# Effective Calibration Transfer via M\"obius and Affine Transformations

## TL;DR

The paper introduces MFPI, a calibration transfer method using quasiconformal maps in the frequency domain, which outperforms traditional methods like DS and PDS in near infrared spectra analysis.

## Contribution

It presents a novel calibration transfer technique based on M"obius and affine transformations, improving accuracy over existing methods.

## Key findings

- MFPI outperforms DS and PDS in transfer and prediction errors.
- Combining MFPI with DS/PDS further reduces predictive errors.
- MFPI leverages physical intuition and quasiconformal maps for spectral transfer.

## Abstract

A novel technique for calibration transfer called the Modified Four Point Interpolant (MFPI) method is introduced for near infrared spectra. The method is founded on physical intuition and utilizes a series of quasiconformal maps in the frequency domain to transfer spectra from a slave instrument to a master instrument's approximated space. Comparisons between direct standardization (DS), piecewise direct standardization (PDS), and MFPI for two publicly available datasets are detailed herein. The results suggest that MFPI can outperform DS and PDS with respect to root mean squared errors of transfer and prediction. Combinations of MFPI with DS/PDS are also shown to reduce predictive errors after transfer.