Function atrous_conv2d

tensorflow/python/ops/nn_ops.py:1455–1588

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

(value, filters, rate, padding, name=None)

@tf_export("nn.atrous_conv2d")
def atrous_conv2d(value, filters, rate, padding, name=None):
  """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](http://arxiv.org/abs/1412.7062).
  The same operation is investigated further in [Multi-Scale Context Aggregation
  by Dilated Convolutions](http://arxiv.org/abs/1511.07122). Previous works
  that effectively use atrous convolution in different ways are, among others,
  [OverFeat: Integrated Recognition, Localization and Detection using
  Convolutional Networks](http://arxiv.org/abs/1312.6229) and [Fast Image
  Scanning with Deep Max-Pooling Convolutional Neural
  Networks](http://arxiv.org/abs/1302.1700).
  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

  ```python
      atrous_conv2d(value, filters, rate, padding=padding)
  ```

  to the following three operations: