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Computes the grayscale dilation of 4-D input and 3-D filters tensors.


The input tensor has shape [batch, in_height, in_width, depth] and the filters tensor has shape [filter_height, filter_width, depth], i.e., each input channel is processed independently of the others with its own structuring function. The output tensor has shape [batch, out_height, out_width, depth]. The spatial dimensions of the output tensor depend on the padding algorithm. We currently only support the default "NHWC" data_format.

In detail, the grayscale morphological 2-D dilation is the max-sum correlation (for consistency with conv2d, we use unmirrored filters):

output[b, y, x, c] =
   max_{dy, dx} input[b,
                      strides[1] * y + rates[1] * dy,
                      strides[2] * x + rates[2] * dx,
                      c] +
                filters[dy, dx, c]

Max-pooling is a special case when the filter has size equal to the pooling kernel size and contains all zeros.

Note on duality: The dilation of input by the filters is equal to the negation of the erosion of -input by the reflected filters.


  • input: A Tensor. Must be one of the following types: float32, float64, int32, uint8, int16, int8, int64, bfloat16, uint16, half, uint32, uint64. 4-D with shape [batch, in_height, in_width, depth].
  • filters: A Tensor. Must have the same type as input. 3-D with shape [filter_height, filter_width, depth].
  • strides: A list of ints that has length >= 4. The stride of the sliding window for each dimension of the input tensor. Must be: [1, stride_height, stride_width, 1].
  • padding: A string from: "SAME", "VALID". The type of padding algorithm to use.
  • data_format: A string, only "NHWC" is currently supported.
  • dilations: A list of ints that has length >= 4. The input stride for atrous morphological dilation. Must be: [1, rate_height, rate_width, 1].
  • name: A name for the operation (optional).


A Tensor. Has the same type as input.