Squared Euclidean Distance (SED)

Squared Euclidean Distance focuses on absolute intensity differences between spectra. By summing the squared band-by-band residuals, SED emphasises magnitude variations—making it ideal when brightness itself carries geophysical meaning (e.g., mineral abundance, moisture level).

How it works #

1. Vector definition $\mathbf{R}={[R_1,R_2,\dots ,R_n]}^{\mathsf{T}}$, $\mathbf{S}={[S_1,S_2,\dots ,S_n]}^{\mathsf{T}}$
2. Raw squared distance ${\text{SED}}_{\text{raw}}=\sum _{i=1}^n{(R_i-S_i)}^2$
3. Scene-adaptive normalisation (0 – 1 scale) Let ${\text{SED}}_{99\%}$ be the 99-th percentile of all raw SED values in the area of interest. We convert distance to similarity: ${\text{SED}}_{\text{norm}}=1-\mathrm{clamp}(\frac{{\text{SED}}_{\text{raw}}}{{\text{SED}}_{99\%}},0,1)$
   • 1 → spectra are identical (zero distance)
   • 0 → spectra differ at or beyond the 99 % scene distance

1. Key properties

Property	Benefit
Brightness-sensitive	Captures absolute reflectance differences—useful when intensity itself is diagnostic.
Simple & fast	Pure arithmetic; scales well to large raster datasets.
Consistent 0–1 output	Easy thresholding, colour-mapping, and cross-metric comparison.

When to use SED #

• Ore-grade estimation: Detect pixels whose reflectance magnitude deviates from a high-grade spectral reference.
• Soil moisture mapping: Brightness increases in certain bands often correlate with drier soils—SED highlights them.
• Quality control: Identify sensor artefacts or poorly calibrated areas that manifest as uniform offsets in radiance.