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Model-Based Object Pose in 25 Lines of Code

D. Dementhon
L. Davis
Journal / Anthology

International Journal of Computer Vision
Year: 1995
Volume: 15
Page range: 123-141

In this paper, we describe a method for finding the pose of an object from a single image. We assume that we can detect and match in the image four or more noncoplanar feature points of the object, and that we know their relative geometry on the object. The method combines two algorithms; the first algorithm, POS (Pose from Orthography and Scaling) approximates the perspective projection with a scaled orthographic projection and finds the rotation matrix and the translation vector of the object by solving a linear system; the second algorithm, POSIT (POS with Iterations), uses in its iteration loop the approximate pose found by POS in order to compute better scaled orthographic projections of the feature points, then applies POS to these projections instead of the original image projections. POSIT converges to accurate pose measurements in a few iterations. POSIT can be used with many feature points at once for added insensitivity to measurement errors and image noise. Compared to classic approaches making use of Newton's method, POSIT does not require starting from an initial guess, and computes the pose using an order of magnitude fewer floating point operations; it may therefore be a useful alternative for real-time operation. When speed is not an issue, POSIT can be written in 25 lines or less in Mathematica; the code is provided in an Appendix.

*Applied Mathematics > Visualization
*Mathematica Technology > Programming > 2D Graphics
*Mathematica Technology > Programming > 3D Graphics