tensorflow Math behind 2D convolution with advanced examples in TF No padding, strides=1
Example
This is the most basic example, with the easiest calculations. Let's assume your input and kernel are:
When you your kernel you will receive the following output: 
, which is calculated in the following way:
- 14 = 4 * 1 + 3 * 0 + 1 * 1 + 2 * 2 + 1 * 1 + 0 * 0 + 1 * 0 + 2 * 0 + 4 * 1
- 6 = 3 * 1 + 1 * 0 + 0 * 1 + 1 * 2 + 0 * 1 + 1 * 0 + 2 * 0 + 4 * 0 + 1 * 1
- 6 = 2 * 1 + 1 * 0 + 0 * 1 + 1 * 2 + 2 * 1 + 4 * 0 + 3 * 0 + 1 * 0 + 0 * 1
- 12 = 1 * 1 + 0 * 0 + 1 * 1 + 2 * 2 + 4 * 1 + 1 * 0 + 1 * 0 + 0 * 0 + 2 * 1
TF's conv2d function calculates convolutions in batches and uses a slightly different format. For an input it is [batch, in_height, in_width, in_channels] for the kernel it is [filter_height, filter_width, in_channels, out_channels]. So we need to provide the data in the correct format:
import tensorflow as tf
k = tf.constant([
[1, 0, 1],
[2, 1, 0],
[0, 0, 1]
], dtype=tf.float32, name='k')
i = tf.constant([
[4, 3, 1, 0],
[2, 1, 0, 1],
[1, 2, 4, 1],
[3, 1, 0, 2]
], dtype=tf.float32, name='i')
kernel = tf.reshape(k, [3, 3, 1, 1], name='kernel')
image = tf.reshape(i, [1, 4, 4, 1], name='image')
Afterwards the convolution is computed with:
res = tf.squeeze(tf.nn.conv2d(image, kernel, [1, 1, 1, 1], "VALID"))
# VALID means no padding
with tf.Session() as sess:
print sess.run(res)
And will be equivalent to the one we calculated by hand.
