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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
Step1:  Understanding Convolutional layer
What is the difference between convolutional layer and linear layer?
What kind of intuition is in behind of using convolutional layer in deep neural network?
This hands on shows some effects by convolutional layer to provide some intution about what convolutional layer do.
Step2:  Above type of diagram often appears in Convolutional neural network field.
Below figure explains its notation.
Cuboid represents the "image" array where this image might not mean the meaningful picture. 
Horizontal axis represents channel number, vertical axis for image height and depth axis for image width respectively.
Convolution layer - basic usage
Input format of convolutional layer is in the order, (batch index, channel, height, width).
Since openCV image format is in the order (height, width, channel), this dimension order 
need to be converted to input to convolution layer.
It can be done by using transpose method.
L.Convolution2D(in_channels, out_channels, ksize)
 - in_channels
Step3:  Convolution2D layer takes 4-dim array as input and outputs 4-dim array.
Graphical meaning of this input-output relation ship is drawn in below figure.
When the in_channels is set to None, its size is determined at the first time when it is used.
i.e., out_image = conv1(image).data in above code.
The internal parameter W is initialized randomly at that time.
As you can see, output_conv1.jpg shows the result after random filter is applied.
Some "feature" can be extracted by applying convolution layer.
For example, random fileter sometimes acts as "blurring" or "edge extracting" image.
To understand the intuitive meaning of convolutional layer in more detail, please see below example.
Step4:  As you can see from the result, each convolution layer acts as emphasizing/extracting the color difference along specific direction.
In this way "filter", also called "kernel" can be considered as feature extractor.
Convolution with stride
The default value of stride is 1.
If this value is specified, convolution layer will reduce output image size.
Practically, stride=2 is often used to generate the output image of the height & width almost half of the input image.
Step5:  As written in the Chainer docs, 
the input and output shape relation is given in below formula
Step6:  Convolutional neural network
By combining above functions with non-linear activation units, Convolutional Neural Network (CNN) can be constructed.
For non-linear activation, relu, leaky_relu, sigmoid or tanh are often used.
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Python Code:
import os
import numpy as np
import matplotlib.pyplot as plt
import cv2
%matplotlib inline
basedir = './src/cnn/images'
def read_rgb_image(imagepath):
    image = cv2.imread(imagepath)  # Height, Width, Channel
    (major, minor, _) = cv2.__version__.split(".")
    if major == '3':
        # version 3 is used, need to convert
        image = cv2.cvtColor(image, cv2.COLOR_BGR2RGB)
    else:
        # Version 2 is used, not necessary to convert
        pass
    return image
def read_gray_image(imagepath):
    image = cv2.imread(imagepath)  # Height, Width, Channel
    (major, minor, _) = cv2.__version__.split(".")
    if major == '3':
        # version 3 is used, need to convert
        image = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)
    else:
        # Version 2 is used, not necessary to convert
        image = cv2.cvtColor(image, cv2.COLOR_RGB2GRAY)
    return image
def plot_channels(array, filepath='out.jpg'):
    Plot each channel component separately
    Args:
        array (numpy.ndarray): 3-D array (width, height, channel)
    
