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Recent work has shown that effective methods for recognising objects or spatio-temporal events can be constructed based on receptive field responses summarised into histograms or other histogram-like image descriptors. This paper presents a set of composed histogram features of higher dimensionality, which give significantly better recognition performance compared to the histogram descriptors of lower dimensionality that were used in the original papers by Swain & Ballard (1991) or Schiele & Crowley (2000). The use of histograms of higher dimensionality is made possible by a sparse representation for efficient computation and handling of higher-dimensional histograms. Results of extensive experiments are reported, showing how the performance of histogram-based recognition schemes depend upon different combinations of cues, in terms of Gaussian derivatives or differential invariants applied to either intensity information, chromatic information or both. It is shown that there exist composed higher-dimensional histogram descriptors with much better performance for recognising known objects than previously used histogram features. Experiments are also reported of classifying unknown objects into visual categories.