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21.8 Distance transforms

# 21.8 Distance transforms

Distance transforms are used to calculate the minimum distance from each element of an object to the background. The following functions implement distance transforms for three different distance metrics: Euclidean, City Block, and Chessboard distances.

 distance_transform_cdt( input, structure="chessboard", return_distances=True, return_indices=False, distances=None, indices=None)
The function distance_transform_cdt uses a chamfer type algorithm to calculate the distance transform of the input, by replacing each object element (defined by values larger than zero) with the shortest distance to the background (all non-object elements). The structure determines the type of chamfering that is done. If the structure is equal to 'cityblock' a structure is generated using generate_binary_structure with a squared distance equal to 1. If the structure is equal to 'chessboard', a structure is generated using generate_binary_structure with a squared distance equal to the rank of the array. These choices correspond to the common interpretations of the cityblock and the chessboard distancemetrics in two dimensions.

In addition to the distance transform, the feature transform can be calculated. In this case the index of the closest background element is returned along the first axis of the result. The return_distances, and return_indices flags can be used to indicate if the distance transform, the feature transform, or both must be returned.

The distances and indices arguments can be used to give optional output arrays that must be of the correct size and type (both Int32).

The basics of the algorithm used to implement this function is described in: G. Borgefors, "Distance transformations in arbitrary dimensions.", Computer Vision, Graphics, and Image Processing, 27:321-345, 1984.

 distance_transform_edt( input, sampling=None, return_distances=True, return_indices=False, distances=None, indices=None)
The function distance_transform_edt calculates the exact euclidean distance transform of the input, by replacing each object element (defined by values larger than zero) with the shortest euclidean distance to the background (all non-object elements).

In addition to the distance transform, the feature transform can be calculated. In this case the index of the closest background element is returned along the first axis of the result. The return_distances, and return_indices flags can be used to indicate if the distance transform, the feature transform, or both must be returned.

Optionally the sampling along each axis can be given by the sampling parameter which should be a sequence of length equal to the input rank, or a single number in which the sampling is assumed to be equal along all axes.

The distances and indices arguments can be used to give optional output arrays that must be of the correct size and type (Float64 and Int32).

The algorithm used to implement this function is described in: C. R. Maurer, Jr., R. Qi, and V. Raghavan, "A linear time algorithm for computing exact euclidean distance transforms of binary images in arbitrary dimensions. IEEE Trans. PAMI 25, 265-270, 2003.

 distance_transform_bf( input, metric="euclidean", sampling=None, return_distances=True, return_indices=False, distances=None, indices=None)
The function distance_transform_bf uses a brute-force algorithm to calculate the distance transform of the input, by replacing each object element (defined by values larger than zero) with the shortest distance to the background (all non-object elements). The metric must be one of "euclidean", "cityblock", or "chessboard".

In addition to the distance transform, the feature transform can be calculated. In this case the index of the closest background element is returned along the first axis of the result. The return_distances, and return_indices flags can be used to indicate if the distance transform, the feature transform, or both must be returned.

Optionally the sampling along each axis can be given by the sampling parameter which should be a sequence of length equal to the input rank, or a single number in which the sampling is assumed to be equal along all axes. This parameter is only used in the case of the euclidean distance transform.

The distances and indices arguments can be used to give optional output arrays that must be of the correct size and type (Float64 and Int32).

Note: This function uses a slow brute-force algorithm, the function distance_transform_cdt can be used to more efficiently calculate cityblock and chessboard distance transforms. The function distance_transform_edt can be used to more efficiently calculate the exact euclidean distance transform.

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