tf.nn.with_space_to_batch

tf.nn.with_space_to_batch(
    input,
    dilation_rate,
    padding,
    op,
    filter_shape=None,
    spatial_dims=None,
    data_format=None
)

Defined in tensorflow/python/ops/nn_ops.py.

See the guide: Neural Network > Morphological filtering

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),

where:

adjusted_dilation_rate is an int64 tensor of shape [max(spatial_dims)], 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 with_space_to_batch operation as follows:

def combined_op(converted_input, num_spatial_dims, _): result = op_1(converted_input, num_spatial_dims, "VALID") ... result = op_k(result, num_spatial_dims, "VALID")

net = with_space_to_batch(net, dilation_rate, "VALID", combined_op)

This eliminates the overhead of k-1 calls to space_to_batch_nd and batch_to_space_nd.

Similarly, a sequence of with_space_to_batch operations with identical (not uniformly 1) dilation_rate parameters, "SAME" padding, and odd filter dimensions

net = with_space_to_batch(net, dilation_rate, "SAME", op_1, filter_shape_1) ... net = with_space_to_batch(net, dilation_rate, "SAME", op_k, filter_shape_k)

can be combined into a single with_space_to_batch operation as follows:

def combined_op(converted_input, num_spatial_dims, _): result = op_1(converted_input, num_spatial_dims, "SAME") ... result = op_k(result, num_spatial_dims, "SAME")

net = with_space_to_batch(net, dilation_rate, "VALID", combined_op)

Args:

• input: Tensor of rank > max(spatial_dims).
• dilation_rate: int32 Tensor of known shape [num_spatial_dims].
• padding: str constant equal to "VALID" or "SAME"
• op: Function that maps (input, num_spatial_dims, padding) -> output
• filter_shape: If padding = "SAME", specifies the shape of the convolution kernel/pooling window as an integer Tensor of shape [>=num_spatial_dims]. If padding = "VALID", filter_shape is ignored and need not be specified.
• spatial_dims: Monotonically increasing sequence of num_spatial_dims integers (which are >= 1) specifying the spatial dimensions of input and output. Defaults to: range(1, num_spatial_dims+1).
• data_format: A string or None. Specifies whether the channel dimension of the input and output is the last dimension (default, or if data_format does not start with "NC"), or the second dimension (if data_format starts with "NC"). For N=1, the valid values are "NWC" (default) and "NCW". For N=2, the valid values are "NHWC" (default) and "NCHW". For N=3, the valid values are "NDHWC" (default) and "NCDHW".

Returns:

The output Tensor as described above, dimensions will vary based on the op provided.

Raises:

• ValueError: if padding is invalid or the arguments are incompatible.
• ValueError: if spatial_dims are invalid.