Abstract

Indirect ophthalmoscopy (IO) is the standard of care for evaluation of the neonatal retina. When recorded on video from a head-mounted camera, IO images have low quality and narrow Field of View (FOV). We present an image fusion methodology for converting a video IO recording into a single, high quality, wide-FOV mosaic that seamlessly blends the best frames in the video. To this end, we have developed fast and robust algorithms for automatic evaluation of video quality, artifact detection and removal, vessel mapping, registration, and multi-frame image fusion. Our experiments show the effectiveness of the proposed methods.

© 2011 OSA

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2010

2009

M. D. Robinson, S. Farsiu, and P. Milanfar, “Optimal registation of aliased images using variable projection with applications to super-resolution,” Comput. J.52, 31–42 (2009).
[CrossRef]

2008

C. Wilson, K. Cocker, M. Moseley, C. Paterson, S. Clay, W. Schulenburg, M. Mills, A. Ells, K. Parker, G. Quinn, A. Fielder, and J. Ng, “Computerized analysis of retinal vessel width and tortuosity in premature infants,” Invest. Ophthalmol. & Visual Sci.49, 3577–3585 (2008).
[CrossRef] [PubMed]

D. K. Wallace, G. E. Quinn, S. F. Freedman, and M. F. Chiang, “Agreement among pediatric ophthalmologists in diagnosing plus and pre-plus disease in retinopathy of prematurity,” J. Am. Assoc. Pediatric Opthalmol. Strabismus12, 352–356 (2008).
[CrossRef]

S. Ahmad, D. Wallace, S. Freedman, and Z. Zhao, “Computer-assisted assessment of plus disease in retinopathy of prematurity using video indirect ophthalmoscopy images,” Retina28, 1458–1462 (2008).
[CrossRef] [PubMed]

2007

D. Wallace, Z. Zhao, and S. Freedman, “A pilot study using” ROPtool” to quantify plus disease in retinopathy of prematurity.” J. Am. Assoc. Pediatric Opthalmol. Strabismus11, 381–387 (2007).
[CrossRef]

K. Simonson, S. Drescher, and F. Tanner, “A statistics-based approach to binary image registration with uncertainty analysis,” IEEE Trans. Pattern Anal. Machine Intell.29, 112–125 (2007).
[CrossRef]

M. Daszykowski, K. Kaczmarek, Y. Vander Heyden, and B. Walczak, “Robust statistics in data analysis–a review:: basic concepts,” Chemometrics Intell. Lab. Syst.85, 203–219 (2007).
[CrossRef]

2006

A. Wong, W. Bishop, and J. Orchard, “Efficient multi-modal least-squares alignment of medical images using quasi-orientation maps,” in Proceedings of International Conference on Image Processing, Computer Vision, and Pattern Recognition (WORLDCOMP, 2006), pp. 74–80.
[PubMed]

R. Szeliski, “Image alignment and stitching: A tutorial,” Found. Trends Comput. Graphics Vision2, 1–104 (2006).
[CrossRef]

J. Soares, J. Leandro, R. Cesar, H. Jelinek, and M. Cree, “Retinal vessel segmentation using the 2-D Gabor wavelet and supervised classification,” IEEE Trans. Med. Imaging25, 1214–1222 (2006).
[CrossRef] [PubMed]

W. Tasman, A. Patz, J. McNamara, R. Kaiser, M. Trese, and B. Smith, “Retinopathy of prematurity: the life of a lifetime disease,” Am. J. Ophthalmol.141, 167–174 (2006).
[CrossRef] [PubMed]

D. Tschumperlé and B. Besserer, “High quality deinterlacing using inpainting and shutter-model directed temporal interpolation,” Comput. Vision Graphics32, 301–307 (2006).
[CrossRef]

2005

R. Gelman, M. Martinez-Perez, D. Vanderveen, A. Moskowitz, and A. Fulton, “Diagnosis of plus disease in retinopathy of prematurity using Retinal Image multiScale Analysis,” Invest. Ophthalmol. & Visual Sci.46, 4734–4738 (2005).
[CrossRef] [PubMed]

2004

J. Staal, M. Abràmoff, M. Niemeijer, M. Viergever, and B. van Ginneken, “Ridge-based vessel segmentation in color images of the retina,” IEEE Trans. Med. Imaging23, 501–509 (2004).
[CrossRef] [PubMed]

C. Kirbas and F. Quek, “A review of vessel extraction techniques and algorithms,” ACM Comput. Surv.36, 81–121 (2004).
[CrossRef]

