Some complex variable transformations and exact power comparisons of two-sided tests of equality of two Hermitian covariance matrices

Chu, Shan; Pillai, K. C. S.

doi:10.1016/0378-3758(80)90012-9

Cited by 3 publications

(2 citation statements)

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“…Roy (1953Roy ( , 1957 initiated an equality test of two real symmetric covariance matrices following the union-intersection principle. This test was then studied by Chu and Pillai (1980) for the equality of two Hermitian covariance matrices.…”

Section: Roy's Largest Eigenvalue-based Edge Detectormentioning

confidence: 99%

“…Let Z x and Z y be two independent complex Wishart matrices distributed as (Krishnaiah, 1976, p. 7). Finding the eigenvalues of is identical to solving the following determinantal equation for a Hermitian pencil (Lewis, 1991;Rao and Rao, 1998;Hartfiel, 2001): , the largest eigenvalue can be used as test statistic (Chu and Pillai, 1980). The cumulative distribution function of the largest eigenvalue under the alternative hypothesis was derived by Sugiyama (1972, p. 91) and given in terms of zonal polynomials as follows:…”

Section: Roy's Largest Eigenvalue-based Edge Detectormentioning

confidence: 99%

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Polarimetric synthetic aperture radar image processing for land cover classification

Lee¹

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This thesis presents the processing design and development towards an improved land cover classification of multi-look POLSAR data. In this context, three related processing aspects, namely edge detection, speckle suppression and region-based segmentation, were investigated. To detect edges in speckle-corrupted POLSAR data, two new edge detectors, which are based separately on the Roy's largest eigenvalue and trace ratio, were proposed. Their capabilities were compared with three other edge detectors, which use the likelihood ratio, Dowson-Landau metric and Euclidean distance, respectively. Applied to nine-look NASA/JPL POLSAR C-and L-band data, both the proposed edge detectors exhibited their satisfactory performance in detecting edges while coping with speckle noise disturbance. For the speckle suppression, a novel spatially adaptive speckle filter was developed, which aims at preserving image features during filtering process. In the experiments, the proposed filter showed its good performance in speckle removal, image feature retention and radiometric preservation. Comparisons with the boxcar, Lee-refined and annealing filters were carried out. In the area of region-based segmentation, an existing hybrid segmentation algorithm was extended for multi-look POLSAR data. The capabilities of the extended algorithm were examined and benchmarked against the HSWO algorithm. From the results, it was noticed that the segmentation outputs from both the algorithms relied strongly on the user-defined region number, which is employed as the termination rule. Finally, the classification of NASA/JPL POLSAR data over a selected area of Kuala Muda in Peninsular Malaysia was carried out based separately on scattering mechanisms and statistical distribution. For the scattering property-based unsupervised classification, three different schemes were examined, namely van Zyl's scattering classification, Freeman-Durden scattering model and Cloude-Pottier target decomposition. The derived scattering mechanisms of different land cover classes were studied. In the supervised complex Wishart classification, the obtained overall accuracies were 63% and 67% for both the C-and L-band, respectively. An improved accuracy of 75% was attained by using the dual-frequency input. Furthermore, comparison between per-pixel and per-segment classification approaches was conducted, where the per-segment approach was expectedly found to improve the classification accuracy. i ACKNOWLEDGEMENT Acknowledgement School of Computer Engineering and Graduate Studies Office Thanks for giving me the opportunity to pursue my Ph.D. study at the NTU. Moreover, without the provided scholarship, I could not proceed with my study. The monthly stipend and the tuition fee are very important and meaningful. Thank you! Dr Timo Rolf Bretschneider TABLE OF CONTENTS xiv 7.4 Classification Based on Complex Wishart Distribution 7.4.1 Assessment of Classification Accuracies 7.4.2 Effect of Radar Frequencies 7.4.3 Comparison between Per-pixel and Per-segment Classification Appro...

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Section: Roy's Largest Eigenvalue-based Edge Detectormentioning

confidence: 99%