    ch_number = array.shape[2]
    fig, axes = plt.subplots(1, ch_number)
    for i in range(ch_number):
        # Save each image
        # cv2.imwrite(os.path.join(basedir, 'output_conv1_{}.jpg'.format(i)), array[:, :, i])
        axes[i].set_title('Channel {}'.format(i))
        axes[i].axis('off')
        axes[i].imshow(array[:, :, i], cmap='gray')
    plt.savefig(filepath)
Explanation: Understanding Convolutional layer
What is the difference between convolutional layer and linear layer?
What kind of intuition is in behind of using convolutional layer in deep neural network?
This hands on shows some effects by convolutional layer to provide some intution about what convolutional layer do.
End of explanation
import chainer.links as L
# Read image from file, save image with matplotlib using `imshow` function
imagepath = os.path.join(basedir, 'sample.jpeg')
image = read_rgb_image(imagepath)
# height and width shows pixel size of this image 
# Channel=3 indicates the RGB channel 
print('image.shape (Height, Width, Channel) = ', image.shape)
conv1 = L.Convolution2D(None, 3, 5)
# Need to input image of the form (batch index, channel, height, width)
image = image.transpose(2, 0, 1)
image = image[np.newaxis, :, :, :]
# Convert from int to float
image = image.astype(np.float32)
print('image shape', image.shape)
out_image = conv1(image).data
print('shape', out_image.shape)
out_image = out_image[0].transpose(1, 2, 0)
print('shape 2', out_image.shape)
plot_channels(out_image,
              filepath=os.path.join(basedir, 'output_conv1.jpg'))
Explanation: Above type of diagram often appears in Convolutional neural network field.
Below figure explains its notation.
Cuboid represents the "image" array where this image might not mean the meaningful picture. 
Horizontal axis represents channel number, vertical axis for image height and depth axis for image width respectively.
Convolution layer - basic usage
Input format of convolutional layer is in the order, (batch index, channel, height, width).
Since openCV image format is in the order (height, width, channel), this dimension order 
need to be converted to input to convolution layer.
It can be done by using transpose method.
L.Convolution2D(in_channels, out_channels, ksize)
 - in_channels:  input channel number. 
 - out_channels: output channel number.
 - ksize:        kernel size.
also, following parameters is often set
pad: padding
stride: stride
To understand the behavior of convolution layer, I recommend to see the animation on conv_arithmetic.
End of explanation
gray_image = read_gray_image(imagepath)
print('gray_image.shape (Height, Width) = ', gray_image.shape)
# Need to input image of the form (batch index, channel, height, width)
gray_image = gray_image[np.newaxis, np.newaxis, :, :]
# Convert from int to float
gray_image = gray_image.astype(np.float32)
conv_vertical = L.Convolution2D(1, 1, 3)
conv_horizontal = L.Convolution2D(1, 1, 3)
print(conv_vertical.W.data)
conv_vertical.W.data = np.asarray([[[[-1., 0, 1], [-1, 0, 1], [-1, 0, 1]]]])
conv_horizontal.W.data = np.asarray([[[[-1., -1, -1], [0, 0., 0], [1, 1, 1]]]])
print('image.shape', image.shape)
out_image_v = conv_vertical(gray_image).data
out_image_h = conv_horizontal(gray_image).data
print('out_image_v.shape', out_image_v.shape)
out_image_v = out_image_v[0].transpose(1, 2, 0)
out_image_h = out_image_h[0].transpose(1, 2, 0)
print('out_image_v.shape (after transpose)', out_image_v.shape)
cv2.imwrite(os.path.join(basedir, 'output_conv_vertical.jpg'), out_image_v[:, :, 0])
cv2.imwrite(os.path.join(basedir, 'output_conv_horizontal.jpg'), out_image_h[:, :, 0])
Explanation: Convolution2D layer takes 4-dim array as input and outputs 4-dim array.
Graphical meaning of this input-output relation ship is drawn in below figure.
When the in_channels is set to None, its size is determined at the first time when it is used.
i.e., out_image = conv1(image).data in above code.
The internal parameter W is initialized randomly at that time.
As you can see, output_conv1.jpg shows the result after random filter is applied.
Some "feature" can be extracted by applying convolution layer.
For example, random fileter sometimes acts as "blurring" or "edge extracting" image.
To understand the intuitive meaning of convolutional layer in more detail, please see below example.
End of explanation
print('image.shape (Height, Width, Channel) = ', image.shape)
conv2 = L.Convolution2D(None, 5, 3, 2)
print('input image.shape', image.shape)
out_image = conv2(conv1(image)).data
print('out_image.shape', out_image.shape)
out_image = out_image[0].transpose(1, 2, 0)
plot_channels(out_image,
              filepath=os.path.join(basedir, 'output_conv2.jpg'))
Explanation: As you can see from the result, each convolution layer acts as emphasizing/extracting the color difference along specific direction.
In this way "filter", also called "kernel" can be considered as feature extractor.
Convolution with stride
The default value of stride is 1.
If this value is specified, convolution layer will reduce output image size.
Practically, stride=2 is often used to generate the output image of the height & width almost half of the input image.
End of explanation
from chainer import functions as F
print('image.shape (Height, Width, Channel) = ', image.shape)
print('input image.shape', image.shape)
out_image = F.max_pooling_2d(image, 2).data
print('out_image.shape', out_image.shape)
out_image = out_image[0].transpose(1, 2, 0)
plot_channels(out_image,
              filepath=os.path.join(basedir, 'output_max_pooling.jpg'))
Explanation: As written in the Chainer docs, 
the input and output shape relation is given in below formula:
$$ h_O = (h_I + 2h_P - h_K) / s_Y + 1 $$
$$ w_O = (w_I + 2w_P - w_K) / s_X + 1 $$
where each symbol means that 
- h: height
- w: width
- I: input
- O: output
- P: padding
- K: kernel size
- s: stride
Max pooling
Convolution layer with stride can be used to look wide range feature,
another popular method is to use max pooling.
Max pooling function extracts the maximum value in the kernel, 
and it dispose the rest pixel's information.
This behavior is beneficial to impose translational symmetry.
For example, consider the dog's picture. Even if the each pixel shifted one pixel, is should be still recognized as dog. So traslational symmetry can be exploited to reduce model's calculation time and number of internal parameters for image classification task.
End of explanation
class SimpleCNN(chainer.Chain):
    def __init__(self):
        super().__init__(
            conv1=L.Convolution2D(None, 5, 3),
            conv2=L.Convolution2D(None, 5, 3),
        )
        
    def __call__(self, x):
        h = F.relu(conv1(x))
        h = F.max_pooling_2d(h, 2)
        h = F.relu(conv2(h))
        h = F.max_pooling_2d(h, 2)
        return h
  
model = SimpleCNN()
print('input image.shape', image.shape)
out_image = model(image).data
print('out_image.shape', out_image.shape)
out_image = out_image[0].transpose(1, 2, 0)
plot_channels(out_image,
              filepath=os.path.join(basedir, 'output_simple_cnn.jpg'))
Explanation: Convolutional neural network
By combining above functions with non-linear activation units, Convolutional Neural Network (CNN) can be constructed.
For non-linear activation, relu, leaky_relu, sigmoid or tanh are often used.
End of explanation
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