tensorflow Math behind 2D convolution with advanced examples in TF Some padding, strides=1
Example
Padding is just a fancy name of telling: surround your input matrix with some constant. In most of the cases the constant is zero and this is why people call it zero padding. So if you want to use a padding of 1 in our original input (check the first example with padding=0, strides=1), the matrix will look like this:
To calculate the values of the convolution you do the same sliding. Notice that in our case many values in the middle do not need to be recalculated (they will be the same as in previous example. I also will not show all the calculations here, because the idea is straight-forward. The result is:
where
- 5 = 0 * 1 + 0 * 0 + 0 * 1 + 0 * 2 + 4 * 1 + 3 * 0 + 0 * 0 + 0 * 1 + 1 * 1
- ...
- 6 = 4 * 1 + 1 * 0 + 0 * 1 + 0 * 2 + 2 * 1 + 0 * 0 + 0 * 0 + 0 * 0 + 0 * 1
TF does not support an arbitrary padding in conv2d function, so if you need some padding that is not supported, use tf.pad(). Luckily for our input the padding 'SAME' will be equal to padding = 1. So we need to change almost nothing in our previous example:
res = tf.squeeze(tf.nn.conv2d(image, kernel, [1, 1, 1, 1], "SAME"))
# 'SAME' makes sure that our output has the same size as input and
# uses appropriate padding. In our case it is 1.
with tf.Session() as sess:
print sess.run(res)
You can verify that the answer will be the same as calculated by hand.
