11.3 Remote Sensing Spectral Signatures, Multispectral Image Classification, and GIS Spatial Analysis

11.3 Remote Sensing Spectral Signatures, Multispectral Image Classification, and GIS Spatial Analysis

Remote Sensing (RS) and Geographic Information Systems (GIS) form the analytical foundation of modern Geodetic Engineering. While photogrammetry focuses primarily on geometric metric extraction, satellite remote sensing measures spectral electromagnetic energy to analyze surface materials, soil properties, vegetation health, and land classification. Integrating remote sensing datasets into GIS spatial analysis frameworks allows geodetic engineers to execute land cover mapping, environmental impact assessments, and hazard zone modeling for Philippine regulatory bodies such as DENR, NAMRIA, and LGU planning offices.

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1. Electromagnetic Spectrum & Remote Sensing Mechanics

Remote sensing systems record Electromagnetic Radiation (EMR) reflected or emitted from Earth surface features across distinct spectral wavebands.

+-----------------------------------------------------------------------------------------+
| Gamma & X-Ray |  UV  | Visible | Near-IR | Short-Wave IR | Thermal IR | Microwave/RADAR |
|               |      | B G R   | (NIR)   | (SWIR)        | (TIR)      |                 |
| < 0.3 µm      | 0.38 | 0.4-0.7 | 0.7-1.1 | 1.1-3.0 µm    | 3-15 µm    | 1 mm - 1 m      |
+-----------------------------------------------------------------------------------------+

Spectral Waveband Divisions

• Visible Band ($0.40 - 0.70\text{ }\mu\text{m}$): Blue ($0.45 - 0.52\text{ }\mu\text{m}$), Green ($0.52 - 0.60\text{ }\mu\text{m}$), and Red ($0.63 - 0.69\text{ }\mu\text{m}$). Absorbed by plant pigments (chlorophyll $a$ and $b$).
• Near-Infrared / NIR ($0.75 - 1.10\text{ }\mu\text{m}$): Unaffected by chlorophyll absorption; heavily reflected and scattered by internal spongy mesophyll cell structures of healthy leaves.
• Short-Wave Infrared / SWIR ($1.30 - 2.50\text{ }\mu\text{m}$): Sensitive to leaf water content and soil moisture. Features strong water absorption troughs at $1.40\text{ }\mu\text{m}$ and $1.90\text{ }\mu\text{m}$.
• Thermal Infrared / TIR ($8.00 - 14.00\text{ }\mu\text{m}$): Measures emitted blackbody kinetic heat radiation from surface materials.
• Microwave ($1\text{ mm} - 1\text{ m}$): Active Synthetic Aperture RADAR (SAR) bands (C-band, L-band, X-band) capable of day/night operation and cloud penetration.

Atmospheric Scattering Types

1. Rayleigh Scattering: Occurs when atmospheric particle diameters are much smaller than the EMR wavelength (e.g., $N_2$ and $O_2$ gas molecules). Scattering intensity is proportional to $1/\lambda^4$. Causes blue light scattering (blue sky appearance) and atmospheric haze in aerial photography.
2. Mie Scattering: Occurs when atmospheric particles are approximately equal in size to the EMR wavelength (e.g., dust, pollen, smoke, water vapor). Dominates under overcast or hazy conditions.
3. Non-Selective Scattering: Occurs when particle diameters are significantly larger than the wavelength (e.g., water droplets in fog/clouds). Scatters all visible wavelengths equally, making clouds appear white.

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2. Spectral Reflectance Curves and Spectral Indices

A spectral reflectance curve plots the percentage of incident solar radiation reflected by a material as a function of wavelength ($\lambda$).

Characteristic Surface Signatures

• Healthy Green Vegetation: Low reflectance in Blue and Red due to chlorophyll absorption; slight peak in Green ($550\text{ nm}$); steep rise ("Red Edge") to extremely high reflectance ($40-50%$) in NIR; absorption dips in SWIR due to leaf liquid water.
• Clear Deep Water: High absorption across all wavelengths; reflects slightly in Blue/Green; near-zero reflectance in NIR and SWIR. Water bodies appear dark/black in NIR band imagery.
• Bare Soil: Reflectance increases monotonically from visible to NIR and SWIR wavebands. Clay and organic matter content decrease overall soil reflectance; moisture creates distinct absorption dips at $1.4\text{ }\mu\text{m}$ and $1.9\text{ }\mu\text{m}$.

