import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'images/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show()
显示图像
定义滤波器，并将其可视化
import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape)
Filter shape: (4, 4)
# Defining four different filters,
# all of which are linear combinations of the `filter_vals` defined above
# define four filters
filter_1 = filter_vals
filter_2 = -filter_1
filter_3 = filter_1.T
filter_4 = -filter_3
filters = np.array([filter_1, filter_2, filter_3, filter_4])
# For an example, print out the values of filter 1
print('Filter 1: \n', filter_1)
Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]]
定义卷积层和池化层¶
将卷积层初始化，使其包含你所创建的所有滤波器。然后添加一个最大池化层（相关文档请通过点击这里查阅），内核大小为（4x4），这样你就可以看到，在这一步之后，图像分辨率已经降低了！
import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (4, 4) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(4, 4) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model)
Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=4, stride=4, padding=0, dilation=1, ceil_mode=False) )
将每个滤波器的输出可视化
首先，我们将定义一个辅助函数viz_layer，它会接收一个特定的层和多个滤波器（可选参数）作为输入，并在图像通过后显示该层的输出。
# helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1, xticks=[], yticks=[]) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1))
让我们看一下应用ReLu激活函数后，该卷积层的输出是什么。
# plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer)
将池化层的输出可视化
然后，看一下池化层的输出。池化层将上面描绘的特征映射图作为输入，并通过一些池化因子，通过在一个给定内核区域中构造一个仅拥有最大（即最亮）值的新的较小图像来减少那些映射图的维度。
# visualize the output of the pooling layer viz_layer(pooled_layer)