Date of download: 7/2/2016 Copyright © 2016 SPIE. All rights reserved. Illustration of quantities in Eq. : Ath is the ratio of the striped area under the ROC curve (numerator) to the maximum area for perfect detection (denominator). A is the area under the ROC curve, and th is the false alarm rate threshold. Perfect detection would be characterized by a step function where Pd=1 for all Pfa. Figure Legend: From: Analysis of false alarm distributions in the development and evaluation of hyperspectral point target detection algorithms Opt. Eng. 2007;46(7): doi: /

Date of download: 7/2/2016 Copyright © 2016 SPIE. All rights reserved. Point target detection algorithm evaluation functional flow. Approach is effective in characterizing algorithm performance for multiple target types and background scenarios. Figure Legend: From: Analysis of false alarm distributions in the development and evaluation of hyperspectral point target detection algorithms Opt. Eng. 2007;46(7): doi: /

Date of download: 7/2/2016 Copyright © 2016 SPIE. All rights reserved. (a) One band taken from the Vis/NIR data cube used in our algorithm analysis. The image was taken at Hanscom Air Force Base. The size of the cube is 161 by 181 pixels by 74 bands. (b) One band of the MWIR data cube used in our algorithm analysis. The image was taken at Hanscom Air Force Base. The size of the cube is 185 by 185 pixels by 74 bands. (c) One band of the HYDICE data cube used in our algorithm analysis. The image was taken over the CART/ARM Site Lamont. The size of the cube is 187 by 159 pixels by 210 bands. Figure Legend: From: Analysis of false alarm distributions in the development and evaluation of hyperspectral point target detection algorithms Opt. Eng. 2007;46(7): doi: /

Date of download: 7/2/2016 Copyright © 2016 SPIE. All rights reserved. (a) One band of the Vis/NIR data cube with local spatial mean removed. For each 3×3 mask in the original image, the average spectrum of the outside 8 pixels is subtracted from the center pixel. (b) Histogram of (a). (c) Output of matched filter: tTΦ−1(x−m), where t is the target signature, x is the original image pixel signature, m is the average background signature of the surrounding pixels, and Φ−1 is the inverse covariance of the original hypercube [as shown in Fig. ] with local m removed [as shown in (a)]. (d) Histogram of (c). (e) Strongest 0.1% of pixels from the matched filter output as shown in (c). (f) Strongest 1% of pixels from the matched filter output as shown in (c). (g) Strongest 10% of pixels from the matched filter output as shown in (c). Figure Legend: From: Analysis of false alarm distributions in the development and evaluation of hyperspectral point target detection algorithms Opt. Eng. 2007;46(7): doi: /

Date of download: 7/2/2016 Copyright © 2016 SPIE. All rights reserved. (a) One band of the Vis/NIR data cube with spatial Max1 removed. For each 3×3 mask in the original image, the maximum value of the outside 8 pixels is subtracted from the center pixel. (b) Histogram of (a). (c) Output of matched filter: tTΦ−1(x−m), where t is the target signature, x is the original image pixel signature, m is the maximum value of the surrounding 8 pixels, and Φ−1 is the inverse covariance of the original hypercube [as shown in Fig. (a)] with local maximum removed [as shown in (a)]. (d) Histogram of (c). (e) Strongest 0.1% of pixels from the matched filter output as shown in (c). (f) Strongest 1% of pixels from the matched filter output as shown in (c). (g) Strongest 10% of pixels from the matched filter output as shown in (c). Figure Legend: From: Analysis of false alarm distributions in the development and evaluation of hyperspectral point target detection algorithms Opt. Eng. 2007;46(7): doi: /

Date of download: 7/2/2016 Copyright © 2016 SPIE. All rights reserved. (a) Normalized area under the ROC curve at the 0.1% false alarm rate as a function of target strength for different background estimation techniques. The Max1 filter outperforms all the other filters for the most difficult false alarms. (b) As in (a) at the 1% false alarm. At this false alarm rate, the Max1 filter and the directional mean filter outperform the mean and median filters because the former minimize false alarms on edge pixels. (c) As in (a) at the 10% false alarm rate. Here the Max1 filter has difficulty detecting targets near bright objects and performs worse than the rest. Figure Legend: From: Analysis of false alarm distributions in the development and evaluation of hyperspectral point target detection algorithms Opt. Eng. 2007;46(7): doi: /

Date of download: 7/2/2016 Copyright © 2016 SPIE. All rights reserved. (a) Sample 3×3 region centered on the test pixel. (b) Numeric example of sample 3×3 region centered on the test pixel. In this example, the directional mean filter estimates the background of the target pixel better than the mean filter. Figure Legend: From: Analysis of false alarm distributions in the development and evaluation of hyperspectral point target detection algorithms Opt. Eng. 2007;46(7): doi: /

Date of download: 7/2/2016 Copyright © 2016 SPIE. All rights reserved. (a) Normalized area under the ROC curve at the 0.1% false alarm rate as a function of the k value for multiple target strengths. The maximum of each curve represents the optimum k value for each target strength. (b) As in (a) at the 1% false alarm rate. (c) As in (a) at the 10% false alarm rate. (d) Optimum k value as a function of target strength for false alarm rates of 0.1%, 1%, and 10%. Figure Legend: From: Analysis of false alarm distributions in the development and evaluation of hyperspectral point target detection algorithms Opt. Eng. 2007;46(7): doi: /

Date of download: 7/2/2016 Copyright © 2016 SPIE. All rights reserved. Normalized area under the ROC curve as a function of target strength for each false alarm rate. Note that division by SD+k∙Avg(SD) showed improvement for all target strengths and false alarm rates. Figure Legend: From: Analysis of false alarm distributions in the development and evaluation of hyperspectral point target detection algorithms Opt. Eng. 2007;46(7): doi: /