Convolutional Neural Networks (CNN)


By Prof. Seungchul Lee
http://iai.postech.ac.kr/
Industrial AI Lab at POSTECH

Table of Contents

1. Convolution

1.1. 1D Convolution


1.2. Convolution on Image (= Convolution in 2D)

Filter (or Kernel)

  • Modify or enhance an image by filtering
  • Filter images to emphasize certain features or remove other features

  • Filtering includes smoothing, sharpening and edge enhancement

  • Discrete convolution can be viewed as element-wise multiplication by a matrix


How to find the right Kernels

  • We learn many different kernels that make specific effect on images

  • Let’s apply an opposite approach

  • We are not designing the kernel, but are learning the kernel from data

  • Can learn feature extractor from data using a deep learning framework

2. Convolutional Neural Networks (CNN)

2.1. Motivation: Learning Visual Features


The bird occupies a local area and looks the same in different parts of an image. We should construct neural networks which exploit these properties.



  • ANN structure for object detecion in image

    • does not seem the best
    • did not make use of the fact that we are dealing with images
    • Spatial organization of the input is destroyed by flattening



  • Locality: objects tend to have a local spatial support
    • fully and convolutionally connected layer $\rightarrow$ locally and convolutionally connected layer



- __Translation invariance__: object appearance is independent of location - Weight sharing: untis connected to different locations have the same weights - We are not designing the kernel, but are learning the kernel from data - _i.e._ We are learning visual feature extractor from data

2.2. Convolutional Operator

Convolution of CNN

  • Local connectivity
  • Weight sharing

  • Typically have sparse interactions

  • Convolutional Neural Networks

    • Simply neural networks that use the convolution in place of general matrix multiplication in at least one of their layers
  • Multiple channels


  • Multiple kernels


2.3 Stride and Padding

  • Strides: increment step size for the convolution operator
    • Reduces the size of the output map
  • No stride and no padding


  • Stride example with kernel size 3×3 and a stride of 2


  • Padding: artificially fill borders of image
    • Useful to keep spatial dimension constant across filters
    • Useful with strides and large receptive fields
    • Usually fill with 0s


2.4. Nonlinear Activation Function


2.5. Pooling

  • Compute a maximum value in a sliding window (max pooling)
    • Reduce spatial resolution for faster computation
    • Achieve invariance to any permutation inside one of the cell


  • Pooling size : $2\times2$ for example

2.6. CNN for Classification

  • CONV and POOL layers output high-level features of input
  • Fully connected layer uses these features for classifying input image
  • Express output as probability of image belonging to a particular class



3. Lab: CNN with TensorFlow (MNIST)

  • MNIST example
  • To classify handwritten digits



3.1. Training

In [1]:
import tensorflow as tf
import numpy as np
import matplotlib.pyplot as plt
In [2]:
mnist = tf.keras.datasets.mnist

(train_x, train_y), (test_x, test_y) = mnist.load_data()

train_x, test_x = train_x/255.0, test_x/255.0
In [3]:
train_x = train_x.reshape((train_x.shape[0], 28, 28, 1))
test_x = test_x.reshape((test_x.shape[0], 28, 28, 1))
In [4]:
model = tf.keras.models.Sequential([
    tf.keras.layers.Conv2D(filters = 32, 
                           kernel_size = (3,3), 
                           activation = 'relu',
                           padding = 'SAME',
                           input_shape = (28, 28, 1)),
    
    tf.keras.layers.MaxPool2D((2,2)),
    
    tf.keras.layers.Conv2D(filters = 64, 
                           kernel_size = (3,3), 
                           activation = 'relu',
                           padding = 'SAME',
                           input_shape = (14, 14, 32)),
    
    tf.keras.layers.MaxPool2D((2,2)),
    
    tf.keras.layers.Flatten(),
    
    tf.keras.layers.Dense(units = 128, activation = 'relu'),
    
    tf.keras.layers.Dense(units = 10, activation = 'softmax')
])
In [5]:
model.compile(optimizer = 'adam',
              loss = 'sparse_categorical_crossentropy',
              metrics = ['accuracy'])
In [6]:
model.fit(train_x, train_y, epochs = 3)

Epoch 1/3
1875/1875 [==============================] - 23s 12ms/step - loss: 0.1257 - accuracy: 0.9614
Epoch 2/3
1875/1875 [==============================] - 25s 13ms/step - loss: 0.0411 - accuracy: 0.9871
Epoch 3/3
1875/1875 [==============================] - 24s 13ms/step - loss: 0.0266 - accuracy: 0.9918
Out[6]:
<tensorflow.python.keras.callbacks.History at 0x21f8d671c50>

3.2. Testing or Evaluating

In [7]:
test_loss, test_acc = model.evaluate(test_x, test_y)

