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This paper describes a robust three-dimensional (3D) head pose estimation method based on face geometry and linear regression model. Given an unknown range image, we extract six invariant facial features based on face curvature characteristics. For estimating the head pose, we estimate the initial head pose using the SVD method, and perform a refinement procedure to compensate for remaining errors for the X and Y axis. To compensate for the Z axis, we orthogonally project feature points onto the Z plane and estimate the face center line based on the linear regression model. Experimental results show that less than a 0.5 degree error on average for each axis has been achieved.