A new decomposition algorithm based on QR factorisation is introduced for processing and comparing irregularly shaped stress and deformation datasets found in structural analysis. The algorithm improves the comparison of two-dimensional data fields from the surface of components where data is missing from the field of view due to obstructed measurement systems or component geometry that results in areas where no data is present. The technique enables the comparison of these irregularly shaped datasets without the need for interpolation or warping of the data. This ensures comparisons are only made between the available data in each dataset and thus similarity metrics are not biased by missing data. The decomposition and comparison technique has been applied during an impact experiment, a modal analysis, and a fatigue study, with the stress and displacement data obtained from finite element analysis, digital image correlation and thermoelastic stress analysis. The results demonstrate that the technique can be used to process data from a range of sources and suggests the technique has the potential for use in a wide variety of applications.