Abstract

As stereoscopic display devices become common, their image quality assessment evaluation becomes increasingly important. Most studies conducted on 3D displays are based on psychophysics experiments with humans rating their experience based on detection tasks. The physical measurements do not map to effects on signal detection performance. Additionally, human observer study results are often subjective and difficult to generalize. We designed a computational stereoscopic observer approach inspired by the mechanisms of stereopsis in human vision for task-based image assessment that makes binary decisions based on a set of image pairs. The stereo-observer is constrained to a left and a right image generated using a visualization operator to render voxel datasets. We analyze white noise and lumpy backgrounds using volume rendering techniques. Our simulation framework generalizes many different types of model observers including existing 2D and 3D observers as well as providing flexibility to formulate a stereo model observer approach following the principles of stereoscopic viewing. This methodology has the potential to replace human observer studies when exploring issues with stereo display devices to be used in medical imaging. We show results quantifying the changes in performance when varying stereo angle as measured by an ideal linear stereoscopic observer. Our findings indicate that there is an increase in performance of about 13–18% for white noise and 20–46% for lumpy backgrounds, where the stereo angle is varied from 0 to 30. The applicability of this observer extends to stereoscopic displays used for in the areas of medical and entertainment imaging applications.

© 2014 Optical Society of America

Full Article  |  PDF Article
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References

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2013 (2)

C. J. D’Orsi, D. J. Getty, R. M. Pickett, I. Sechopoulos, M. S. Newell, K. R. Gundry, S. R. Bates, R. M. Nishikawa, E. A. Sickles, A. Karellas, and E. M. D’Orsi, “Stereoscopic digital mammography: improved specificity and reduced rate of recall in a prospective clinical trial,” Radiology. 266(1), 81–88 (2013).
[Crossref]

A. Wunderlich and F. Noo, “New theoretical results on channelized hotelling observer performance estimation with known difference of class means,” IEEE Transactions on Nuclear Science,  60(1), 182–193 (2013).
[Crossref]

2012 (1)

A. Badano, “Predicting perceived image quality: a critique of Lin and Kuo,” Perceptual and Motor Skills 114(1), 236–238 (2012).
[Crossref] [PubMed]

2011 (4)

L. Platisa, B. Goossens, E. Vanteenkiste, S. Park, B. D. Gallas, A. Badano, and W. Philips, “Channelized hotelling observers for the assessment of volumetric data sets,” J. Opt. Soc. Am. 28(6), 1145–1163 (2011).
[Crossref]

X. H. Wang, J. E. Durick, A. Lu, D. L. Herbert, C. R. Fuhrman, J. M. Lacomis, C. A. Britton, D. C. Strollo, S. S. Shang, S. K. Golla, and W. F. Good, “Compare display schemes for lung nodule CT screening,” J. Digital Imaging 24(3), 478–484 (2011).
[Crossref]

M. Freed, J. A. D. Zwart, J. T. Loud, R. H. E. Khouli, K. J. Myers, M. H. Greene, J. H. Duyn, and A. Badano, “An anthropomorphic phantom for quantitative evaluation of breast MRI,” Med. Phys. 38(2), 743–753 (2011).
[Crossref] [PubMed]

M. Freed, J. A. D. Zwart, P. Hariharan, K. J. Myers, and A. Badano, “Development and characterization of a dynamic lesion phantom for the quantitative evaluation of dynamic contrast-enhanced MRI,” Med. Phys. 38(10), 5601–5611 (2011).
[Crossref] [PubMed]

2010 (1)

A. Abildgaard, A. K. Witwit, J. S. Karlsen, E. A. Jacobson, B. Tennoe, G. Ringstad, and P. D. Tonnessen, “An autostereoscopic 3D display can improve visualization of 3D models from intracranial MR angiography,” International Journal of Computer Assisted Radiology and Surgery 5(5), 549–554 (2010).
[Crossref] [PubMed]

2009 (2)

