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Error Characterization of the Alpha Residuals Emissivity Extraction Technique Michael C. Baglivio, Dr. John Schott, Scott Brown Center for Imaging Science Rochester Institute of Technology

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Overview Hypothesis What’s the significance of this study? What is an Alpha Residual? –How does it work? Data sets Results Conclusion

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Hypothesis The error associated with Wein’s approximation in the Alpha Residuals emissivity extraction technique can be characterized as a function of temperature and applied to real imagery.

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Significance Algorithm assigns emissivity to each pixel of image Knowledge of spectral characteristics aids in material identification –pollution control –military vehicles –agriculture

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What is an Alpha Residual? yields approximation to shape of emissivity spectrum one per spectral channel equations derived from Wein’s Approximation which is believed to be source of error

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Alpha Residual from real data XL XL XX iii ii iii ln

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Alpha Residual from library data Now take average of X i spectrum to compute: C iiiiiii ln 1 5 X XX iii Chc C ch k 1 2 2 2 and C T 2

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How does it work? Alpha Residuals computed for each channel of real input data and library data iterative process that operates on 1 pixel –computes Alpha Residual for all library emissivity spectra –each library Alpha Residual spectrum then compared to real input Alpha Residual spectrum –a pixels emissivity spectrum assigned to library emissivity which yields spectrum most similar to real input alpha residual

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Data Sets Frequency –Simulated emissivity curves generated cosine waves of varying frequency Sampling and spectral response –different numbers of sample points per channel varied along with width of gaussian spectral response curve

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Simulated Input Emissivity

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Error of Simulated Emissivities

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Analysis Low frequency emissivity spectra produce a slightly greater error relative to mid and high frequency spectra. Considering the change is over such a small region however, the difference is insignificant and frequency effects are negligible.

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Real Input Emissivities

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Error of Real Input

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Average Error for Each Material

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Spectral Error Averaged Over Temperature

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Analysis The difference between the material with the greatest error and the least error is 0.000328. Again, the error from material to material is negligible, telling us the algorithm will provide acceptable results regardless of what we’re looking at. Error is independent of emissivity magnitude.

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Relationship of Samples Points to Response Width Relative width of spectral response function of the number of sample points input by user 1 2 3 4 5 Sample points1 sample points: 1 response width: 3 sample points: 5 response width: 7

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Effect of Sample Points on Total Error

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Effect of Response Width

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Comparison of the Two Effects

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Analysis The three previous graphs show us that error has a direct relationship with response width and an inverse relationship with sample point. If you take more sample points, the error will be less but your making a sacrifice with respect to run-time.

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Spectral Difference of Alpha Residuals

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Analysis By adjusting the alpha residual spectrum from the real input by the inverse of the values on the previous graph, the results yielded would be more accurate.

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Conclusion error reduced by 0.5% high spectral resolution sensors increase accuracy general error correction can be applied to any image due to the negligible amount of difference in error between materials

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THE END Any Questions?

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