Multi-Task Deep Learning for Joint Depth-Map Reconstruction and Iso-Point Prediction from Hyperspectral Images of Turbid Phantoms

Hyperspectral imaging (HSI) of turbid, tissue-mimicking media entangles the geometry of subsurface inclusions with the optical properties of the surrounding matrix in every spectrum. From HSI cubes of polyurethane phantoms with obliquely drilled inclusions we recover two physically distinct quantities: a dense depth map of the inclusion and the scalar iso-point wavelength, the point of near-invariance at which the depth-dependent modulation of the diffuse reflectance cancels. A single multi-task U-Net is a poor compromise for such complementary targets, the dense and scalar heads reaching their optima at different epochs while global pooling destroys the spectral-position information a wavelength target needs. We therefore decompose the problem into two specialised networks sharing one pipeline: a Bin Latent Transformer (BiLT) cross-attention scanner for the iso-point and a masked, zero-padded U-Net for the depth map. Under a strict cross-phantom split the depth network reaches a mean relative error of 6.07±0.71% (R2=0.934±0.014), against 19.4% for the analytic two-band index of earlier work and about 12.9% for the multi-task baseline. Zero-padding with a masked loss, preserving the inclusion-width information that cropping discards, is the decisive ingredient, and conditioning depth on the iso-point yields no further gain. The iso-point network reaches 5.03±0.93 nm RMSE (R2=0.630±0.085) from the spectra alone. Plausible settings of the iso-point detector change the labels themselves by 2.6 to 3.9 nm root-mean-square, while the retrained network stays between 4.8 and 5.3 nm. Together with oracle and per-patch-detection diagnostics, this identifies the ceiling as a detector-limited label-noise floor rather than a model deficiency. Averaging over a whole inclusion lowers the RMSE to a 3.27 nm plateau, separating an averageable random error from an irreducible regression-to-the-mean bias. For the straight, obliquely drilled bores tested here the depth task is solved to deployable accuracy, and the iso-point network gives a useful per-segment estimate where direct optical determination fails.