AndrewNG-CV 基础

1 The Basics of Convolutional Neural Networks

1.1 Edge detection

Use filter to do the convolution operation

One Example

image-20210811183228302

image-20210811183734299

Convolution function in tensorflow: tf.nn.conv2d

Other Examples

image-20210812114628935

  • 1->-1: light->dark
  • -1->1: dark->light

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Furthermore, treat the 9 numbers as parameters, and use backward propagation to improve them.

1.2 Padding(填充)

To preserve the information on the edges and corners.

  • Valid convolutions:
    • No padding
    • $n\times n$ * $f\times f$​ ——> $(n-f+1)\times(n-f+1)$
  • Same convolutions:
    • Pad so that output size is the same as the input size.
    • $n+2p-f+1=n$ ==> $p=\frac{f-1}{2}$​
    • f 通常是奇数

1.3 Strided Convolutions

  • with $n\times n$​ image, $f\times f$​​ filter, padding p, stride s, the ouput size is:

$$ \bigg\lfloor\frac{n+2p-f}{s}+1\bigg\rfloor\times\bigg\lfloor\frac{n+2p-f}{s}+1\bigg\rfloor $$

1.4 Convolutions over volumes

channels（depths, 第三个维度）相等

image-20210812233547145

multiple filters：

image-20210812233900130

1.5 One Layer of a CNN

If layer l is a convolution layer:

  • $f^{[l]}=$filter size
  • $p^{[l]}=$​padding
  • $s^{[l]}=$​stride
  • $n_C^{[l]}=$​number of filters
  • Each filter is: $f^{[l]}\times f^{[l]}\times n_C^{[l-1]}$​
  • Weights: $f^{[l]}\times f^{[l]}\times n_C^{[l-1]}\times n_C^{[l]}$​
  • bias: $n_C{[l]}$ — (1,1,1,$n_C{[l]}$)
  • Input: $n^{[l-1]}_H\times n^{[l-1]}_W\times n^{[l-1]}_C$​​
  • Output: $a^{[l]}=n^{[l]}_H\times n^{[l]}_W\times n^{[l]}_C$​​​

$$ n^{[l]}=\bigg\lfloor\frac{n^{[l-1]}+2p^{[l]}-f^{[l]}}{s^{[l]}}+1\bigg\rfloor $$

1.6 Example ConvNet

image-20210818172112985

Height and Width stay the same for a while, and gradually trend down as you go deeper in the neural network.

The number of channels gradually increase.

Types of layer in a convolutional network:

  • Convolution (CONV)
  • Pooling (POOL)
  • Fully connected (FC)

1.7 Pooling layers

  • Max pooling

only has hyperparameters(fixed), doesn’t has parameters.

image-20210819122112750 $$ n^{[l]}=\bigg\lfloor\frac{n^{[l-1]}+2p^{[l]}-f^{[l]}}{s^{[l]}}+1\bigg\rfloor $$

1.8 Neural network example

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2 Deep Convolutional Models: Case Study

2.1 Classic Networks

LeNet-5

  • trained on grayscale images(灰度图片)

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AlexNet

  • Similar to LeNet, but much bigger.
  • $\approx60M$ parameters.
  • Use ReLU

image-20210829202734063

VGG-16

  • 共16个layer
  • CONV层的卷积核和POOLING层的格式都是固定的
  • $\approx138M$ parameters.
  • 核VGG-19的表现不相上下

image-20210829203437393

3 Residual Networks (ResNets 残差网络)

Residual block

  • Add “short cut” (skip connection)

image-20210829205525706