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# medpy.metric.binary.obj_tpr¶

medpy.metric.binary.obj_tpr(result, reference, connectivity=1)[source]

The true positive rate of distinct binary object detection.

The true positive rates gives a percentage measure of how many distinct binary objects in the first array also exists in the second array. A partial overlap (of minimum one voxel) is here considered sufficient.

In cases where two distinct binary object in the first array overlaps with a single distinct object in the second array, only one is considered to have been detected successfully.

Parameters: result : array_like Input data containing objects. Can be any type but will be converted into binary: background where 0, object everywhere else. reference : array_like Input data containing objects. Can be any type but will be converted into binary: background where 0, object everywhere else. connectivity : int The neighbourhood/connectivity considered when determining what accounts for a distinct binary object. This value is passed to scipy.ndimage.morphology.generate_binary_structure and should usually be $$> 1$$. The decision on the connectivity is important, as it can influence the results strongly. If in doubt, leave it as it is. tpr : float A percentage measure of how many distinct binary objects in result also exists in reference. It has the range $$[0, 1]$$, where a $$1$$ denotes an ideal score. RuntimeError If the reference object is empty.

Notes

This is not a real metric, as it is directed. Whatever array is considered as reference should be passed second. A perfect score of $$1$$ tells that all distinct binary objects in the reference array also exist in the result array, but does not reveal anything about additional binary objects in the result array (use obj_fpr for this).

Examples

>>> arr2 = numpy.asarray([[1,0,0],[1,0,1],[0,0,1]])
>>> arr1 = numpy.asarray([[0,0,1],[1,0,1],[0,0,1]])
>>> arr2
array([[1, 0, 0],
[1, 0, 1],
[0, 0, 1]])
>>> arr1
array([[0, 0, 1],
[1, 0, 1],
[0, 0, 1]])
>>> obj_tpr(arr1, arr2)
1.0
>>> obj_tpr(arr2, arr1)
1.0


Example of directedness:

>>> arr2 = numpy.asarray([1,0,1,0,1])
>>> arr1 = numpy.asarray([1,0,1,0,0])
>>> obj_tpr(arr1, arr2)
0.6666666666666666
>>> obj_tpr(arr2, arr1)
1.0


Examples of multiple overlap treatment:

>>> arr2 = numpy.asarray([1,0,1,0,1,1,1])
>>> arr1 = numpy.asarray([1,1,1,0,1,0,1])
>>> obj_tpr(arr1, arr2)
0.6666666666666666
>>> obj_tpr(arr2, arr1)
0.6666666666666666

>>> arr2 = numpy.asarray([1,0,1,1,1,0,1])
>>> arr1 = numpy.asarray([1,1,1,0,1,1,1])
>>> obj_tpr(arr1, arr2)
0.6666666666666666
>>> obj_tpr(arr2, arr1)
1.0

>>> arr2 = numpy.asarray([[1,0,1,0,0],
[1,0,0,0,0],
[1,0,1,1,1],
[0,0,0,0,0],
[1,0,1,0,0]])
>>> arr1 = numpy.asarray([[1,1,1,0,0],
[0,0,0,0,0],
[1,1,1,0,1],
[0,0,0,0,0],
[1,1,1,0,0]])
>>> obj_tpr(arr1, arr2)
0.8
>>> obj_tpr(arr2, arr1)
1.0