Normalized Difference Vegetation Index (NDVI)

$$\text{NDVI} = \frac{\text{NIR} - \text{Red}}{\text{NIR} + \text{Red}}$$

NDVI values range strictly from $-1.0$ to $+1.0$:

• Dense, Healthy Forest Canopy: $+0.60 \text{ to } +0.90$
• Sparse Grassland / Agriculture: $+0.20 \text{ to } +0.50$
• Bare Soil / Rock: $+0.05 \text{ to } +0.15$
• Water Bodies / Clouds: $-1.00 \text{ to } 0.00$

Other Key Remote Sensing Indices

1. Normalized Difference Water Index (NDWI): $$\text{NDWI} = \frac{\text{Green} - \text{NIR}}{\text{Green} + \text{NIR}}$$
2. Normalized Difference Built-up Index (NDBI): $$\text{NDBI} = \frac{\text{SWIR} - \text{NIR}}{\text{SWIR} + \text{NIR}}$$

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3. Satellite Sensors and Image Classification

Comparison of Major Satellite Constellations

Image Classification Algorithms

1. Supervised Classification: The engineer defines representative homogenous ground sites ("training sites") for each land cover category. The algorithm calculates statistical parameters (mean vector, covariance matrix) to assign unclassified image pixels:
   • Maximum Likelihood Classifier (MLC): Assumes normal multivariate distribution of spectral data; calculates posterior probability of pixel belonging to each class.
   • Minimum Distance to Means: Assigns pixels to the class with the shortest Euclidean spectral distance to the mean.
   • Random Forest / SVM: Non-parametric machine learning classifiers robust against non-normal multi-modal distributions.
2. Unsupervised Classification: Automated spectral clustering without prior ground truth training sites:
   • K-Means: Partitioning algorithm that iteratively clusters pixels into $K$ spectral clusters by minimizing within-cluster variance.
   • ISODATA (Iterative Self-Organizing Data Analysis): Advanced clustering algorithm allowing split, merge, and deletion of clusters across iterative passes.

Accuracy Assessment: The Confusion (Error) Matrix

A confusion matrix evaluates classification performance against ground truth verification points.

Accuracy Metrics Formulas

• Overall Accuracy ($OA$): $$OA = \frac{\sum_{i=1}^{k} n_{ii}}{N}$$
• Producer's Accuracy ($PA_i$) (Measures Omission Error = $1 - PA$): $$PA_i = \frac{n_{ii}}{n_{+i}}$$
• User's Accuracy ($UA_i$) (Measures Commission Error = $1 - UA$): $$UA_i = \frac{n_{ii}}{n_{i+}}$$
• Cohen's Kappa Coefficient ($\kappa$): $$\kappa = \frac{N \sum_{i=1}^{k} n_{ii} - \sum_{i=1}^{k} (n_{i+} \cdot n_{+i})}{N^2 - \sum_{i=1}^{k} (n_{i+} \cdot n_{+i})}$$

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4. GIS Data Models and Spatial Analysis

GIS integrates spatial locations with descriptive attribute databases.

Vector vs. Raster Data Models

• Vector Data Model: Uses discrete coordinate geometry—Points ($X,Y$), Lines (connected vertices), and Polygons (closed loops)—to represent distinct spatial boundaries. Employs explicit topological relationships (connectivity, adjacency, containment). Preferred for cadastral boundaries and road networks.
• Raster Data Model: Represents space as a continuous regular grid of square cells (pixels), each holding a specific attribute value. Simple data structure ideal for continuous elevation, surface rainfall, and satellite imagery.

Vector Spatial Overlay Operations

• Intersect (AND): Preserves only overlapping spatial features common to both input layers.
• Union (OR): Combines all spatial features and attributes of both input polygon layers.
• Clip: Cuts out input features using the outer polygon boundary of a clipping layer (like a cookie cutter).
• Buffer: Generates a polygon zone around point, line, or polygon features at a specified horizontal distance.

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5. Spatial Interpolation Methods

Spatial interpolation estimates attribute values at unsampled locations using known values from surrounding sample points.

Inverse Distance Weighting (IDW)

IDW is a deterministic interpolation algorithm based on the assumption that closer sample points exert greater influence than points farther away:

$$Z(x_0) = \frac{\sum_{i=1}^{n} \frac{Z_i}{d_i^p}}{\sum_{i=1}^{n} \frac{1}{d_i^p}}$$

Where:

• $Z(x_0) = \text{estimated value at unsampled location } x_0$
• $Z_i = \text{known sample value at point } i$
• $d_i = \text{distance between sample point } i \text{ and location } x_0$
• $p = \text{distance weighting exponent (typically } p = 2\text{)}$

Kriging (Geostatistical Interpolation)

Kriging models spatial autocorrelation using an empirical semivariogram $\gamma(h)$:

$$\gamma(h) = \frac{1}{2 N(h)} \sum_{i=1}^{N(h)} [Z(x_i) - Z(x_i + h)]^2$$

Key semivariogram parameters include:

• Nugget Effect: Variance at zero distance ($h \to 0$), representing measurement noise and microscale variation.
• Sill: The plateau value reached by the semivariogram, representing total variance.
• Range: The threshold distance beyond which spatial correlation ceases.

