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The fourth course, the first week, Convolutional Neural Networks

1.1 Problems encountered in computer vision

One challenge faced when applying computer vision isData InputIt could be very large.

• The data size of a 64×64 small image is 64×64×3 (3 color channels). So our feature vector$x$The dimension is 12288.
• For a 1000×1000 image, the dimension of the feature vector reaches 1000×1000×3.
• If there are 1000 hidden units in the first hidden layer, and all weights form the matrix $W^{[1]}$. The size of this matrix in a standard fully connected network is 1000×3 million. To do this, we need to perform convolution calculations.

1.2 Convolution operation example: Edge detection example

Convolution operation is the most basic component of convolutional neural network. Edge detection is used as an introductory example.

1.2.1 Steps of edge detection

When detecting objects in an image, we can detect vertical edges in the image.

Take a 6×6 grayscale image. Because it is a grayscale image, it is a 6×6×1 matrix.

• To detect vertical edges in an image, you can construct a 3×3 matrix (filter/kernel) [ 1 0 − 1 1 0 − 1 1 0 − 1 ] begin{bmatrix}1
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