2003

B. Zitova and J. Flusser, “Image registration methods: a survey,” Image Vision Comput.21, 977–1000 (2003).
[CrossRef]

C. Stewart, C. Tsai, and B. Roysam, “The dual-bootstrap iterative closest point algorithm with application to retinal image registration,” IEEE Trans. Med. Imaging22, 1379–1394 (2003).
[CrossRef] [PubMed]

D. Tsai and C. Chou, “A fast focus measure for video display inspection,” Machine Vision Appl.14, 192–196 (2003).

S. Lin, Y. Chang, and L. Chen, “Motion adaptive interpolation with horizontal motion detection for deinterlacing,” IEEE Trans. Consumer Electron.49, 1256–1265 (2003).
[CrossRef]

2002

J. Kautsky, J. Flusser, and B. Zitová, “A new wavelet-based measure of image focus,” Pattern Recognition Lett.23, 1785–1794 (2002).
[CrossRef]

2001

H. Cheng, X. Jiang, Y. Sun, and J. Wang, “Color image segmentation: advances and prospects,” Pattern Recognition34, 2259–2281 (2001).
[CrossRef]

2000

Y. Zhang, Y. Zhang, and C. Wen, “A new focus measure method using moments,” Image Vision Comput.18, 959–965 (2000).
[CrossRef]

1999

S. Fox, R. Silver, E. Kornegay, and M. Dagenais, “Focus and edge detection algorithms and their relevance to the development of an optical overlay calibration standard,” Proc. SPIE3677, 95–106 (1999).
[CrossRef]

1998

M. Subbarao and J. Tyan, “Selecting the optimal focus measure for autofocusing and depth-from-focus,” IEEE Trans. Pattern Anal. Machine Intell.20, 864–870 (1998).
[CrossRef]

J. Maintz and M. Viergever, “A survey of medical image registration,” Med. Image Anal.2, 1–36 (1998).
[CrossRef]

1996

B. Srinivasa and B. Chatterji, “An FFT-based technique for translation, rotation, and scale-invariant image registration,” IEEE Trans. Image Process.5, 1266–1271 (1996).
[CrossRef]

1992

H. Van der Vorst, “Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems,” SIAM J. Sci. Statist. Comput.13, 631–644 (1992).
[CrossRef]

L. Brown, “A survey of image registration techniques,” ACM Comput. Surv.24, 325–376 (1992).
[CrossRef]

P. Besl and N. McKay, “A method for registration of 3-d shapes,” IEEE Trans. Pattern Anal. Machine Intell.14, 239–256 (1992).
[CrossRef]

1990

1987

1983

P. Burt and E. Adelson, “A multiresolution spline with application to image mosaics,” ACM Trans. Graphics2, 217–236 (1983).
[CrossRef]

1976

R. Fletcher, “Conjugate gradient methods for indefinite systems,” Numerical Anal.506, 73–89 (1976).
[CrossRef]

Abràmoff, M.

J. Staal, M. Abràmoff, M. Niemeijer, M. Viergever, and B. van Ginneken, “Ridge-based vessel segmentation in color images of the retina,” IEEE Trans. Med. Imaging23, 501–509 (2004).
[CrossRef] [PubMed]

Acharya, T.

T. Acharya and A. Ray, Image Processing: Principles and Applications (Wiley-Interscience, 2005).
[CrossRef]

Adelson, E.

P. Burt and E. Adelson, “A multiresolution spline with application to image mosaics,” ACM Trans. Graphics2, 217–236 (1983).
[CrossRef]

Ahmad, S.

S. Ahmad, D. Wallace, S. Freedman, and Z. Zhao, “Computer-assisted assessment of plus disease in retinopathy of prematurity using video indirect ophthalmoscopy images,” Retina28, 1458–1462 (2008).
[CrossRef] [PubMed]

Besl, P.

P. Besl and N. McKay, “A method for registration of 3-d shapes,” IEEE Trans. Pattern Anal. Machine Intell.14, 239–256 (1992).
[CrossRef]

Besserer, B.

D. Tschumperlé and B. Besserer, “High quality deinterlacing using inpainting and shutter-model directed temporal interpolation,” Comput. Vision Graphics32, 301–307 (2006).
[CrossRef]

Bhattacharya, P.

Q. Li, J. You, L. Zhang, and P. Bhattacharya, “Automated retinal vessel segmentation using Gabor filters and scale multiplication,” in Proceedings International Conference on Image Processing, Computer Vision, and Pattern Recognition (WORLDCOMP, 2006), pp. 3521–3527.
[PubMed]

Bishop, W.

