What does tf.nn.conv2d do in tensorflow?

by

Ok I think this is about the simplest way to explain it all.

Your example is 1 image, size 2×2, with 1 channel. You have 1 filter, with size 1×1, and 1 channel (size is height x width x channels x number of filters).

For this simple case the resulting 2×2, 1 channel image (size 1x2x2x1, number of images x height x width x x channels) is the result of multiplying the filter value by each pixel of the image.

Now let’s try more channels:

input = tf.Variable(tf.random_normal([1,3,3,5]))
filter = tf.Variable(tf.random_normal([1,1,5,1]))

op = tf.nn.conv2d(input, filter, strides=[1, 1, 1, 1], padding='VALID')

Here the 3×3 image and the 1×1 filter each have 5 channels. The resulting image will be 3×3 with 1 channel (size 1x3x3x1), where the value of each pixel is the dot product across channels of the filter with the corresponding pixel in the input image.

Now with a 3×3 filter

input = tf.Variable(tf.random_normal([1,3,3,5]))
filter = tf.Variable(tf.random_normal([3,3,5,1]))

op = tf.nn.conv2d(input, filter, strides=[1, 1, 1, 1], padding='VALID')

Here we get a 1×1 image, with 1 channel (size 1x1x1x1). The value is the sum of the 9, 5-element dot products. But you could just call this a 45-element dot product.

Now with a bigger image

input = tf.Variable(tf.random_normal([1,5,5,5]))
filter = tf.Variable(tf.random_normal([3,3,5,1]))

op = tf.nn.conv2d(input, filter, strides=[1, 1, 1, 1], padding='VALID')

The output is a 3×3 1-channel image (size 1x3x3x1).
Each of these values is a sum of 9, 5-element dot products.

Each output is made by centering the filter on one of the 9 center pixels of the input image, so that none of the filter sticks out. The xs below represent the filter centers for each output pixel.

.....
.xxx.
.xxx.
.xxx.
.....

Now with “SAME” padding:

input = tf.Variable(tf.random_normal([1,5,5,5]))
filter = tf.Variable(tf.random_normal([3,3,5,1]))

op = tf.nn.conv2d(input, filter, strides=[1, 1, 1, 1], padding='SAME')

This gives a 5×5 output image (size 1x5x5x1). This is done by centering the filter at each position on the image.

Any of the 5-element dot products where the filter sticks out past the edge of the image get a value of zero.

So the corners are only sums of 4, 5-element dot products.

Now with multiple filters.

input = tf.Variable(tf.random_normal([1,5,5,5]))
filter = tf.Variable(tf.random_normal([3,3,5,7]))

op = tf.nn.conv2d(input, filter, strides=[1, 1, 1, 1], padding='SAME')

This still gives a 5×5 output image, but with 7 channels (size 1x5x5x7). Where each channel is produced by one of the filters in the set.

Now with strides 2,2:

input = tf.Variable(tf.random_normal([1,5,5,5]))
filter = tf.Variable(tf.random_normal([3,3,5,7]))

op = tf.nn.conv2d(input, filter, strides=[1, 2, 2, 1], padding='SAME')

Now the result still has 7 channels, but is only 3×3 (size 1x3x3x7).

This is because instead of centering the filters at every point on the image, the filters are centered at every other point on the image, taking steps (strides) of width 2. The x‘s below represent the filter center for each output pixel, on the input image.

x.x.x
.....
x.x.x
.....
x.x.x

And of course the first dimension of the input is the number of images so you can apply it over a batch of 10 images, for example:

input = tf.Variable(tf.random_normal([10,5,5,5]))
filter = tf.Variable(tf.random_normal([3,3,5,7]))

op = tf.nn.conv2d(input, filter, strides=[1, 2, 2, 1], padding='SAME')

This performs the same operation, for each image independently, giving a stack of 10 images as the result (size 10x3x3x7)

More Related Contents:

  1. What’s the difference between sparse_softmax_cross_entropy_with_logits and softmax_cross_entropy_with_logits?
  2. How to count total number of trainable parameters in a tensorflow model?
  3. should I use float or classes as output for the final layer in my neural network?
  4. How to make a custom activation function with only Python in Tensorflow?
  5. Keras input explanation: input_shape, units, batch_size, dim, etc
  6. Test labels for regression caffe, float not allowed?
  7. How to choose cross-entropy loss in TensorFlow?
  8. Keras + Tensorflow and Multiprocessing in Python
  9. How to assign a value to a TensorFlow variable?
  10. What is the meaning of the word logits in TensorFlow? [duplicate]
  11. Tensorflow: How to replace or modify gradient?
  12. Tensorflow: How to write op with gradient in python?
  13. How to calculate the number of parameters for convolutional neural network?
  14. Multivariate LSTM with missing values
  15. LSTM module for Caffe
  16. caffe data layer example step by step
  17. Loading a trained Keras model and continue training
  18. How do I check if keras is using gpu version of tensorflow?
  19. What is the purpose of the add_loss function in Keras?
  20. Pytorch, what are the gradient arguments
  21. Multiple outputs in Keras
  22. Tensor is not an element of this graph
  23. Tensorflow : Memory leak even while closing Session?
  24. scale the loss value according to “badness” in caffe
  25. In Keras, what exactly am I configuring when I create a stateful `LSTM` layer with N `units`?
  26. Tensorflow One Hot Encoder?
  27. What is right batch normalization function in Tensorflow?
  28. caffe: model definition: write same layer with different phase using caffe.NetSpec()
  29. 2-D convolution as a matrix-matrix multiplication [closed]
  30. Choosing number of Steps per Epoch

Leave a Comment