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Problems requiring accurate determination of parameters from image-based quantities arise often in computer vision. Two recent, independently developed frameworks for estimating such parameters are the FNS and HEIV schemes. Here it is shown that FNS (fundamental numerical scheme) and a core version of HEIV (heteroscedastic errors-in-variables) are essentially equivalent, solving a common underlying equation via different means. The analysis is driven by the search for a nondegenerate form of a certain generalised eigenvalue problem, and effectively leads to a new derivation of the relevant case of the HEIV algorithm. This work may be seen as an extension of previous efforts to rationalise and inter-relate a spectrum of estimators, including the renormalisation method of Kanatani and the normalised eight-point method of Hartley.