A. Wunderlich and F. Noo, “Estimation of channelized hotelling observer performance with known class means or known difference of class means,” IEEE Transactions on Medical Imaging 28(8), 1198–1207 (2009).
[Crossref] [PubMed]

J. Hakkinen, J. Takatalo, M. Kilpelainen, M. Salmimaa, and G. Nyman, “Determining limits to avoid double vision in an autostereoscopic display: disparity and image element width,” J. Soc. Inf. Disp. May,  17(5), 443–444 (2009).
[Crossref]

2008 (1)

H. Liang, S. Park, B. D. Gallas, K. J. Myers, and A. Badano, “Image browsing in slow medical liquid crystal displays,” Acad Radiol. 15(3), 370–382 (2008).
[Crossref] [PubMed]

2007 (1)

2005 (2)

L. P. Yaroslavsky, J. Campos, M. Espinola, and I. Ideses, “Redundancy of stereoscopic images: experimental evaluation,” Opt. Express 13(26), 10895–10907 (2005).
[Crossref] [PubMed]

H. P. Chan, M. M. Goodsitt, M. A. Helvie, L. M. Hadjiiski, J. T. Lydick, M. A. Roubidoux, J. E. Bailey, A. Nees, C. E. Blane, and B. Sahiner, “ROC study of the effect of stereoscopic imaging on assessment of breast lesions,” Med Phys. 32(4), 1001–1009 (2005).
[Crossref] [PubMed]

2001 (1)

D. J. Getty, R. M. Pickett, and C. J. D’Orsi, “Stereoscopic digital mammography: improving detection and diagnosis of breast cancer,” International Congress Series,  1230, 74–79 (2001).
[Crossref]

1999 (1)

H. P. Chan, B. Sahiner, R. F. Wagner, and N. Petrick, “Classifier design for computer-aided diagnosis: Effects of finite sample size on the mean performance of classical and neural network classifiers,” Med. Phys. 26(12), 2654–2668 (1999).
[Crossref]

1992 (1)

1987 (1)

1986 (1)

T. L. Kay and J. T. Kajuya, “Ray tracing complex scenes,” ACM SIGGRAPH Computer Graphics,  20(4), 269–278 (1986).
[Crossref]

1985 (1)

R. F. Wagner and D. G. Brown, “Unified SNR analysis of medical imaging system,” Phys. Med. Biol. 30(6), 489–518 (1985).
[Crossref]

Abildgaard, A.

A. Abildgaard, A. K. Witwit, J. S. Karlsen, E. A. Jacobson, B. Tennoe, G. Ringstad, and P. D. Tonnessen, “An autostereoscopic 3D display can improve visualization of 3D models from intracranial MR angiography,” International Journal of Computer Assisted Radiology and Surgery 5(5), 549–554 (2010).
[Crossref] [PubMed]

Arva, J.

E. Haines, P Hanrahan, R. L. Cook, J. Arva, D. Kirk, P. S. Heckbert, and A. S. Glassner, An overview of ray tracing (Academic Press Inc. I edition 1989).

Ashikhmin, M.

P. Shirley, M. Ashikhmin, S. R. Marschner, E. r., K. Sung, W. B. Thompson, and P. Willemsen, Fundamentals of Computer Graphics (A K Peters/CRCIInd edition 2005).

Badano, A.

A. Badano, “Predicting perceived image quality: a critique of Lin and Kuo,” Perceptual and Motor Skills 114(1), 236–238 (2012).
[Crossref] [PubMed]

L. Platisa, B. Goossens, E. Vanteenkiste, S. Park, B. D. Gallas, A. Badano, and W. Philips, “Channelized hotelling observers for the assessment of volumetric data sets,” J. Opt. Soc. Am. 28(6), 1145–1163 (2011).
[Crossref]

M. Freed, J. A. D. Zwart, J. T. Loud, R. H. E. Khouli, K. J. Myers, M. H. Greene, J. H. Duyn, and A. Badano, “An anthropomorphic phantom for quantitative evaluation of breast MRI,” Med. Phys. 38(2), 743–753 (2011).
[Crossref] [PubMed]

