  Perspective-$n$-Point (P$n$P) stands as a fundamental algorithm for pose
estimation in various applications. In this paper, we present a new approach to
the P$n$P problem with relaxed constraints, eliminating the need for precise 3D
coordinates, which is especially suitable for object pose estimation where
corresponding object models may not be available in practice. Built upon the
classical EP$n$P solver, we refer to it as AEP$n$P due to its ability to handle
unknown anisotropic scaling factors in addition to the common 6D
transformation. Through a few algebraic manipulations and a well-chosen frame
of reference, this new problem can be boiled down to a simple linear null-space
problem followed by point registration-based identification of a similarity
transformation. Experimental results on both simulated and real datasets
demonstrate the effectiveness of AEP$n$P as a flexible and practical solution
to object pose estimation. Code: https://github.com/goldoak/AEPnP.
