Enhanced Image Analysis using Model-Based Algorithms for Optimal Model Matching

1. Chapter 23 Model Based Algorithms

3. Figure 1 Model Matching Input Parameters Observed Values • e.g. • pressure depth, column, water vapor, and aerosol amount • concentration of chlorophyll, suspended materials and dissolved organics in water column Physics Based Model e.g. spectral radiance vector, spectral reflectance vector Adjust Model Inputs To Optimize Match

4. Figure 2 Model Matching Concept Observation (O) Model (m) (l) (l) (l) Observed signal Initial model input Optimization function Adjust model input parameters Match model with observation Generate error metrics Re-run model to predict model estimates of observed signal m(λ) Note the number of comparison points must equal or exceed the number of inputs to the model

5. Figure 3 Enhanced Image Analysis Using Physics Based Models and Multi-parameter Observations Atmospheric Model Class A Phenomenology Model Model Match Model Matching • Class Condition/ Quantification • e.g. • water quality parameters • vegetation stress • soil moisture Raw Image Data Preprocessing Atmospheric Correction/ Quantification Class B Phenomenology Model Model Matching Land Cover Classes Class C Phenomenology Model ¼ ¼

7. Figure 4 Simple Empirical Regression Approach ground truth measurements corresponding to observed values generate least square regression models • a0, a1, b0, b1… are the regression coefficients • e1, e2… are the errors associated with the regression model • this approach typically works well only if the ground measurements e.g. i1 and i2 are individually highly correlated with some subset of the entries in the observed vector <m> <m> Simple model based regression approach: generate m estimates of observed values (Ô) using m sets of inputs (Î) to the physics based model generate least square regression models <m> <m> Physics Based Model

8. Figure 5 Higher Order Statistical Tools (e.g. canonical correlation regression analysis) generate multi-parameter statistical model f( ) relating predicted observation vectors Ô to model input parameter vectors Î <m> <m> Physics Based Model • Note this approach is required for the common situation where the observed value (e.g. spectral radiance) is a function of multiple unconstrained model input parameters (e.g. target temperature, atmospheric temperature profile…).

9. Figure 6 Use of Physics Based Models for Training Algorithms <m> Class A e.g. trees Samples of Training Class Database of measurements of model inputs that describes Class A Parametric or Non-parametric Physics Based Model CLASSIFIER Classification procedures for any vector of the form <m> Class B e.g. road Database of measurements of model inputs that describes Class B Physics Based Model <m> <m>

10. Figure 7 Exploitation Using Image Based Models Many possible manifestations of scene Constrain imaging variables as much as possible (altitude, target, background...) Construct nominal scene Modify scene descriptors or observation parameters to simulate the range of possible scenes Estimate mean & variability of unconstrained variables Construct training data describing targets,backgrounds, interactions Truth maps Train Algorithm (spatial, spectral) Compare Observed image data Trained Algorithm Improved information products Digital Imaging and Remote Sensing Laboratory