An Approach for Bone Pose Estimation via Three External Ellipsoid Pressure Points

Abstract

The accurate reproduction of bone motion during normal gait using noninvasive external sensors is still an open issue: Using skin markers may lead to large artifacts due to skin sliding, while using newer technologies such as fluoroscopy allows only for short exposure in small regions due to radiation limits, and bone pins used in the past are today prohibited due to the risk of inflammations and pain. This paper presents a simple method for noninvasive bone motion estimation based on palpating prominent bone landmarks via tracked pressure foil planes, where three such landmarks suffice for bone pose estimation. Its mathematical formulation corresponds to determining the pose of a rigid body carrying three ellipsoids when the “pressure points”, i.e. the perpendicular feet of the extremal distance points of the ellipsoids on the three pressure foil planes are given. In a previous paper, we showed that the planar case is akin to the 3PPR manipulator, but yielding instead of two solutions up to 64 complex and (up to now found) 48 real solutions. In this paper we treat the 3D case, which is solved numerically, and validate the concept by experimental measurements. It is shown that the method is numerically stable, yielding an accuracy of $0.8{^{{\circ }}}$ for flexion/extension and $1.2{^{{\circ }}}$ for abduction/adduction motion of the lower leg.