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6. Map Algebra (Tomlin's Operations)

Map Algebra executes mathematical functions on grid raster layers:

1. Local Operations: Cell-by-cell math across overlapping layers (e.g., computing NDVI raster from NIR and Red rasters).
2. Focal Operations: Cell value derived from immediate spatial neighborhood cells (e.g., $3 \times 3$ low-pass spatial smoothing filter, slope calculation).
3. Zonal Operations: Computes summary statistics (mean, sum) for raster cells within defined polygon zones (e.g., average slope per municipality).
4. Global Operations: Functions computed over the entire raster dataset (e.g., Euclidean distance map).

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7. Step-by-Step Worked Numerical Examples

Example 1: NDVI Calculation & Land Cover Interpretation

Problem: A Sentinel-2 satellite pixel records surface reflectance values of $\text{Red} = 0.06$ (Band 4) and $\text{NIR} = 0.48$ (Band 8). Calculate:

1. The NDVI value of the pixel.
2. Determine the likely land cover type.

Solution:

$$\text{NDVI} = \frac{\text{NIR} - \text{Red}}{\text{NIR} + \text{Red}} = \frac{0.48 - 0.06}{0.48 + 0.06} = \frac{0.42}{0.54} = +0.7778$$

Answer: The NDVI is $+0.78$, indicating dense, healthy green vegetation/forest canopy.

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Example 2: Confusion Matrix Accuracy Assessment

Problem: A land cover classification accuracy assessment yields the following confusion matrix for 200 verification check points:

Calculate:

1. Overall Accuracy ($OA$).
2. Producer's Accuracy ($PA$) and User's Accuracy ($UA$) for the Forest class.
3. Cohen's Kappa Coefficient ($\kappa$).

Solution:

Step 1: Compute Overall Accuracy

$$\text{Correct Samples} = 70 + 55 + 46 = 171$$ $$OA = \frac{171}{200} = 0.8550 = 85.50\%$$

Step 2: Compute Producer's and User's Accuracy for Forest

$$PA_{\text{Forest}} = \frac{n_{11}}{n_{+1}} = \frac{70}{80} = 0.8750 = 87.50\%$$ $$UA_{\text{Forest}} = \frac{n_{11}}{n_{1+}} = \frac{70}{77} = 0.9091 = 90.91\%$$

Step 3: Compute Expected Agreement for Kappa

$$\sum (n_{i+} \cdot n_{+i}) = (77 \times 80) + (65 \times 68) + (58 \times 52) = 6,160 + 4,420 + 3,016 = 13,596$$ $$\kappa = \frac{N \sum n_{ii} - \sum (n_{i+} \cdot n_{+i})}{N^2 - \sum (n_{i+} \cdot n_{+i})} = \frac{(200 \times 171) - 13,596}{200^2 - 13,596}$$ $$\kappa = \frac{34,200 - 13,596}{40,000 - 13,596} = \frac{20,604}{26,404} = 0.7803$$

Answer: The Overall Accuracy is $85.50%$, Forest Producer's Accuracy is $87.50%$, Forest User's Accuracy is $90.91%$, and Kappa is $0.780$.

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Example 3: Inverse Distance Weighting (IDW) Interpolation

Problem: Estimate the ground elevation $Z(x_0)$ at an unsampled location $P_0$ using IDW with power $p = 2$. Three neighboring sample points are measured:

• Point 1: $Z_1 = 120.0\text{ m}$, distance $d_1 = 100\text{ m}$
• Point 2: $Z_2 = 135.0\text{ m}$, distance $d_2 = 150\text{ m}$
• Point 3: $Z_3 = 110.0\text{ m}$, distance $d_3 = 200\text{ m}$

Solution:

Step 1: Compute inverse squared weights ($w_i = 1 / d_i^2$)

$$w_1 = \frac{1}{100^2} = \frac{1}{10,000} = 0.000100$$ $$w_2 = \frac{1}{150^2} = \frac{1}{22,500} = 0.00004444$$ $$w_3 = \frac{1}{200^2} = \frac{1}{40,000} = 0.000025$$ $$\sum w_i = 0.000100 + 0.00004444 + 0.000025 = 0.00016944$$

Step 2: Compute weighted elevation sum

$$\sum (w_i \cdot Z_i) = (0.000100 \times 120.0) + (0.00004444 \times 135.0) + (0.000025 \times 110.0)$$ $$\sum (w_i \cdot Z_i) = 0.01200 + 0.00600 + 0.00275 = 0.02075$$

Step 3: Calculate interpolated elevation $Z(x_0)$

$$Z(x_0) = \frac{0.02075}{0.00016944} = 122.462\text{ m}$$

Answer: The IDW estimated elevation at $P_0$ is $122.46\text{ meters}$.