  This work introduces two new distance metrics for comparing labeled arrays,
which are common outputs of image segmentation algorithms. Each pixel in an
image is assigned a label, with binary segmentation providing only two labels
('foreground' and 'background'). These can be represented by a simple binary
matrix and compared using pixel differences. However, many segmentation
algorithms output multiple regions in a labeled array. We propose two distance
metrics, named LAD and MADLAD, that calculate the distance between two labeled
images. By doing so, the accuracy of different image segmentation algorithms
can be evaluated by measuring their outputs against a 'ground truth' labeling.
Both proposed metrics, operating with a complexity of $O(N)$ for images with
$N$ pixels, are designed to quickly identify similar labeled arrays, even when
different labeling methods are used. Comparisons are made between images
labeled manually and those labeled by segmentation algorithms. This evaluation
is crucial when searching through a space of segmentation algorithms and their
hyperparameters via a genetic algorithm to identify the optimal solution for
automated segmentation, which is the goal in our lab, SEE-Insight. By measuring
the distance from the ground truth, these metrics help determine which
algorithm provides the most accurate segmentation.