M. Freed, J. A. D. Zwart, P. Hariharan, K. J. Myers, and A. Badano, “Development and characterization of a dynamic lesion phantom for the quantitative evaluation of dynamic contrast-enhanced MRI,” Med. Phys. 38(10), 5601–5611 (2011).
[Crossref] [PubMed]

H. Liang, S. Park, B. D. Gallas, K. J. Myers, and A. Badano, “Image browsing in slow medical liquid crystal displays,” Acad Radiol. 15(3), 370–382 (2008).
[Crossref] [PubMed]

F. Zafar, J. Dorband, and A. Badano, “Computational observer approach for the assessment of stereoscopic visualizations for 3D medical images,” Proc. SPIE, Medical Imaging: Image Perception, Observer Performance, and Technology Assessment, 2012.
[Crossref]

Bailey, J. E.

H. P. Chan, M. M. Goodsitt, M. A. Helvie, L. M. Hadjiiski, J. T. Lydick, M. A. Roubidoux, J. E. Bailey, A. Nees, C. E. Blane, and B. Sahiner, “ROC study of the effect of stereoscopic imaging on assessment of breast lesions,” Med Phys. 32(4), 1001–1009 (2005).
[Crossref] [PubMed]

Barrett, H. H.

Bates, S. R.

C. J. D’Orsi, D. J. Getty, R. M. Pickett, I. Sechopoulos, M. S. Newell, K. R. Gundry, S. R. Bates, R. M. Nishikawa, E. A. Sickles, A. Karellas, and E. M. D’Orsi, “Stereoscopic digital mammography: improved specificity and reduced rate of recall in a prospective clinical trial,” Radiology. 266(1), 81–88 (2013).
[Crossref]

Beutel, J.

R. L. V. Metter, J. Beutel, and H. L. Kundel, Handbook of medical imaging (SPIE1st edition 2009).

Blane, C. E.

H. P. Chan, M. M. Goodsitt, M. A. Helvie, L. M. Hadjiiski, J. T. Lydick, M. A. Roubidoux, J. E. Bailey, A. Nees, C. E. Blane, and B. Sahiner, “ROC study of the effect of stereoscopic imaging on assessment of breast lesions,” Med Phys. 32(4), 1001–1009 (2005).
[Crossref] [PubMed]

Britton, C. A.

X. H. Wang, J. E. Durick, A. Lu, D. L. Herbert, C. R. Fuhrman, J. M. Lacomis, C. A. Britton, D. C. Strollo, S. S. Shang, S. K. Golla, and W. F. Good, “Compare display schemes for lung nodule CT screening,” J. Digital Imaging 24(3), 478–484 (2011).
[Crossref]

Brown, D. G.

R. F. Wagner and D. G. Brown, “Unified SNR analysis of medical imaging system,” Phys. Med. Biol. 30(6), 489–518 (1985).
[Crossref]

Campos, J.

Chan, H. P.

H. P. Chan, M. M. Goodsitt, M. A. Helvie, L. M. Hadjiiski, J. T. Lydick, M. A. Roubidoux, J. E. Bailey, A. Nees, C. E. Blane, and B. Sahiner, “ROC study of the effect of stereoscopic imaging on assessment of breast lesions,” Med Phys. 32(4), 1001–1009 (2005).
[Crossref] [PubMed]

H. P. Chan, B. Sahiner, R. F. Wagner, and N. Petrick, “Classifier design for computer-aided diagnosis: Effects of finite sample size on the mean performance of classical and neural network classifiers,” Med. Phys. 26(12), 2654–2668 (1999).
[Crossref]

Cook, R. L.

E. Haines, P Hanrahan, R. L. Cook, J. Arva, D. Kirk, P. S. Heckbert, and A. S. Glassner, An overview of ray tracing (Academic Press Inc. I edition 1989).

D’Orsi, C. J.