A. Wong, W. Bishop, and J. Orchard, “Efficient multi-modal least-squares alignment of medical images using quasi-orientation maps,” in Proceedings of International Conference on Image Processing, Computer Vision, and Pattern Recognition (WORLDCOMP, 2006), pp. 74–80.
[PubMed]

Brown, L.

L. Brown, “A survey of image registration techniques,” ACM Comput. Surv.24, 325–376 (1992).
[CrossRef]

Burt, P.

P. Burt and E. Adelson, “A multiresolution spline with application to image mosaics,” ACM Trans. Graphics2, 217–236 (1983).
[CrossRef]

Candes, E.

J. Starck, F. Murtagh, E. Candes, and D. Donoho, “Gray and color image contrast enhancement by the curvelet transform,” IEEE Trans. Image Processing12, 706–717 (2003).
[CrossRef]

Cesar, R.

J. Soares, J. Leandro, R. Cesar, H. Jelinek, and M. Cree, “Retinal vessel segmentation using the 2-D Gabor wavelet and supervised classification,” IEEE Trans. Med. Imaging25, 1214–1222 (2006).
[CrossRef] [PubMed]

Chang, Y.

S. Lin, Y. Chang, and L. Chen, “Motion adaptive interpolation with horizontal motion detection for deinterlacing,” IEEE Trans. Consumer Electron.49, 1256–1265 (2003).
[CrossRef]

Chatterjee, S.

S. Chaudhuri, S. Chatterjee, N. Katz, M. Nelson, and M. Goldbaum, “Detection of blood vessels in retinal images using two-dimensional matched filters,” IEEE Trans. Med. Imaging8, 263–269 (1989).
[CrossRef] [PubMed]

Chatterji, B.

B. Srinivasa and B. Chatterji, “An FFT-based technique for translation, rotation, and scale-invariant image registration,” IEEE Trans. Image Process.5, 1266–1271 (1996).
[CrossRef]

Chaudhuri, S.

S. Chaudhuri, S. Chatterjee, N. Katz, M. Nelson, and M. Goldbaum, “Detection of blood vessels in retinal images using two-dimensional matched filters,” IEEE Trans. Med. Imaging8, 263–269 (1989).
[CrossRef] [PubMed]

Chen, L.

S. Lin, Y. Chang, and L. Chen, “Motion adaptive interpolation with horizontal motion detection for deinterlacing,” IEEE Trans. Consumer Electron.49, 1256–1265 (2003).
[CrossRef]

Cheng, H.

H. Cheng, X. Jiang, Y. Sun, and J. Wang, “Color image segmentation: advances and prospects,” Pattern Recognition34, 2259–2281 (2001).
[CrossRef]

Chiang, M. F.

D. K. Wallace, G. E. Quinn, S. F. Freedman, and M. F. Chiang, “Agreement among pediatric ophthalmologists in diagnosing plus and pre-plus disease in retinopathy of prematurity,” J. Am. Assoc. Pediatric Opthalmol. Strabismus12, 352–356 (2008).
[CrossRef]

Chou, C.

D. Tsai and C. Chou, “A fast focus measure for video display inspection,” Machine Vision Appl.14, 192–196 (2003).

Christmas, W.

A. Fitch, A. Kadyrov, W. Christmas, and J. Kittler, “Fast robust correlation,” IEEE Trans. Image Process.14, 1063–1073 (2005).
[CrossRef] [PubMed]

Clay, S.

C. Wilson, K. Cocker, M. Moseley, C. Paterson, S. Clay, W. Schulenburg, M. Mills, A. Ells, K. Parker, G. Quinn, A. Fielder, and J. Ng, “Computerized analysis of retinal vessel width and tortuosity in premature infants,” Invest. Ophthalmol. & Visual Sci.49, 3577–3585 (2008).
[CrossRef] [PubMed]

Cocker, K.

C. Wilson, K. Cocker, M. Moseley, C. Paterson, S. Clay, W. Schulenburg, M. Mills, A. Ells, K. Parker, G. Quinn, A. Fielder, and J. Ng, “Computerized analysis of retinal vessel width and tortuosity in premature infants,” Invest. Ophthalmol. & Visual Sci.49, 3577–3585 (2008).
[CrossRef] [PubMed]

Cree, M.

J. Soares, J. Leandro, R. Cesar, H. Jelinek, and M. Cree, “Retinal vessel segmentation using the 2-D Gabor wavelet and supervised classification,” IEEE Trans. Med. Imaging25, 1214–1222 (2006).
[CrossRef] [PubMed]

Dagenais, M.

