1. Hourglass Processing Approach (AIG)
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Hourglass Processing Approach (AIG)
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2. The developers of the ENVI tool at AIG suggest an approach they describe as the Hourglass. The name comes from the shape of the process flow diagram shown in Figure 1 indicating a dimensionality reduction to an “optimal” set of end members and then a mapping over the entire image using the end members and a background suppressed matched filter they refer to as the mixture tuned matched filter.
Comment: This process is assembled from notes taken at various presentations. I haven’t seen a document on this though I suspect it is probably documented in the AIG-ENVI training classes.
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3. Step 1 Convert radiance data to reflectance (ACORN 4)
Step 2 Polish the reflectance data
A correction vector is generated from the ratio of truth to inverted
reflectance values i.e.
(1)
Step 1 Convert radiance data to reflectance (ACORN 4)
Step 2 Polish the reflectance data
I haven’t seen this step included in the Hourglass process though it is a logical step and may be considered part of the atmospheric correction.
This step removes spectral noise structure from the reflectance data usually by comparing an inverted spectrum to a “truth” spectrum for as bright and flat a target as possible. A correction vector is generated from the ratio of truth to inverted reflectance values i.e.
(1)
where ci is the correction factor for the ith band,ri is the truth reflectance in the ith band, ri’ is the inverted reflectance for the truth target in the ith band. The correction factor is used on all pixels to generate polished reflectance values according to:
(2)
The correction factor is used on all pixels to generate polished
reflectance values according to:
(2)
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4. Step 3 Apply the Minimum Noise Fraction (MNF) transform
Step 4 Apply Pixel Purity Index to transformed data
Step 5 N-D Visualizer
Step 3 Apply the Minimum Noise Fraction (MNF) transform
This whitens the noise and then reduces the dimensionality (see discussion in these notes) by truncating the transform bands with low eigen values in the transform.
Step 4 Apply Pixel Purity Index to transformed data
This generates a large number of candidate end member pixels.
Step 5 N-D Visualizer
This is an interactive step where candidate end members can be selected and if desired, suppressed by projection onto each other (i.e. onto the subspace perpendicular to the difference).
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5. Step 6 The output from N-D Visualizer is the selection of a set of
end members to be mapped or suppressed depending on the
application.
Step7 Apply Mixture Tuned Matched Filter (MTMF)
Step 6 The output from N-D Visualizer is the selection of a set of end members to be mapped or suppressed depending on the application.
Step7 Apply Mixture Tuned Matched Filter (MTMF)
Note: This section is from a personal conversation with Dr. Joe Boardman of AIG. I haven’t located a technical description of the (MTMF) algorithm.
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6. This algorithm is designed to map each end member to produce a score (similar to abundance) and infeasibility (this metric takes into account the variability in the data and is designed to suppress false alarms). The processing is done on the MNF transformed data (to reduce the processing), which is further transformed onto a subspace that nulls the background (while not specified this can be done with the subspace projection described by Harsanyi (see discussion in these notes)) using all end members except the one of interest. This can also be done by generating a set of basis vectors to be nulled using the covariance (or correlation matrix) and singular value decomposition. Note this approach makes more sense if we are seeking to find a low abundance target and the entire scene is viewed as background. After nulling the background, the matched filter is achieved by projecting each “nulled” image pixel onto the subspace orthogonal to the plane containing the target and the nulled background. Targets should have high values in this projection since they will be far from the nulled background (cf. Figure 2). On the other hand, anomalous pixels (not suppressed but not target like) may also have high scores at this point, since they are not effectively suppressed by this process. This can be mapped using an infeasibility map achieved based on the variability of the background data when processed through the background suppression and target matching process.
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7. Figure 1 Atmospheric Correction (ACORN 4)
AIG Hour Glass Procedure using ENVI Software
Atmospheric Correction (ACORN 4)
Reflectance Correction - Polishing
Minimum Noise Fraction (MNF)
Pixel Purity Index (PPI)
This defines the background variability (cf. Figure 2). Similarly, the known target vectors are projected through the same operations and their variability computed (cf. Figure 2). Each pixel can then be assigned a score based on its distance from the background in the direction of the target mean and an infeasibility based on where it falls in the hypercone described by the variability in target and background data. As illustrated in Figure 2, high scores must be close to the target background line (low sigma = low infeasibility) to be considered targets. On the other hand, lower scores need not to be so close to achieve low infeasibilities because of the high variability in backgrounds close to the null space.
ND Visualizer
End Member Extraction
Mixture Tuned Matched Filter
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8. Figure 2
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