Spectral Profile

Overview

The spectral_profile module computes and visualizes the average spectral signatures across multi-spectral satellite image collections. In remote sensing, a spectral profile (or spectral signature) charts how a target surface reflects electromagnetic radiation across different wavelengths. This signature serves as a diagnostic fingerprint for characterizing dominant surface materials and evaluating radiometric variations between land-cover classes.

This module unifies separate spectral bands—typically including the visible spectrum (Red, Green, Blue), Near-Infrared (NIR), and Short-Wave Infrared (SWIR1, SWIR2)—and aggregates their spatial grids. By extracting the mathematical mean of each band, the SpectralProfileCalculator produces a discrete line graph ($f(\text{band}) = \mu_{\text{band}}$) that captures the baseline radiometric identity of the entire scene.

       [6 Ingested Single-Band Layers] (Red, Green, Blue, NIR, SWIR1, SWIR2)
                      │
                      ▼
       ┌──────────────────────────────┐
       │     Valid Band Extraction    │ ──► Drops None values, unifies into 
       │      & Dictionary Staging    │     ordered list via insertion flags.
       └──────────────┬───────────────┘
                      │
                      ▼
       ┌──────────────────────────────┐
       │   Global Spatial Averaging   │ ──► Evaluates vector means via:
       │  $\mu = \frac{1}{HW}\sum I$  │     $\mu_{\text{band}} = \text{np.mean}(I_{\text{band}})$
       └──────────────┬───────────────┘
                      │
                      ▼
       ┌──────────────────────────────┐
       │ Data Vector Synchronization  │ ──► Maps structural axes arrays:
       │     (xaxis $\leftrightarrow$ yaxis)     │     $\text{xaxis} = \text{Bands}$, $\text{yaxis} = \text{Means}$
       └──────────────┬───────────────┘
                      │
                      ▼
       ┌──────────────────────────────┐
       │   Diagnostic Axis Plotting   │ ──► Draws line graph and attaches
       │   (Fixed Lifecycle Execution)│     the FEZrs system watermark.
       └──────────────────────────────┘

2. Mathematical Processing Framework

2.1. Spatial Band Aggregation

The calculator filters the incoming files to extract valid, non-null bands and stores them in an ordered layout:

\text{image}\textunderscore\text{columns} = \lbrace \text{band}\textunderscore\text{name} : I_{\text{band}}(x, y) \mid I_{\text{band}} \neq \text{None} \rbrace

This collection is converted into a structurally indexed array where the dictionary keys determine the $X$-axis tracking names:

\text{image}\textunderscore\text{columns}\textunderscore\text{list}\textunderscore\text{of}\textunderscore\text{bands} = [b_1, b_2, \dots, b_m] \quad \text{where } m \le 6

2.2. Global Spatial Averaging

For each valid single-channel raster layer $I_{\text{band}}$ of height $H$ and width $W$, the engine calculates the overall radiometric mean ($\mu_{\text{band}}$). This scalar value represents the arithmetic average of the entire pixel population:

$$\mu_{\text{band}} = \frac{1}{H \times W} \sum_{x=1}^{H} \sum_{y=1}^{W} I_{\text{band}}(x, y)$$

This calculation reduces the 2D spatial array to a single statistical weight, balancing local anomalies to capture the broad thematic signature of the scene.

2.3. Vector Coordinate Mapping

The calculated data points are synchronized into two matching operational vectors that define the plot tracking coordinates:

$$\text{xaxis} = [b_1, b_2, \dots, b_m]$$

$$\text{yaxis} = [\mu_{b_1}, \mu_{b_2}, \dots, \mu_{b_m}]$$

This vector pair creates a discrete function $f(\text{band}) = \mu_{\text{band}}$ that visualizes variations in surface reflectance across the measured spectrum.

3. Remote Sensing Interpretation Profiles

The shape of the resulting curve reveals the dominant environmental features and land-cover types across the scene:

• Vegetation Signature (NIR Peak & Red Dip): Healthy green vegetation absorbs red light to power photosynthesis while strongly scattering near-infrared energy via leaf structures. This produces a distinct drop in the $\text{Red}$ band followed by a sharp increase ($\mu_{\text{NIR}} \gg \mu_{\text{Red}}$).

• Open Water / Shadow Signature (Flat & Low): Water bodies and deep shadows absorb most incident light across reflective infrared wavelengths. This results in a low, flat signature line that approaches zero in the $\text{NIR}$ and $\text{SWIR}$ regions.

• Bare Soil Signature (Gradually Increasing): Exposed soils, gravel fields, and bedrocks show a steady, linear increase in reflectance from the visible bands through the short-wave infrared spectrum.

• Urban / Burn Scars Signature (SWIR Dominant): Man-made materials (like concrete and asphalt) and burned areas show low near-infrared reflectance but reflect strongly in the short-wave infrared region ($\mu_{\text{SWIR2}} > \mu_{\text{NIR}}$).