A method is developed to characterise highly irregular shape patterns, especially those appearing in biomedical settings. A collection of best-fitting ellipsoids is found using principal component analysis, and features are defined based on these ellipsoids in four different ways. The method is defined in a general setting, but is illustrated using two-dimensional images of dimorphic yeast exhibiting pseudohyphal growth, three-dimensional images of cancellous bone and three-dimensional images of marbling in beef. Classifiers successfully distinguish between the yeast colonies with a mean classification accuracy of 0.843 (SD= 0.021), and between cancellous bone from rats in different experimental groups with a mean classification accuracy of 0.745 (SD= 0.024). A strong correlation (R 2= 0.797) is found between marbling ratio and a shape feature. Key aspects of the method are that local shape patterns, including orientation, are learned automatically from the data, and the method applies to objects that are irregular in shape to the point where landmark points cannot be identified between samples.