Quaternion-based determination of 3D objects orientation

The problem of 3D objects orientation recognition in a three-dimensional image space is considered in this paper. The used method is a quaternion-based approach applied to images acquired by CT-like devices. The concept of orientation recognition comes from the well-known Ballard method of arbitrary shapes detection in two-dimensional images, now commonly known as the generalized Hough transform. Aside from quaternions, used as the main mathematical tool, the orientation recognition is based on determination of an accumulator array for Euler angles. Values in the accumulator are received using so called counting method, adopted here for voxels. Objects orientation is determined by coordinates of an element in the accumulator array with a maximum number of votes received. The elaborated method may be useful in the area of robotic surgery, especially in cases of penetrating injuries caused by foreign bodies.