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Most previous efforts in developing computer-aided detection (CADe) of colonic polyps apply similar measures or parameters to detect polyps regardless of their locations under an implicit assumption that all the polyps reside in a similar local environment, e.g. on a relatively flat colon wall. In reality, this implicit assumption is frequently invalid, because the haustral folds can have a very different local environment from that of the relatively flat colon wall. We conjecture that this assumption may be a major cause of missing the detection of polyps, especially small polyps (<10 mm linear size) located on the haustral folds. In this paper, we take the concept of adaptiveness and present an adaptive paradigm for CADe of colonic polyps. Firstly, we decompose the complicated colon structure into two simplified sub-structures, each of which has similar properties, of (1) relatively flat colon wall and (2) ridge-shaped haustral folds. Then we develop local environment descriptions to adaptively reflect each of these two simplified sub-structures. To show the impact of the adaptiveness of the local environment descriptions upon the polyp detection task, we focus on the local geometrical measures of the volume data for both the detection of initial polyp candidates (IPCs) and the reduction of false positives (FPs) in the IPC pool. The experimental outcome using the local geometrical measures is very impressive such that not only the previously-missed small polyps on the folds are detected, but also the previously miss-removed small polyps on the folds during FP reduction are retained. It is expected that this adaptive paradigm will have a great impact on detecting the small polyps, measuring their volumes and volume changes over time, and optimizing their management plan. [ABSTRACT FROM AUTHOR]