# Algorithms for Grey-Weighted Distance Computations

## TL;DR

This paper compares various algorithms for grey-weighted distance transforms, highlighting the label-setting algorithms with hierarchical heaps as the most efficient choice in most scenarios, and providing practical guidelines.

## Contribution

It offers a comprehensive performance comparison of algorithms for grey-weighted distance computations and recommends optimal data structures based on scenario and memory constraints.

## Key findings

- Label-setting algorithms outperform others in all scenarios.
- Hierarchical heap with pointer array is the best priority queue.
- Dial and Untidy priority queues are preferable when memory is limited.

## Abstract

With the increasing size of datasets and demand for real time response for interactive applications, improving runtime for algorithms with excessive computational requirements has become increasingly important. Many different algorithms combining efficient priority queues with various helper structures have been proposed for computing grey-weighted distance transforms. Here we compare the performance of popular competitive algorithms in different scenarios to form practical guidelines easy to adopt. The label-setting category of algorithms is shown to be the best choice for all scenarios. The hierarchical heap with a pointer array to keep track of nodes on the heap is shown to be the best choice as priority queue. However, if memory is a critical issue, then the best choice is the Dial priority queue for integer valued costs and the Untidy priority queue for real valued costs.