Performs op on the space-to-batch representation of input.

This has the effect of transforming sliding window operations into the corresponding "atrous" operation in which the input is sampled at the specified dilation_rate.

In the special case that dilation_rate is uniformly 1, this simply returns:

op(input, num_spatial_dims, padding)

Otherwise, it returns:

batch_to_space_nd( op(space_to_batch_nd(input, adjusted_dilation_rate, adjusted_paddings), num_spatial_dims, "VALID") adjusted_dilation_rate, adjusted_crops),


adjusted_dilation_rate is an int64 tensor of shape [max(spatialdims)], adjusted{paddings,crops} are int64 tensors of shape [max(spatial_dims), 2]

defined as follows:

We first define two int64 tensors paddings and crops of shape [num_spatial_dims, 2] based on the value of padding and the spatial dimensions of the input:

If padding = "VALID", then:

paddings, crops = required_space_to_batch_paddings( input_shape[spatial_dims], dilation_rate)

If padding = "SAME", then:

dilated_filter_shape = filter_shape + (filter_shape - 1) * (dilation_rate - 1)

paddings, crops = required_space_to_batch_paddings( input_shape[spatial_dims], dilation_rate, [(dilated_filter_shape - 1) // 2, dilated_filter_shape - 1 - (dilated_filter_shape - 1) // 2])

Because space_to_batch_nd and batch_to_space_nd assume that the spatial dimensions are contiguous starting at the second dimension, but the specified spatial_dims may not be, we must adjust dilation_rate, paddings and crops in order to be usable with these operations. For a given dimension, if the block size is 1, and both the starting and ending padding and crop amounts are 0, then space_to_batch_nd effectively leaves that dimension alone, which is what is needed for dimensions not part of spatial_dims. Furthermore, space_to_batch_nd and batch_to_space_nd handle this case efficiently for any number of leading and trailing dimensions.

For 0 <= i < len(spatial_dims), we assign:

adjusted_dilation_rate[spatial_dims[i] - 1] = dilation_rate[i] adjusted_paddings[spatial_dims[i] - 1, :] = paddings[i, :] adjusted_crops[spatial_dims[i] - 1, :] = crops[i, :]

All unassigned values of adjusted_dilation_rate default to 1, while all unassigned values of adjusted_paddings and adjusted_crops default to 0.

Note in the case that dilation_rate is not uniformly 1, specifying "VALID" padding is equivalent to specifying padding = "SAME" with a filter_shape of [1]*N.

Advanced usage. Note the following optimization: A sequence of with_space_to_batch operations with identical (not uniformly 1) dilation_rate parameters and "VALID" padding

net = with_space_to_batch(net, dilation_rate, "VALID", op_1) ... net = with_space_to_batch(net, dilation_rate, "VALID", op_k)

can be combined into a single wit