C. J. D’Orsi, D. J. Getty, R. M. Pickett, I. Sechopoulos, M. S. Newell, K. R. Gundry, S. R. Bates, R. M. Nishikawa, E. A. Sickles, A. Karellas, and E. M. D’Orsi, “Stereoscopic digital mammography: improved specificity and reduced rate of recall in a prospective clinical trial,” Radiology. 266(1), 81–88 (2013).
[Crossref]

D. J. Getty, R. M. Pickett, and C. J. D’Orsi, “Stereoscopic digital mammography: improving detection and diagnosis of breast cancer,” International Congress Series,  1230, 74–79 (2001).
[Crossref]

D’Orsi, E. M.

C. J. D’Orsi, D. J. Getty, R. M. Pickett, I. Sechopoulos, M. S. Newell, K. R. Gundry, S. R. Bates, R. M. Nishikawa, E. A. Sickles, A. Karellas, and E. M. D’Orsi, “Stereoscopic digital mammography: improved specificity and reduced rate of recall in a prospective clinical trial,” Radiology. 266(1), 81–88 (2013).
[Crossref]

Dorband, J.

F. Zafar, J. Dorband, and A. Badano, “Computational observer approach for the assessment of stereoscopic visualizations for 3D medical images,” Proc. SPIE, Medical Imaging: Image Perception, Observer Performance, and Technology Assessment, 2012.
[Crossref]

Durick, J. E.

X. H. Wang, J. E. Durick, A. Lu, D. L. Herbert, C. R. Fuhrman, J. M. Lacomis, C. A. Britton, D. C. Strollo, S. S. Shang, S. K. Golla, and W. F. Good, “Compare display schemes for lung nodule CT screening,” J. Digital Imaging 24(3), 478–484 (2011).
[Crossref]

Duyn, J. H.

M. Freed, J. A. D. Zwart, J. T. Loud, R. H. E. Khouli, K. J. Myers, M. H. Greene, J. H. Duyn, and A. Badano, “An anthropomorphic phantom for quantitative evaluation of breast MRI,” Med. Phys. 38(2), 743–753 (2011).
[Crossref] [PubMed]

E. r.,

P. Shirley, M. Ashikhmin, S. R. Marschner, E. r., K. Sung, W. B. Thompson, and P. Willemsen, Fundamentals of Computer Graphics (A K Peters/CRCIInd edition 2005).

Engel, K.

K. Engel, M. Hadwinger, J. M. Kniss, C. R. Salama, and D. Weiskopf, Real-Time Volume Graphics (A K Peters1st edition 2006).

Espinola, M.

Freed, M.

M. Freed, J. A. D. Zwart, P. Hariharan, K. J. Myers, and A. Badano, “Development and characterization of a dynamic lesion phantom for the quantitative evaluation of dynamic contrast-enhanced MRI,” Med. Phys. 38(10), 5601–5611 (2011).
[Crossref] [PubMed]

M. Freed, J. A. D. Zwart, J. T. Loud, R. H. E. Khouli, K. J. Myers, M. H. Greene, J. H. Duyn, and A. Badano, “An anthropomorphic phantom for quantitative evaluation of breast MRI,” Med. Phys. 38(2), 743–753 (2011).
[Crossref] [PubMed]

Fuhrman, C. R.

X. H. Wang, J. E. Durick, A. Lu, D. L. Herbert, C. R. Fuhrman, J. M. Lacomis, C. A. Britton, D. C. Strollo, S. S. Shang, S. K. Golla, and W. F. Good, “Compare display schemes for lung nodule CT screening,” J. Digital Imaging 24(3), 478–484 (2011).
[Crossref]

Funakoshi, M.

M. Funakoshi, K. Shidoji, and M. Ogawa, “Perception of absolute and relative distances in stereoscopic image,” SPIE: Stereoscopic Displays and Applications XXI, (2010).

Gallas, B. D.

L. Platisa, B. Goossens, E. Vanteenkiste, S. Park, B. D. Gallas, A. Badano, and W. Philips, “Channelized hotelling observers for the assessment of volumetric data sets,” J. Opt. Soc. Am. 28(6), 1145–1163 (2011).
[Crossref]

H. Liang, S. Park, B. D. Gallas, K. J. Myers, and A. Badano, “Image browsing in slow medical liquid crystal displays,” Acad Radiol. 15(3), 370–382 (2008).
[Crossref] [PubMed]

Getty, D. J.

