title="What are deep ConvNets learning?">What are deep ConvNets learning?</a></li><li><a class="toc-href" href="#cost-function" title="Cost Function">Cost Function</a></li><li><a class="toc-href" href="#content-cost-function" title="Content Cost Function">Content Cost Function</a></li><li><a class="toc-href" href="#style-cost-function" title="Style Cost Function">Style Cost Function</a></li><li><a class="toc-href" href="#1d-and-3d-generalizations" title="1D and 3D Generalizations">1D and 3D Generalizations</a></li></ul></li></ul></div>
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