S. Fox, R. Silver, E. Kornegay, and M. Dagenais, “Focus and edge detection algorithms and their relevance to the development of an optical overlay calibration standard,” Proc. SPIE3677, 95–106 (1999).
[CrossRef]

Daszykowski, M.

M. Daszykowski, K. Kaczmarek, Y. Vander Heyden, and B. Walczak, “Robust statistics in data analysis–a review:: basic concepts,” Chemometrics Intell. Lab. Syst.85, 203–219 (2007).
[CrossRef]

Donoho, D.

J. Starck, F. Murtagh, E. Candes, and D. Donoho, “Gray and color image contrast enhancement by the curvelet transform,” IEEE Trans. Image Processing12, 706–717 (2003).
[CrossRef]

Drescher, S.

K. Simonson, S. Drescher, and F. Tanner, “A statistics-based approach to binary image registration with uncertainty analysis,” IEEE Trans. Pattern Anal. Machine Intell.29, 112–125 (2007).
[CrossRef]

Elad, M.

S. Farsiu, M. Elad, and P. Milanfar, “Constrained, globally optimal, multi-frame motion estimation,” in Proceedings of IEEE Workshop on Statistical Signal Processing (IEEE, 2005), pp. 1396–1401.

Ells, A.

C. Wilson, K. Cocker, M. Moseley, C. Paterson, S. Clay, W. Schulenburg, M. Mills, A. Ells, K. Parker, G. Quinn, A. Fielder, and J. Ng, “Computerized analysis of retinal vessel width and tortuosity in premature infants,” Invest. Ophthalmol. & Visual Sci.49, 3577–3585 (2008).
[CrossRef] [PubMed]

Farsiu, S.

M. D. Robinson, C. A. Toth, J. Y. Lo, and S. Farsiu, “Efficient Fourier-wavelet super-resolution,” IEEE Trans. Image Process.19, 2669–2681 (2010).
[CrossRef] [PubMed]

Y. K. Tao, S. Farsiu, and J. A. Izatt, “Interlaced spectrally encoded confocal scanning laser ophthalmoscopy and spectral domain optical coherence tomography,” Biomed. Opt. Express1, 431–440 (2010).
[CrossRef]

M. D. Robinson, S. Farsiu, and P. Milanfar, “Optimal registation of aliased images using variable projection with applications to super-resolution,” Comput. J.52, 31–42 (2009).
[CrossRef]

S. Farsiu, M. Elad, and P. Milanfar, “Constrained, globally optimal, multi-frame motion estimation,” in Proceedings of IEEE Workshop on Statistical Signal Processing (IEEE, 2005), pp. 1396–1401.

Fielder, A.

C. Wilson, K. Cocker, M. Moseley, C. Paterson, S. Clay, W. Schulenburg, M. Mills, A. Ells, K. Parker, G. Quinn, A. Fielder, and J. Ng, “Computerized analysis of retinal vessel width and tortuosity in premature infants,” Invest. Ophthalmol. & Visual Sci.49, 3577–3585 (2008).
[CrossRef] [PubMed]

Fitch, A.

A. Fitch, A. Kadyrov, W. Christmas, and J. Kittler, “Fast robust correlation,” IEEE Trans. Image Process.14, 1063–1073 (2005).
[CrossRef] [PubMed]

Fletcher, R.

R. Fletcher, “Conjugate gradient methods for indefinite systems,” Numerical Anal.506, 73–89 (1976).
[CrossRef]

Flusser, J.

B. Zitova and J. Flusser, “Image registration methods: a survey,” Image Vision Comput.21, 977–1000 (2003).
[CrossRef]

J. Kautsky, J. Flusser, and B. Zitová, “A new wavelet-based measure of image focus,” Pattern Recognition Lett.23, 1785–1794 (2002).
[CrossRef]

Fox, S.

S. Fox, R. Silver, E. Kornegay, and M. Dagenais, “Focus and edge detection algorithms and their relevance to the development of an optical overlay calibration standard,” Proc. SPIE3677, 95–106 (1999).
[CrossRef]

Freedman, S.

S. Ahmad, D. Wallace, S. Freedman, and Z. Zhao, “Computer-assisted assessment of plus disease in retinopathy of prematurity using video indirect ophthalmoscopy images,” Retina28, 1458–1462 (2008).
[CrossRef] [PubMed]

D. Wallace, Z. Zhao, and S. Freedman, “A pilot study using” ROPtool” to quantify plus disease in retinopathy of prematurity.” J. Am. Assoc. Pediatric Opthalmol. Strabismus11, 381–387 (2007).
[CrossRef]

Freedman, S. F.