C. J. D’Orsi, D. J. Getty, R. M. Pickett, I. Sechopoulos, M. S. Newell, K. R. Gundry, S. R. Bates, R. M. Nishikawa, E. A. Sickles, A. Karellas, and E. M. D’Orsi, “Stereoscopic digital mammography: improved specificity and reduced rate of recall in a prospective clinical trial,” Radiology. 266(1), 81–88 (2013).
[Crossref]

D. J. Getty, R. M. Pickett, and C. J. D’Orsi, “Stereoscopic digital mammography: improving detection and diagnosis of breast cancer,” International Congress Series,  1230, 74–79 (2001).
[Crossref]

Glassner, A. S.

E. Haines, P Hanrahan, R. L. Cook, J. Arva, D. Kirk, P. S. Heckbert, and A. S. Glassner, An overview of ray tracing (Academic Press Inc. I edition 1989).

Golla, S. K.

X. H. Wang, J. E. Durick, A. Lu, D. L. Herbert, C. R. Fuhrman, J. M. Lacomis, C. A. Britton, D. C. Strollo, S. S. Shang, S. K. Golla, and W. F. Good, “Compare display schemes for lung nodule CT screening,” J. Digital Imaging 24(3), 478–484 (2011).
[Crossref]

Good, W. F.

X. H. Wang, J. E. Durick, A. Lu, D. L. Herbert, C. R. Fuhrman, J. M. Lacomis, C. A. Britton, D. C. Strollo, S. S. Shang, S. K. Golla, and W. F. Good, “Compare display schemes for lung nodule CT screening,” J. Digital Imaging 24(3), 478–484 (2011).
[Crossref]

Goodsitt, M. M.

H. P. Chan, M. M. Goodsitt, M. A. Helvie, L. M. Hadjiiski, J. T. Lydick, M. A. Roubidoux, J. E. Bailey, A. Nees, C. E. Blane, and B. Sahiner, “ROC study of the effect of stereoscopic imaging on assessment of breast lesions,” Med Phys. 32(4), 1001–1009 (2005).
[Crossref] [PubMed]

Goossens, B.

L. Platisa, B. Goossens, E. Vanteenkiste, S. Park, B. D. Gallas, A. Badano, and W. Philips, “Channelized hotelling observers for the assessment of volumetric data sets,” J. Opt. Soc. Am. 28(6), 1145–1163 (2011).
[Crossref]

Greene, M. H.

M. Freed, J. A. D. Zwart, J. T. Loud, R. H. E. Khouli, K. J. Myers, M. H. Greene, J. H. Duyn, and A. Badano, “An anthropomorphic phantom for quantitative evaluation of breast MRI,” Med. Phys. 38(2), 743–753 (2011).
[Crossref] [PubMed]

Gropp, W.

W. Gropp, E. Lusk, and A. Skjellum, Using MPI, Portable Parallel Programming with the Message-Passing Interface (The MIT PressII edition 1999).

Gundry, K. R.

C. J. D’Orsi, D. J. Getty, R. M. Pickett, I. Sechopoulos, M. S. Newell, K. R. Gundry, S. R. Bates, R. M. Nishikawa, E. A. Sickles, A. Karellas, and E. M. D’Orsi, “Stereoscopic digital mammography: improved specificity and reduced rate of recall in a prospective clinical trial,” Radiology. 266(1), 81–88 (2013).
[Crossref]

Hadjiiski, L. M.

H. P. Chan, M. M. Goodsitt, M. A. Helvie, L. M. Hadjiiski, J. T. Lydick, M. A. Roubidoux, J. E. Bailey, A. Nees, C. E. Blane, and B. Sahiner, “ROC study of the effect of stereoscopic imaging on assessment of breast lesions,” Med Phys. 32(4), 1001–1009 (2005).
[Crossref] [PubMed]

Hadwinger, M.

