Recovering the 3D coordinates of various joints of the human body from an image is a critical first step for several model-based human tracking and optical motion capture systems. Unlike previous approaches that have used a restrictive camera model or assumed a calibrated camera, our work deals with the general case of a perspective uncalibrated camera and is thus well suited for archived video. The input to the system is an image of the human body and correspondences of several body landmarks, while the output is the set of 3D coordinates of the landmarks in a body-centric coordinate system. Using ideas from 3D model based invariants, we set up a polynomial system of equations in the unknown head pitch, yaw and roll angles. If we are able to make the often-valid assumption that torso twist is small, we show that there exists a finite number of solutions to the head-orientation which can be computed readily. Once the head orientation is computed, the epipolar geometry of the camera is recovered, leading to solutions to the 3D joint positions. Results are presented on synthetic and real images.