313/313 [==============================] - 1s 3ms/step - loss: 0.0266 - accuracy: 0.9907
In [8]:
test_img = test_x[[1495]]

predict = model.predict_on_batch(test_img)
mypred = np.argmax(predict, axis = 1)

plt.figure(figsize = (12,5))

plt.subplot(1,2,1)
plt.imshow(test_img.reshape(28, 28), 'gray')
plt.axis('off')
plt.subplot(1,2,2)
plt.stem(predict[0])
plt.show()

print('Prediction : {}'.format(mypred[0]))

Prediction : 3

4. Lab: CNN with Tensorflow (Steel Surface Defects)

  • NEU steel surface defects example
  • To classify defects images into 6 classes



Download NEU steel surface defects images and labels

4.1. Training

In [9]:
train_x = np.load('./data_files/NEU_train_imgs.npy')
train_y = np.load('./data_files/NEU_train_labels.npy')
test_x = np.load('./data_files/NEU_test_imgs.npy')
test_y = np.load('./data_files/NEU_test_labels.npy')

n_train = train_x.shape[0]
n_test = test_x.shape[0]

print ("The number of training images : {}, shape : {}".format(n_train, train_x.shape))
print ("The number of testing images : {}, shape : {}".format(n_test, test_x.shape))

The number of training images : 1500, shape : (1500, 200, 200, 1)
The number of testing images : 300, shape : (300, 200, 200, 1)
In [10]:
model = tf.keras.models.Sequential([
    tf.keras.layers.Conv2D(filters = 32, 
                           kernel_size = (3,3), 
                           activation = 'relu',
                           padding = 'SAME',
                           input_shape = (200, 200, 1)),
    
    tf.keras.layers.MaxPool2D((2,2)),
    
    tf.keras.layers.Conv2D(filters = 64, 
                           kernel_size = (3,3), 
                           activation = 'relu',
                           padding = 'SAME',
                           input_shape = (100, 100, 32)),
    
    tf.keras.layers.MaxPool2D((2,2)),
    
    tf.keras.layers.Conv2D(filters = 128, 
                           kernel_size = (3,3), 
                           activation = 'relu',
                           padding = 'SAME',
                           input_shape = (50, 50, 64)),
    
    tf.keras.layers.MaxPool2D((2,2)),
    
    tf.keras.layers.Flatten(),    
    tf.keras.layers.Dense(units = 128, activation = 'relu'),    
    tf.keras.layers.Dense(units = 6, activation = 'softmax')
])
In [11]:
model.compile(optimizer = 'adam',
              loss = 'sparse_categorical_crossentropy',
              metrics = ['accuracy'])
In [12]:
model.fit(train_x, train_y, epochs = 4)

Epoch 1/4
47/47 [==============================] - 31s 655ms/step - loss: 1.7424 - accuracy: 0.2793
Epoch 2/4
47/47 [==============================] - 30s 641ms/step - loss: 1.0081 - accuracy: 0.6240
Epoch 3/4
47/47 [==============================] - 29s 614ms/step - loss: 0.6069 - accuracy: 0.7853
Epoch 4/4
47/47 [==============================] - 30s 629ms/step - loss: 0.4119 - accuracy: 0.8447
Out[12]:
<tensorflow.python.keras.callbacks.History at 0x21f94715668>

4.2. Testing or Evaluating

In [13]:
test_loss, test_acc = model.evaluate(test_x, test_y)

10/10 [==============================] - 2s 144ms/step - loss: 0.3800 - accuracy: 0.8633
In [20]:
name = ['scratches', 'rolled-in scale', 'pitted surface', 'patches', 'inclusion', 'crazing']

idx = np.random.choice(test_x.shape[0], 1)
test_img = test_x[idx]
test_label = test_y[idx]

predict = model.predict_on_batch(test_img)
mypred = np.argmax(predict, axis = 1)

plt.figure(figsize = (12,5))

plt.subplot(1,2,1)
plt.imshow(test_img.reshape(200, 200), 'gray')
plt.axis('off')
plt.subplot(1,2,2)
plt.stem(predict[0])
plt.show()

print('Prediction : {}'.format(name[mypred[0]]))
print('True Label : {}'.format(name[test_label[0]]))

Prediction : scratches
True Label : scratches

5. Video Lectures

In [1]:
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width="420" height="315" frameborder="0" allowfullscreen></iframe></center>
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<center><iframe src="https://www.youtube.com/embed/L1cRsCs7E-w?rel=0" 
width="420" height="315" frameborder="0" allowfullscreen></iframe></center>
In [3]:
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<center><iframe src="https://www.youtube.com/embed/2VHBhkC9zw8?rel=0" 
width="420" height="315" frameborder="0" allowfullscreen></iframe></center>
In [18]:
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