tf.nn.atrous_conv2d( value, filters, rate, padding, name=None )
Defined in tensorflow/python/ops/nn_ops.py
.
See the guide: Neural Network > Convolution
Atrous convolution (a.k.a. convolution with holes or dilated convolution).
This function is a simpler wrapper around the more general tf.nn.convolution
, and exists only for backwards compatibility. You can use tf.nn.convolution
to perform 1-D, 2-D, or 3-D atrous convolution.
Computes a 2-D atrous convolution, also known as convolution with holes or dilated convolution, given 4-D value
and filters
tensors. If the rate
parameter is equal to one, it performs regular 2-D convolution. If the rate
parameter is greater than one, it performs convolution with holes, sampling the input values every rate
pixels in the height
and width
dimensions. This is equivalent to convolving the input with a set of upsampled filters, produced by inserting rate - 1
zeros between two consecutive values of the filters along the height
and width
dimensions, hence the name atrous convolution or convolution with holes (the French word trous means holes in English).
More specifically:
output[batch, height, width, out_channel] = sum_{dheight, dwidth, in_channel} ( filters[dheight, dwidth, in_channel, out_channel] * value[batch, height + rate*dheight, width + rate*dwidth, in_channel] )
Atrous convolution allows us to explicitly control how densely to compute feature responses in fully convolutional networks. Used in conjunction with bilinear interpolation, it offers an alternative to conv2d_transpose
in dense prediction tasks such as semantic image segmentation, optical flow computation, or depth estimation. It also allows us to effectively enlarge the field of view of filters without increasing the number of parameters or the amount of computation.
For a description of atrous convolution and how it can be used for dense feature extraction, please see: Semantic Image Segmentation with Deep Convolutional Nets and Fully Connected CRFs. The same operation is investigated further in Multi-Scale Context Aggregation by Dilated Convolutions. Previous works that effectively use atrous convolution in different ways are, among others, OverFeat: Integrated Recognition, Localization and Detection using Convolutional Networks and Fast Image Scanning with Deep Max-Pooling Convolutional Neural Networks. Atrous convolution is also closely related to the so-called noble identities in multi-rate signal processing.
There are many different ways to implement atrous convolution (see the refs above). The implementation here reduces
atrous_conv2d(value, filters, rate, padding=padding)
to the following three operations:
paddings = ... net = space_to_batch(value, paddings, block_size=rate) net = conv2d(net, filters, strides=[1, 1, 1, 1], padding="VALID") crops = ... net = batch_to_space(net, crops, block_size=rate)
Advanced usage. Note the following optimization: A sequence of atrous_conv2d
operations with identical rate
parameters, 'SAME' padding
, and filters with odd heights/ widths:
net = atrous_conv2d(net, filters1, rate, padding="SAME") net = atrous_conv2d(net, filters2, rate, padding="SAME") ... net = atrous_conv2d(net, filtersK, rate, padding="SAME")
can be equivalently performed cheaper in terms of computation and memory as:
pad = ... # padding so that the input dims are multiples of rate net = space_to_batch(net, paddings=pad, block_size=rate) net = conv2d(net, filters1, strides=[1, 1, 1, 1], padding="SAME") net = conv2d(net, filters2, strides=[1, 1, 1, 1], padding="SAME") ... net = conv2d(net, filtersK, strides=[1, 1, 1, 1], padding="SAME") net = batch_to_space(net, crops=pad, block_size=rate)
because a pair of consecutive space_to_batch
and batch_to_space
ops with the same block_size
cancel out when their respective paddings
and crops
inputs are identical.
value
: A 4-D Tensor
of type float
. It needs to be in the default "NHWC" format. Its shape is [batch, in_height, in_width, in_channels]
.filters
: A 4-D Tensor
with the same type as value
and shape [filter_height, filter_width, in_channels, out_channels]
. filters
' in_channels
dimension must match that of value
. Atrous convolution is equivalent to standard convolution with upsampled filters with effective height filter_height + (filter_height - 1) * (rate - 1)
and effective width filter_width + (filter_width - 1) * (rate - 1)
, produced by inserting rate - 1
zeros along consecutive elements across the filters
' spatial dimensions.rate
: A positive int32. The stride with which we sample input values across the height
and width
dimensions. Equivalently, the rate by which we upsample the filter values by inserting zeros across the height
and width
dimensions. In the literature, the same parameter is sometimes called input stride
or dilation
.padding
: A string, either 'VALID'
or 'SAME'
. The padding algorithm.name
: Optional name for the returned tensor.A Tensor
with the same type as value
. Output shape with `'VALID`` padding is:
[batch, height - 2 * (filter_width - 1), width - 2 * (filter_height - 1), out_channels].
Output shape with 'SAME'
padding is:
[batch, height, width, out_channels].
ValueError
: If input/output depth does not match filters
' shape, or if padding is other than 'VALID'
or 'SAME'
.
© 2018 The TensorFlow Authors. All rights reserved.
Licensed under the Creative Commons Attribution License 3.0.
Code samples licensed under the Apache 2.0 License.
https://www.tensorflow.org/api_docs/python/tf/nn/atrous_conv2d