D. K. Wallace, G. E. Quinn, S. F. Freedman, and M. F. Chiang, “Agreement among pediatric ophthalmologists in diagnosing plus and pre-plus disease in retinopathy of prematurity,” J. Am. Assoc. Pediatric Opthalmol. Strabismus12, 352–356 (2008).
[CrossRef]

Fulton, A.

R. Gelman, M. Martinez-Perez, D. Vanderveen, A. Moskowitz, and A. Fulton, “Diagnosis of plus disease in retinopathy of prematurity using Retinal Image multiScale Analysis,” Invest. Ophthalmol. & Visual Sci.46, 4734–4738 (2005).
[CrossRef] [PubMed]

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R. Gelman, M. Martinez-Perez, D. Vanderveen, A. Moskowitz, and A. Fulton, “Diagnosis of plus disease in retinopathy of prematurity using Retinal Image multiScale Analysis,” Invest. Ophthalmol. & Visual Sci.46, 4734–4738 (2005).
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Figures (12)

Fig. 4
Fig. 4

Frames classified by quality scores: Frames from a 2500-frame video ranked based on the (a) HSV and (b) spatial frequency scores. Scores decrease from left to right and top to bottom. The frames in (c) are ranked by the convex combination (7) of the two scores, with υ = 0.3. The convex combination score balances crispness with coverage. Each collage shows frames with ranks 1 through 10. Images are best viewed on screen.

Fig. 1
Fig. 1

VIO frame artifacts: Three sample VIO frames, from three different videos, display a number of common artifacts. Each arrow’s number and color indicate the type of artifact: (1) (white) black regions; (2) (red) white spots; (3) (magenta) artificial colors; (4) (blue) saturation near the lens’ rim; (5) (yellow) interlacing artifacts. All but the interlacing artifacts are produced by the optics of the hand-held condensing lens.

Fig. 2
Fig. 2

Retinal mosaicing pipeline: Our proposed pipeline generates a single, high quality mosaic from a raw VIO recording. We select frames based on a hue-saturation-value (HSV) quality score, a spatial frequency measure, and a combination of the two measures. We then remove artifacts present in the selected frames and compute a high contrast vessel map from each of them. We register the selected frames based on these maps and fuse the registered frames into a single mosaic, suitable for human and semi-automated analysis.

Fig. 3
Fig. 3

Frame HSV color distribution: (a) A sample VIO frame. (b) The scatter plot of the HSV color values of the sample frame. Retinal pixels (green), exhibit a narrow color distribution in HSV space relative to the rest of the image (blue). While the retinal pixels constitute 30% of the image, they are more tightly clustered than the non-retinal pixels. (c) Color-coded frame: retinal pixels are shown in green and non-retinal pixels in blue.

Fig. 5
Fig. 5

Accumulating artifacts can overwhelm naive frame fusion: (a) A close-up of the naive fusion of five frames with no artifact removal. White spots, speckles, distorted colors and other artifacts from various frames accumulate in the mosaic. Following the labeling scheme of Fig. 1, the colored arrows indicate the different types of artifacts: (2) (red) white spots; (3) (magenta) distorted colors; (4) (blue) saturation caused by the lens’ rim; (6) (black) spurious inter-frame borders. In (b) and (c), two of the originating frames are shown, which exhibit fewer artifacts in the same region.

Fig. 6
Fig. 6

The steps of directional local contrast filtering: (a) The original frame. (b) The local median for a 50 × 50 pixel filtering window Vp. (c) Pixels that far exceed the local median brightness are marked as invalid (black in the image). (d) Invalid pixels are replaced with the local median values. This removes white spots and speckles.

Fig. 7
Fig. 7

Distorted color adjustment: (a) Frame affected by distorted colors arising from the lens’s optics. (b) HSV masking without distorted color adjustment (c) HSV masking with distorted color adjustment. Note that the retinal area is significantly larger in (c) than in (b).

Fig. 8
Fig. 8

HSV masking: Pixels in (a) that fall outside the HSV boundary S are flagged and discarded from further processing. Non-retinal pixels are shown as black in (b).

Fig. 9
Fig. 9

Registration between two frames: (a) Source frame. (b) Target frame. (c) Source correspondence points on Gabor image. (d) Matched points on target image. Poorly matched source points are discarded. (e) Registered green channel overlay. The source frame is correctly aligned with the target frame.

