The Fast Integration of a Rotated Rectangle Applied to the Rotated Haar-Like Features for Rotated Objects Detection

The Integral Image technique, used by Viola and Jones, is generally used to calculate the integral of a rectangular filter in an input picture. This filter is a rectilinear rectangle. We propose a method to integrate a rotated one by any angle of rotation inside an image based on the Bresenham algorithm of drawing a segment. We use some pixels – called key points that forms the four segments of a rotated rectangle, to calculate its Integral Image. Our method focuses on three essential tasks; the first is to determine the rule for drawing a segment (SDR), the second is to identify all the key points of the rectangle r, and the third is to calculate the integral image. The speed of this method depends on the size and angle of rotation of the rectangle. To demonstrate the efficiency of our idea, we applied it to the rotated Haar-like features that we proposed in a later work [12], which had as objectives the improvement of the Viola and Jones algorithm to detect the rotated faces in a given image. We performed tests on more widespread databases of images, which showed that the application of this technique to rotated Haar-Like features improves the performance of object detectors, in general, and faces in particular.