tf.space_to_batch_nd

TensorFlow 1 version

SpaceToBatch for N-D tensors of type T.

tf.space_to_batch_nd(
    input, block_shape, paddings, name=None
)

This operation divides "spatial" dimensions [1, ..., M] of the input into a grid of blocks of shape block_shape, and interleaves these blocks with the "batch" dimension (0) such that in the output, the spatial dimensions [1, ..., M] correspond to the position within the grid, and the batch dimension combines both the position within a spatial block and the original batch position. Prior to division into blocks, the spatial dimensions of the input are optionally zero padded according to paddings. See below for a precise description.

This operation is equivalent to the following steps:

1. Zero-pad the start and end of dimensions [1, ..., M] of the input according to paddings to produce padded of shape padded_shape.

2. Reshape padded to reshaped_padded of shape:

   [batch] + [padded_shape[1] / block_shape[0], block_shape[0], ..., padded_shape[M] / block_shape[M-1], block_shape[M-1]] + remaining_shape

3. Permute dimensions of reshaped_padded to produce permuted_reshaped_padded of shape:

   block_shape + [batch] + [padded_shape[1] / block_shape[0], ..., padded_shape[M] / block_shape[M-1]] + remaining_shape

4. Reshape permuted_reshaped_padded to flatten block_shape into the batch dimension, producing an output tensor of shape:

   [batch * prod(block_shape)] + [padded_shape[1] / block_shape[0], ..., padded_shape[M] / block_shape[M-1]] + remaining_shape

Some examples:

(1) For the following input of shape [1, 2, 2, 1], block_shape = [2, 2], and paddings = [[0, 0], [0, 0]]:

x = [[[[1], [2]], [[3], [4]]]]

The output tensor has shape [4, 1, 1, 1] and value:

[[[[1]]], [[[2]]], [[[3]]], [[[4]]]]

(2) For the following input of shape [1, 2, 2, 3], block_shape = [2, 2], and paddings = [[0, 0], [0, 0]]:

x = [[[[1, 2, 3], [4, 5, 6]],
      [[7, 8, 9], [10, 11, 12]]]]

The output tensor has shape [4, 1, 1, 3] and value:

[[[[1, 2, 3]]], [[[4, 5, 6]]], [[[7, 8, 9]]], [[[10, 11, 12]]]]

(3) For the following input of shape [1, 4, 4, 1], block_shape = [2, 2], and paddings = [[0, 0], [0, 0]]:

x = [[[[1],   [2],  [3],  [4]],
      [[5],   [6],  [7],  [8]],
      [[9],  [10], [11],  [12]],
      [[13], [14], [15],  [16]]]]

The output tensor has shape [4, 2, 2, 1] and value:

x = [[[[1], [3]], [[9], [11]]],
     [[[2], [4]], [[10], [12]]],
     [[[5], [7]], [[13], [15]]],
     [[[6], [8]], [[14], [16]]]]

(4) For the following input of shape [2, 2, 4, 1], block_shape = [2, 2], and paddings = [[0, 0], [2, 0]]:

x = [[[[1],   [2],  [3],  [4]],
      [[5],   [6],  [7],  [8]]],
     [[[9],  [10], [11],  [12]],
      [[13], [14], [15],  [16]]]]

The output tensor has shape [8, 1, 3, 1] and value:

x = [[[[0], [1], [3]]], [[[0], [9], [11]]],
     [[[0], [2], [4]]], [[[0], [10], [12]]],
     [[[0], [5], [7]]], [[[0], [13], [15]]],
     [[[0], [6], [8]]], [[[0], [14], [16]]]]

Among others, this operation is useful for reducing atrous convolution into regular convolution.