Fig. 10
Fig. 10

VIO mosaic: A mosaic generated from five frames selected from a single VIO video. (a)–(e): each original frame; (f): the five-frame mosaic. Note the larger FOV of the mosaic relative to each individual frame, and the lack of artifacts in the final image. All images are at the same scale, and are best viewed on screen.

Fig. 11
Fig. 11

VIO mosaic: A mosaic generated from six frames selected from a single VIO video. (a)–(f): each original frame; (g): the six-frame mosaic. Note the larger FOV of the mosaic relative to each individual frame, and the lack of artifacts in the final image. All images are at the same scale, and are best viewed on screen.

Fig. 12
Fig. 12

ROPTool analysis comparison: ROPTool analysis of the mosaics of Fig. 10 and 11 as well as the best hand-picked frames from the corresponding videos: (a), (c) Hand-picked frames; (b), (d) Mosaics. Images are best viewed on screen. The blue lines inside the large blue circle indicate the vessel paths obtained with ROPTool. At least one, but preferably two major vessels from each quadrant are needed to provide a full ROP diagnosis. ROPTool is able to extract longer and more numerous vessels when analyzing the mosaics than the hand-picked frames. Furthermore, ROPTool analysis of the mosaics is faster due to fewer ROPTool mistakes. The examination times (in minutes) were: (a) 2:45, (b) 2:00, (c) 2:35, (d) 1:30

Tables (1)

Tables Icon

Table 1 Quantitative ROPTool analysis of 31 mosaics and their corresponding best hand-picked frames

Equations (34)

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I ( p ) = v .
h ( I ) = | P R | | P | .
𝒩 σ m = 1 2 π σ m 2 e [ ( u μ u ) 2 / 2 σ m 2 + ( v μ v ) 2 / σ m 2 ] , 𝒩 σ l = 1 2 π σ l 2 e [ ( u μ u ) 2 / 2 σ l 2 + ( v μ v ) 2 / 2 σ l 2 ] .
F m ( u , v ) = F h ( u , v ) 𝒩 σ m ( u , v ) .
F l ( u , v ) = F m ( u , v ) 𝒩 σ l ( u , v ) .
b ( I ) = F m F l 1 F h F m 1 .
q ( I ) = υ h ( I ) + ( 1 υ ) b ( I ) , I I .
c o = m o m b m b ,
c p = v g m b g ( p ) m b g ( p ) ,
c p > t c I ( p ) m b ( p ) .
S d = S \ S .
v HSV S d v HSV h v HSV h ± t p .
L σ ( p ; σ ) = ( 2 𝒩 ( p ; σ ) ) * I g ( p ) ,
L ( p ) = max σ L σ ( p ; σ ) .
B ( p ; λ , Σ , θ ) = s ( p ; λ ) 𝒩 ( p ; Σ , θ ) ,
G ( p ) = max λ , Σ , θ ( L ( p ) * B ( p ; λ , Σ , θ ) ) .
d b , θ b = argmin d , θ SSD d , θ ,
SSD d , θ = p P ( G t ( p ) G s ( R p + d ) ) 2 , R = [ cos θ sin θ sin θ cos θ ] .
SSD d , θ = p P ( G t ( p ) ) 2 + p P ( G s ( R p + d ) ) 2 2 p P G t ( p ) G s ( R p + d ) .
PSSD θ = 1 { { ( G s ( R p ) ) 2 } { U ( p ) } } 2 1 { { G t ( p ) } { G s ( R p ) } } ,
θ b = argmin θ i PSSD θ i , i [ 1 , Q ] ,
c 1 s = argmax p P G s ( p ) .
f ( p ) < t d G s ( p ) ϕ .
f ( p ) = min c C s p c 2
c k s = argmax p P ϕ G s ( p ) ,
d k , θ k = argmin d , θ p W k s ( W k s ( p ) W k t ( R p + d ) ) 2 .
c k t = R k c k s + d k .
A L 1 = argmin A A C s C t 1 .
d a , R a = argmin d , R p P J ( p ) ( R I ( p ) + d ) 2 2 .
w E ( p ) = min p i P R p p i 2 ,
w ( p ) = 1 1 + e λ w E ( p ) , λ > 0
M C h ( p ) = max n I n h ( p ) , n [ 1 , N ] ,
M ^ G ( p ) = min n G ^ n ( p ) , n [ 1 , N ] .
M = α M c + ( 1 α ) M ^ G .

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