mirror padding for theano

mirror_padding.py

def mirror_padding(images, filter_size):
    """
    Mirror padding is used to apply a 2D convolution avoiding the border
    effects that one normally gets with zero padding.

    We assume that the filter has an odd size.

    To obtain a filtered tensor with the same output size, substitute
    a ``conv2d(images, filters, mode="half")`` with
    ``conv2d(mirror_padding(images, filters.shape), filters, mode="valid")``.

    Parameters
    ----------
    images : Tensor
        4D tensor containing a set of images.
    filter_size : tuple
        Spatial size of the filter (height, width).

    Returns
    -------
    padded : Tensor
        4D tensor containing the padded set of images.

    """

    if (filter_size[0] % 2) == 0 or (filter_size[1] % 2) == 0:
        raise ValueError('Filter size must be odd in both dimensions.')

    h_pad = filter_size[0] // 2
    w_pad = filter_size[1] // 2

    # Allocate space for padded images.
    s = images.shape
    padded_shape = (s[0], s[1], s[2] + 2*h_pad, s[3] + 2*w_pad)
    x_padded = zeros(padded_shape)

    # Copy the original image to the central part.
    x_padded = set_subtensor(
        x_padded[:, :, h_pad:s[2]+h_pad, w_pad:w_pad+s[3]],
        images,
    )

    # Copy borders.
    # Note that we don't mirror starting at pixel number 0: assuming that
    # we have a symmetric, odd filter, the central element of the filter
    # will run along the original border, and we need to match the
    # statistics of the elements around it.
    x_padded = set_subtensor(
        x_padded[:, :, :h_pad, w_pad:-w_pad],
        images[:, :, h_pad:0:-1, :],
    )
    x_padded = set_subtensor(
        x_padded[:, :, -h_pad:, w_pad:-w_pad],
        images[:, :, -2:-h_pad-2:-1, :],
    )
    x_padded = set_subtensor(
        x_padded[:, :, :, :w_pad],
        x_padded[:, :, :, 2*w_pad:w_pad:-1],
    )
    x_padded = T.set_subtensor(
        x_padded[:, :, :, -w_pad:],
        x_padded[:, :, :, -w_pad-2:-2*w_pad-2:-1],
    )

    return x_padded