Cindy Daniell,
Abhijit Mahalanobis,
and Rod Goodman
C. Daniell (daniell@hrl.com) is with HRL Laboratories, LLC, 3011 Malibu Canyon Road, RL69, Malibu, California 90265.
A. Mahalanobis is with Lockheed Martin, 5600 Sandlake Road, MS 450, Orlando, Florida 32819. R. Goodman is with Cyrano Sciences, 73 North Vinedo Avenue, Pasadena, California 91107.
Cindy Daniell, Abhijit Mahalanobis, and Rod Goodman, "Object recognition in subband transform-compressed images by use of correlation filters," Appl. Opt. 42, 6474-6487 (2003)
We introduce subband correlation filters (SCFs) as a solution to the problem of object recognition at multiple resolution levels in quantized transformed imagery. The approach synthesizes correlation filters that operate directly on subband coefficients rather than on image data. We explore two techniques to accomplish the reduced-resolution recognition: (1) training the correlation filters to incorporate downsampling tolerance and (2) adaptation of the subband decomposition filters to accommodate the reduced resolutions. For compression ratios of 20:1, SCFs demonstrate recognition performance of at least 90%, 85%, and 75%, respectively, on 2-, 4-, and 8-ft-resolution synthetic aperture radar data.
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Performance Metrics of the Baseline and Shift-Tolerant QMFa
Measure
Baseline QMF
Shift-Tolerant QMF
PSNR
105 dB
67 dB
MSE
2× 10-6
1× 10-2
Shift-sensitivity metric
317
239
Compression metric
4.9
2.4
PSNR and MSE are reported from a three-level decomposition of one of the preprocessed BMP training image. The filter has better performance when the shift-tolerant metric is smaller and when the compression metric is larger.
We show the probability of correct classification, error, and rejection for both the original training data and the same set after a diagonal shift of one pixel has been applied to all the images. Equivalent results between the two data sets indicate good downsampling tolerance.
Reconstruction measures are due only to the QMF of the system. Thus systems with the same QMF achieve the same performance. Both PSNR and MSE are given from the reconstruction of one of the BMP test images.
Table 4
Multiresolution Performance of Baseline and Shift-Tolerant QMFa
Measure
Baseline QMF-Shift Training
Shift-Tolerant QMF-Shift Training
Level one Pc
96%
93%
Level two Pc
85%
64%
Level three Pc
75%
54%
PSNR
105 dB
67 dB
MSE
2 × 10-6
1 × 10-2
One of the BMP test images provides the PSNR and MSE values given above.
Table 5
Subbands Dropped at Low Bit Rates
Approximate Rate (bpp)
Subbands Dropped
1
On level one: HL, LH, HH
On level two: HH
On level three: HH
0.5
On level one: HL, LH, HH
On level two: HH
On level three: HH
0.25
On level one: HL, LH, HH
On level two: HL, LH, HH
On level three: LH, HH
0.125
On level one: HL, LH, HH
On level two: HL, LH, HH
On level three: HL, LH, HH
Table 6
Multiresolution Performance Summary of SCF Systema
Subband Level
Probability of Correct Classification
Level one
96.2%, R ≤ 2:1
(2-ft resolution)
89.9%, R ≤ 20:1
Level two
84.8%, R ≤ 8:1
(4-ft resolution)
82.3%, R ≤ 26:1
Level three
74.7%, R ≤ 8:1
(8-ft resolution)
64.6%, R ≤ 32:1
The table reports that the SCF achieves 96.2% correct classification at compression ratios, R, equal to or less than 2:1 on 2-ft-resolution data; likewise, the system results in 89.9% accuracy at compression ratios equal to or less than 20:1 on the same data. The remaining data are read in an analogous manner.
Tables (6)
Table 1
Performance Metrics of the Baseline and Shift-Tolerant QMFa
Measure
Baseline QMF
Shift-Tolerant QMF
PSNR
105 dB
67 dB
MSE
2× 10-6
1× 10-2
Shift-sensitivity metric
317
239
Compression metric
4.9
2.4
PSNR and MSE are reported from a three-level decomposition of one of the preprocessed BMP training image. The filter has better performance when the shift-tolerant metric is smaller and when the compression metric is larger.
We show the probability of correct classification, error, and rejection for both the original training data and the same set after a diagonal shift of one pixel has been applied to all the images. Equivalent results between the two data sets indicate good downsampling tolerance.
Reconstruction measures are due only to the QMF of the system. Thus systems with the same QMF achieve the same performance. Both PSNR and MSE are given from the reconstruction of one of the BMP test images.
Table 4
Multiresolution Performance of Baseline and Shift-Tolerant QMFa
Measure
Baseline QMF-Shift Training
Shift-Tolerant QMF-Shift Training
Level one Pc
96%
93%
Level two Pc
85%
64%
Level three Pc
75%
54%
PSNR
105 dB
67 dB
MSE
2 × 10-6
1 × 10-2
One of the BMP test images provides the PSNR and MSE values given above.
Table 5
Subbands Dropped at Low Bit Rates
Approximate Rate (bpp)
Subbands Dropped
1
On level one: HL, LH, HH
On level two: HH
On level three: HH
0.5
On level one: HL, LH, HH
On level two: HH
On level three: HH
0.25
On level one: HL, LH, HH
On level two: HL, LH, HH
On level three: LH, HH
0.125
On level one: HL, LH, HH
On level two: HL, LH, HH
On level three: HL, LH, HH
Table 6
Multiresolution Performance Summary of SCF Systema
Subband Level
Probability of Correct Classification
Level one
96.2%, R ≤ 2:1
(2-ft resolution)
89.9%, R ≤ 20:1
Level two
84.8%, R ≤ 8:1
(4-ft resolution)
82.3%, R ≤ 26:1
Level three
74.7%, R ≤ 8:1
(8-ft resolution)
64.6%, R ≤ 32:1
The table reports that the SCF achieves 96.2% correct classification at compression ratios, R, equal to or less than 2:1 on 2-ft-resolution data; likewise, the system results in 89.9% accuracy at compression ratios equal to or less than 20:1 on the same data. The remaining data are read in an analogous manner.