Spectral Feature Extraction - Cornell University

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CEE 615: Digital Image Processing 8 W. Philpot, Cornell University Spectral Differencing (subtraction) Subtracting gray values from different spectral bands. k' = a 0 + a 1 k 1 + a 2 k 2 • The vector, a = (a 1 ,a 2 ), defines the direction of changing gray value: a 2 = m a 1 • The coefficients may be defined by choosing (k 11 , k 21 ) => k min = minimum gray value in the new image, and (k 12 , k 22 ) => k max = maximum gray value in the new image. The coefficients are given by: a 2 = m a 1 where: m = slope of a line parallel to a a 1 = k max − k min ( k − k ) + m( k − k ) 12 11 22 21 a 0 = k min – a 1 (k 11 + m k 21 ) k min = a 0 + a 1 k 11 + a 2 k 21 k max = a 0 + a 1 k 12 + a 2 k 22 • Spectral differencing is another partitioning of the measurement space. • The space is partitioned into plane-parallel regions which are perpendicular to the direction of the coefficient vector a = (a 1 , a 2 ). • Color information extraction will be optimized if the coefficient vector, is perpendicular to the direction of highest correlation. Band 1 Band 2 Band 2 – Band 1 • Pixels that are bright in the difference image are brighter in band 2. • Pixels that are dark in the difference image are brighter in band 1. • Gray indicates little or no color change.
CEE 615: Digital Image Processing 9 W. Philpot, Cornell University Image ratioing (division) • Ratioing tends to extract information that is uncorrelated from image to image. • Ideally, ratioing adjusts for differences in intensity while emphasizing color differences. • The output image gray value, k o , is given by: k 0 = ak 1 /k 2 where: k 1 , k 2 = gray value for image 1 and image 2, respectively a = coefficient • Ratioing partitions measurement space into radial segments. • A simple ratio will partition the space into unequal radial segments which emanate from an origin at (0,0). • The implicit assumption is that (0,0) represents black (zero intensity) and that distance from (0,0) corresponds to an increase in intensity. Consider the assumption that: - (0,0) represents black (zero intensity) and that - distance from (0,0) corresponds to an increase in intensity. • In remote sensing imagery this is frequently not the case, largely due to atmospheric effects on the observed radiation. The true zero intensity point is usually offset in measurement space. • It would also be more effective to make the partitioning uniform A reasonable scaling is given by: ⎡ ⎛ ⎞ ⎤ min ⎥ ⎣ ⎝ ⎠ ⎦ n − n f 0 −1 k − b 2 2 k ' = tan −θ ( θ −θ ) ⎢ ⎜ ⎟ k −b max min 1 1 where: q min = minimum angle q max = maximum angle n f = maximum gray value in output image (usually 255) n 0 = minimum gray value in output image (usually 0) b 1 , b 0 = offsets of the zero-intensity point in measurement space.
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Spectral Feature Extraction - Cornell University

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