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Computes the grayscale erosion of 4-D value and 3-D filters tensors.

    value, filters, strides, padding, data_format, dilations, name=None

The value tensor has shape [batch, in_height, in_width, depth] and the filters tensor has shape [filters_height, filters_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 erosion is given by:

output[b, y, x, c] =
   min_{dy, dx} value[b,
                      strides[1] * y - dilations[1] * dy,
                      strides[2] * x - dilations[2] * dx,
                      c] -
                filters[dy, dx, c]

Duality: The erosion of value by the filters is equal to the negation of the dilation of -value by the reflected filters.


  • value: A Tensor. 4-D with shape [batch, in_height, in_width, depth].
  • filters: A Tensor. Must have the same type as value. 3-D with shape [filters_height, filters_width, depth].
  • strides: A list of ints that has length >= 4. 1-D of 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. 1-D of length 4. The input stride for atrous morphological dilation. Must be: [1, rate_height, rate_width, 1].
  • name: A name for the operation (optional). If not specified "erosion2d" is used.


A Tensor. Has the same type as value. 4-D with shape [batch, out_height, out_width, depth].


  • ValueError: If the value depth does not match filters' shape, or if padding is other than 'VALID' or 'SAME'.