Identify the true temperature among permitted solutions without emissivity information

Determine which temperature–emissivity pair among the continuum of permitted solutions that exactly reproduce multiwavelength spectral radiance measurements corresponds to the actual physical temperature when no a priori emissivity information about the emissivity spectrum is available.

Background

Multiwavelength thermometry (MWT) is intrinsically underdetermined: at n wavelengths there are n emissivity values plus temperature to recover from only n radiance measurements, yielding a continuous infinity of exact solutions ("permitted solutions"). The paper emphasizes that this multiplicity persists even when measurement noise is present, as noise simply propagates to the inferred emissivity spectra without removing the non-uniqueness.

In the random-error analysis, the authors underline that any temperature combined with its corresponding permitted emissivity spectrum can perfectly explain the measured (noisy) radiance. Without introducing external emissivity information, the true solution cannot be singled out from the infinite set of permitted solutions. This explicit knowledge gap motivates the need for emissivity information to localize the true temperature.

References

One of them is the true one and we don't know which one until we get information on the true emissivity.

— Multiwavelength thermometry without a priori emissivity information: from promise to disillusionment  (2504.20853 - Krapez, 29 Apr 2025) in Section 5.1 (Effect of random errors on measurements)

TAP3D focuses on depth as the primary geometric primitive for 3D reconstruction. The multi-primitive learning framework injects physical constraints to better isolate depth-related information, while precise multi-primitive estimation remains an interesting and challenging direction for future work.

— TAP3D: Thermal-Assisted 3D Human Point Clouds  (2610.11241 - Zhang et al., 8 Oct 2026) in Section 8, Subsection “Precise multi-primitive estimation”