K. Engel, M. Hadwinger, J. M. Kniss, C. R. Salama, and D. Weiskopf, Real-Time Volume Graphics (A K Peters1st edition 2006).

Haines, E.

E. Haines, P Hanrahan, R. L. Cook, J. Arva, D. Kirk, P. S. Heckbert, and A. S. Glassner, An overview of ray tracing (Academic Press Inc. I edition 1989).

Hakkinen, J.

J. Hakkinen, J. Takatalo, M. Kilpelainen, M. Salmimaa, and G. Nyman, “Determining limits to avoid double vision in an autostereoscopic display: disparity and image element width,” J. Soc. Inf. Disp. May,  17(5), 443–444 (2009).
[Crossref]

Hanrahan, P

E. Haines, P Hanrahan, R. L. Cook, J. Arva, D. Kirk, P. S. Heckbert, and A. S. Glassner, An overview of ray tracing (Academic Press Inc. I edition 1989).

Hariharan, P.

M. Freed, J. A. D. Zwart, P. Hariharan, K. J. Myers, and A. Badano, “Development and characterization of a dynamic lesion phantom for the quantitative evaluation of dynamic contrast-enhanced MRI,” Med. Phys. 38(10), 5601–5611 (2011).
[Crossref] [PubMed]

Heckbert, P. S.

E. Haines, P Hanrahan, R. L. Cook, J. Arva, D. Kirk, P. S. Heckbert, and A. S. Glassner, An overview of ray tracing (Academic Press Inc. I edition 1989).

Heilbrun, M.

A. Wunderlich, F. Noo, and M. Heilbrun, “Exact confidence intervals for channelized hotelling observer performance,” Proc. of SPIE, Medical Imaging: Image Perception, Observer Performance, and Technology Assessment8673 (2013).
[Crossref]

Helvie, M. A.

H. P. Chan, M. M. Goodsitt, M. A. Helvie, L. M. Hadjiiski, J. T. Lydick, M. A. Roubidoux, J. E. Bailey, A. Nees, C. E. Blane, and B. Sahiner, “ROC study of the effect of stereoscopic imaging on assessment of breast lesions,” Med Phys. 32(4), 1001–1009 (2005).
[Crossref] [PubMed]

Herbert, D. L.

X. H. Wang, J. E. Durick, A. Lu, D. L. Herbert, C. R. Fuhrman, J. M. Lacomis, C. A. Britton, D. C. Strollo, S. S. Shang, S. K. Golla, and W. F. Good, “Compare display schemes for lung nodule CT screening,” J. Digital Imaging 24(3), 478–484 (2011).
[Crossref]

Huang, K. C.

K. C. Huang, J. C. Yang, C. L. Wu, K. Lee, and S. L. Hwang, “System-crosstalk effect on stereopsis human factor study for 3D displays,” SPIE: Stereoscopic Displays and Applications XXI, (2010).

Hwang, S. L.

K. C. Huang, J. C. Yang, C. L. Wu, K. Lee, and S. L. Hwang, “System-crosstalk effect on stereopsis human factor study for 3D displays,” SPIE: Stereoscopic Displays and Applications XXI, (2010).

Ideses, I.

Jacobson, E. A.

A. Abildgaard, A. K. Witwit, J. S. Karlsen, E. A. Jacobson, B. Tennoe, G. Ringstad, and P. D. Tonnessen, “An autostereoscopic 3D display can improve visualization of 3D models from intracranial MR angiography,” International Journal of Computer Assisted Radiology and Surgery 5(5), 549–554 (2010).
[Crossref] [PubMed]

Kajuya, J. T.

T. L. Kay and J. T. Kajuya, “Ray tracing complex scenes,” ACM SIGGRAPH Computer Graphics,  20(4), 269–278 (1986).
[Crossref]

Karellas, A.

C. J. D’Orsi, D. J. Getty, R. M. Pickett, I. Sechopoulos, M. S. Newell, K. R. Gundry, S. R. Bates, R. M. