This paper describes a method for integrating object detectors that reduces the expected computational cost of evaluating all the detectors whilst obtaining the same logical behaviour as running the detectors independently. The method combines the decision trees of the different object detectors into a single composite decision structure controlling the evaluation of the classifiers from all of the original object detectors. The method intersperses the classifiers from the different object detectors allowing the evaluation of any object detector to be dependent on classifier results from other object detectors. The method exploits these extra results to rearrange the order in which classifiers from a particular object detector are evaluated. These rearrangements preserve the logical behaviour of the object detector whilst changing the expected computational cost of evaluating the decision structure. All the object detectors are rare event detectors and so this method improves performance by exploiting the common need to reject the majority of patches being searched. Simplistically improved performance is obtained by rejecting non-object patches as soon as possible. The main contribution of this paper is the language used to formally express the problem of integrating the decision structures of different object detectors to obtain improved performance. Expressions for the expected computational cost of the integration are given, and the data structures defined for the single composite data structure. However additional work is needed to quantify the improved performance. The paper was initially written as a HP invention disclosure which resulted in a patent application. The patent application is more complex and difficult to read because it generalised the method to work with a set of more general decision structures and adapted the method to be used with chaining or binning by allowing rearrangements of decision structures that did not preserve logical behaviour. More information on these generalisations is given on the web page: http://w3.hpl.hp.com/people/dag/integrating_object_det ectors/overview.htm 18 Pages