The Para-Perspective Projection as an Approximation of the Perspective Projection for Recovering 3D Motion in Real Time
We present a new algorithm for determining 3D motion of a moving rigid object in real-time image sequences relative to a single camera. In the case where features are two-dimensional (2D), they are obtained by projective transformations of the 3D features on the object surface under perspective model. The perspective model has formulated in nonlinear least square problem to determine 3D motions as characterized by rotation and translation iteratively. In practice, it is numerically ill-conditioned and may converge slowly or even fail to converge, if it starts with not good enough initial guess. However, since para-perspective projection model closely approximates perspective projection for recovering the 3D motion and shape of the object in Euclidean space, we used the results provided from para-perspective projection model as an initial value of nonlinear optimization refinement under perspective model equations.
KeywordsPara-perspective model Perspective model 3D motion
The work in this paper was supported by the grant of National University of Mongolia (No. P2017-2469) and MJEED, JICA (JR14B16).
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