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Connected-component labelling remains an important and widely-used technique for processing and analysing images and other forms of data in various application areas. Different data sources produce components with different structural features and may be more or less suited to certain connected-component labelling algorithms. Although many efficient serial algorithms exist, determining connected-components on Graphical Processing Units (GPUs) is of interest as many applications use GPUs for processing other parts of the application and labelling on the GPU can avoid expensive memory transfers. The general problem of connected-component labelling is discussed and two existing GPU-based algorithms are discussed—label-equivalence and Komura-equivalence. A new GPU-based, parallel component-labelling algorithm is presented that identifies and eliminates redundant operations in the previous methods for rectilinear two- and three-dimensional datasets. A set of test-cases with a range of structural features and systems sizes is presented and used to evaluate the new labelling algorithm on modern NVIDIA GPU devices and compare it to existing algorithms. The results of the performance evaluation are presented and show that the new algorithm can provide a meaningful performance improvement over previous methods across a range of test cases. [ABSTRACT FROM AUTHOR]