Fast and efficient rotated haar-like features using rotated integral images

This paper introduces an extended set of Haarlike features beyond the standard vertically and horizontally aligned Haar-like features [Viola and Jones, 2001a; 2001b] and the 45o twisted Haar-like features [Lienhart and Maydt, 2002; Lienhart et al., 2003a; 2003b]. The extended rotated Haar-like features are based on the standard Haar-like features that have been rotated based on whole integer pixel based rotations. These rotated feature values can also be calculated using rotated integral images which means that they can be fast and efficiently calculated with just 8 operations irrespective of the feature size. In general each feature requires another 8 operations based on an identity integral image so that appropriate scaling corrections can be applied. These scaling corrections are needed due to the rounding errors associated with scaling the features. The errors introduced by these rotated features on natural images are small enough to allow rotated classifiers to be implemented using a classifier trained on only vertically aligned images. This is a significant improvement in training time for a classifier that is invariant to the rotations represented in the parallel classifier.