C5 ยท Publication Volume 15

Hyperspectral Geological Mapping

mineral groups, spectral libraries and classification confidence

Learning goals

This lesson builds a defensible workflow for imaging spectroscopy, also called hyperspectral imaging. The learner should be able to inspect a spectral cube and its quality; mask unusable wavelengths and pixels; control noise and dimensionality; obtain candidate endmembers without circular validation; compare feature fitting, angle, unmixing and classification methods; map confidence and unknown; and design spatially independent field validation.

Hundreds of channels do not create hundreds of independent mineral facts. The cube contains correlated signal, atmospheric residuals, detector structure, mixed pixels and spatial context. A classifier is useful only when its inputs, assumptions, rejection rule and error are visible.

Spectral cube anatomy and quality screening

An imaging-spectrometer cube has two spatial dimensions and one spectral dimension, but delivered files may store radiance, apparent reflectance, surface-related reflectance, quality, geometry and uncertainty separately. Inspect wavelength centres, response widths, full width at half maximum, calibration shifts, signal-to-noise ratio, no-data, saturation, detector modules and geolocation before analysis.

Remove or flag strong atmospheric absorption intervals, low-signal edges, uncalibrated channels, detector joins, stripes, dropouts and excessive noise. Spectral smile varies wavelength across the field; keystone varies spatial registration with wavelength. Uncorrected effects can create false feature shifts or coloured edges.

Plot random and targeted pixel spectra, band histograms and spatial maps of diagnostic residuals. A smooth RGB preview can conceal spectral failures. Keep the original band mask and pixel-quality mask as first-class outputs.

Noise, dimensionality and transformations

Adjacent channels are highly correlated. Principal-component transformations order variance but do not distinguish geological signal from atmosphere or brightness. Noise-adjusted transforms use an estimated noise covariance and can concentrate coherent information, yet their components remain data-dependent and need physical interpretation.

Smoothing can improve apparent signal-to-noise ratio while broadening or shifting features. Derivatives suppress continuum but amplify high-frequency noise. Baseline and continuum removal impose anchors. Every transform requires parameter sensitivity and a route to the original spectrum.

Estimate effective dimensionality rather than using every band blindly. Split data into calibration, model-selection and validation support. Do not estimate noise from heterogeneous geological boundaries and then claim the resulting transform is independent of geology.

Endmembers, libraries and feature fitting

An endmember is a spectrum used to represent a component or class. It may come from a laboratory library, field measurement, image-derived pure-looking pixel or physical model. Each source has different scale and transfer limitations. Image endmembers share atmosphere and sensor response but may be mixtures; library endmembers may be pure and mismatched to field state.

Endmember extraction methods find spectral extremes under mathematical criteria, not guaranteed minerals. Inspect their spatial locations, quality and physical features. Include confounders such as vegetation, shadow, water, soil, roads and calibration artefacts. Avoid naming an extreme before independent evidence.

Feature fitting compares continuum-removed absorption shape, depth and centre with convolved references. It is interpretable but depends on selected intervals. Use multiple compatible features where possible, propagate wavelength and noise uncertainty, and retain residual spectra. A feature absent in low-signal or masked wavelengths is unknown, not negative evidence.

Classification, spectral angle and unmixing

Spectral angle compares vector direction and reduces sensitivity to overall magnitude, but ignores scale information and can favour noisy dark pixels unless screened. Matched filters target a reference relative to background covariance; their result depends strongly on background definition. Machine-learning classifiers can model complex boundaries but require representative, independent labels and calibrated probabilities.

Linear unmixing represents a pixel spectrum as \mathbf r\approx M\mathbf f+\boldsymbol\epsilon, where columns of M are endmembers and fractions \mathbf f may be constrained to be non-negative and sum to one. Residuals reveal model inadequacy. Intimate mixing, shade, variable endmembers and nonlinear scattering violate the simple model.

No method removes the need for rejection. Set thresholds using validation and consequence, not map aesthetics. Report alternative candidates and an unknown class. Compare maps from physically different methods and investigate disagreements rather than voting them away.

Spatial context, confidence and uncertainty

Spectral classifications have spatial structure. Isolated single-pixel detections may be real subpixel exposures, noise or artefacts. Morphological filtering changes minimum mapping unit and can erase small valid targets. Record every spatial rule and evaluate before/after counts.

Confidence should combine spectral fit, margin between candidates, signal quality, exposure fraction, atmospheric and geometric quality, and domain of the training data. A softmax probability alone is not calibrated confidence. Map uncertainty and excluded support alongside the preferred class.

Use spatially blocked validation so nearby correlated pixels do not appear in both training and testing. Report class-specific precision, recall and confusion, plus performance by terrain, cover and signal-quality strata. Accuracy averaged over a dominant background can hide complete failure on a rare geological target.

Worked synthetic example

A synthetic cube contains two hydroxyl-bearing materials, dry vegetation, bright soil and shadow. The materials differ by a small feature-centre shift that is resolvable in high-signal pixels. A spectral-angle classifier maps both materials but also labels some shadow because vector direction is similar after noise. A feature-fit classifier rejects shadow but confuses the materials where a detector-column wavelength shift is uncorrected.

After applying the spectral calibration field and a minimum signal rule, the maps agree over exposed cores. Mixture zones remain group-level. Spatially blocked validation shows high precision for the group but insufficient support for separating its members. The released product maps group compatibility, a high-confidence subset, unknown, and required field sites; it does not force two mineral names.

Interpretation and decision. Connect class to observed features and model domain. State which wavelengths, endmembers and quality rules support each pixel. A decision may prioritise a transect across high-confidence and ambiguous areas. Field sites should sample expected positives, confounders, boundaries and apparent negatives, not just the strongest colours.

Practice and audit checklist

Build a synthetic cube from five endmembers with variable illumination, mixtures, correlated noise, a bad detector column and a wavelength shift. Compare feature fitting, spectral angle and constrained linear unmixing. Use blocked validation and create maps of preferred class, residual, confidence and unknown. Explain disagreements in measurement space.

Audit questions: Are bad bands and pixels explicit? Was response convolution applied? Are endmembers independent of validation? Is the background definition recorded? Are thresholds tied to consequence? Is unknown allowed? Are spatial filters declared? Do residuals expose model failure? Are field sites representative of alternatives and cover conditions?

Quality screening, endmembers, feature models, residuals and independent validation turn a spectral cube into a conditional map
Quality screening, endmembers, feature models, residuals and independent validation turn a spectral cube into a conditional map

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