# scipy.ndimage.distance_transform_bf

scipy.ndimage.distance_transform_bf(input, metric='euclidean', sampling=None, return_distances=True, return_indices=False, distances=None, indices=None)

  Distance transform function by a brute force algorithm.

  This function calculates the distance transform of the input, by replacing each foreground (non-zero) element, with its shortest distance to the background (any zero-valued element).

  In addition to the distance transform, the feature transform can be calculated. In this case the index of the closest background element to each foreground element is returned in a separate array.

  Parameters:
    input array_like

      Input

    metric{‘euclidean’, ‘taxicab’, ‘chessboard’}, optional

      ‘cityblock’ and ‘manhattan’ are also valid, and map to ‘taxicab’. The default is ‘euclidean’.

    sampling float, or sequence of float, optional

      This parameter is only used when metric is ‘euclidean’. Spacing of elements along each dimension. If a sequence, must be of length equal to the input rank; if a single number, this is used for all axes. If not specified, a grid spacing of unity is implied.

    return_distances bool, optional

      Whether to calculate the distance transform. Default is True.

    return_indices bool, optional

      Whether to calculate the feature transform. Default is False.

    distances ndarray, optional

      An output array to store the calculated distance transform, instead of returning it. return_distances must be True. It must be the same shape as input, and of type float64 if metric is ‘euclidean’, uint32 otherwise.

    indices int32 ndarray, optional

      An output array to store the calculated feature transform, instead of returning it. return_indicies must be True. Its shape must be (input.ndim,) + input.shape.

  Returns:
    distances ndarray, optional

      The calculated distance transform. Returned only when return_distances is True and distances is not supplied. It will have the same shape as the input array.

    indices int32 ndarray, optional

      The calculated feature transform. It has an input-shaped array for each dimension of the input. See distance_transform_edt documentation for an example. Returned only when return_indices is True and indices is not supplied.

  See also

  `distance_transform_cdt`

    Faster distance transform for taxicab and chessboard metrics

  `distance_transform_edt`

    Faster distance transform for euclidean metric

  Notes

  This function employs a slow brute force algorithm, see also the function `distance_transform_cdt` for more efficient taxicab [1] and chessboard algorithms [2].

  References

  [1]

  Taxicab distance. Wikipedia, 2023. https://en.wikipedia.org/wiki/Taxicab_geometry

  [2]

  Chessboard distance. Wikipedia, 2023. https://en.wikipedia.org/wiki/Chebyshev_distance

  Examples

  Import the necessary modules.

      >>> import numpy as np
      >>> from scipy.ndimage import distance_transform_bf
      >>> import matplotlib.pyplot as plt
      >>> from mpl_toolkits.axes_grid1 import ImageGrid

  First, we create a toy binary image.

      >>> def add_circle(center_x, center_y, radius, image, fillvalue=1):
      ...     # fill circular area with 1
      ...     xx, yy = np.mgrid[:image.shape[0], :image.shape[1]]
      ...     circle = (xx - center_x) ** 2 + (yy - center_y) ** 2
      ...     circle_shape = np.sqrt(circle) < radius
      ...     image[circle_shape] = fillvalue
      ...     return image
      >>> image = np.zeros((100, 100), dtype=np.uint8)
      >>> image[35:65, 20:80] = 1
      >>> image = add_circle(28, 65, 10, image)
      >>> image = add_circle(37, 30, 10, image)
      >>> image = add_circle(70, 45, 20, image)
      >>> image = add_circle(45, 80, 10, image)

  Next, we set up the figure.

      >>> fig = plt.figure(figsize=(8, 8))  # set up the figure structure
      >>> grid = ImageGrid(fig, 111, nrows_ncols=(2, 2), axes_pad=(0.4, 0.3),
      ...                  label_mode="1", share_all=True,
      ...                  cbar_location="right", cbar_mode="each",
      ...                  cbar_size="7%", cbar_pad="2%")
      >>> for ax in grid:
      ...     ax.axis('off')  # remove axes from images

  The top left image is the original binary image.

      >>> binary_image = grid[0].imshow(image, cmap='gray')
      >>> cbar_binary_image = grid.cbar_axes[0].colorbar(binary_image)
      >>> cbar_binary_image.set_ticks([0, 1])
      >>> grid[0].set_title("Binary image: foreground in white")

  The distance transform calculates the distance between foreground pixels and the image background according to a distance metric. Available metrics in `distance_transform_bf` are: `euclidean` (default), `taxicab` and `chessboard`. The top right image contains the distance transform based on the `euclidean` metric.

      >>> distance_transform_euclidean = distance_transform_bf(image)
      >>> euclidean_transform = grid[1].imshow(distance_transform_euclidean,
      ...                                      cmap='gray')
      >>> cbar_euclidean = grid.cbar_axes[1].colorbar(euclidean_transform)
      >>> colorbar_ticks = [0, 10, 20]
      >>> cbar_euclidean.set_ticks(colorbar_ticks)
      >>> grid[1].set_title("Euclidean distance")

  The lower left image contains the distance transform using the `taxicab` metric.

      >>> distance_transform_taxicab = distance_transform_bf(image,
      ...                                                    metric='taxicab')
      >>> taxicab_transformation = grid[2].imshow(distance_transform_taxicab,
      ...                                         cmap='gray')
      >>> cbar_taxicab = grid.cbar_axes[2].colorbar(taxicab_transformation)
      >>> cbar_taxicab.set_ticks(colorbar_ticks)
      >>> grid[2].set_title("Taxicab distance")

  Finally, the lower right image contains the distance transform using the `chessboard` metric.

      >>> distance_transform_cb = distance_transform_bf(image,
      ...                                               metric='chessboard')
      >>> chessboard_transformation = grid[3].imshow(distance_transform_cb,
      ...                                            cmap='gray')
      >>> cbar_taxicab = grid.cbar_axes[3].colorbar(chessboard_transformation)
      >>> cbar_taxicab.set_ticks(colorbar_ticks)
      >>> grid[3].set_title("Chessboard distance")
      >>> plt.show()