The Cubic Rational Polynomial Camera Model

It is empirically demonstrated that a SAR sensor is very accurately approximated by a cubic camera, but not by any linear camera model, and an algorithm for estimating the parameters of the cubic camera is outlined, given a set of image to world correspondences.

Abstract

This paper desc#xw es an implementation of the Cubic Rational Polynomial Camera model developed as part of the FOCUS projec# . FOCUS ([1]) is on ongoing "shared vision" IR&D projec# jointly sponsored by Loc kheed Martin Missiles and Spac e (LMMSS/Sunnyvale) and General Elec# ric CR&D. A c# bic c amera has the advantage that allc ameras, suc h as projec tive, a#ne and the linear pushbroom, whic h map the image points as rational polynomial func tions (of degree no greater than 3) of thec oordinates of a world point,c## be treated as spec#wz c ases of the c ubic c amera. This paper demonstrates that thec ubic c amerac an very e#ec tively model even thosec ameras whic h express the image points as c#3 plic#, ed func tions of worldc# ordinates, suc h as radic#wzfi In partic# - lar, it is empiric##xA demonstrated that a SAR sensor is veryac#3 rately approximated by ac ubic c amera, but not by any linearc amera model. The paper also outlines an algorithm for estimating the parameters of thec ubic c amera, given a set of image to worldc orrespondenc es. The non-linear nature of thisc amerac an make parameter estimation a very unstable proc ess. The slightest noise in thec oe#c ients of the nonlinear termsc an lead to ac ompletely unrealistic model of thec amera. This paper disc usses some refinements suc h as avoiding degenerac ies, data normalization, and regularization whic h arenec#9 sary for ac#w#3 te estimation of the c# bic c amera parameters and minimization of noise in the c# e#c#[3 ts of the higher degree terms. 1 Introducti on A basic requ#- ement of the FOCUS ([1]) project is to be able to compu#/ camera models and do modelbu#II8&D u sing complexand general camera models. To thispu# pose, aCu#8# Rational Polynomial camera model has been developed in FOCUS to aid in...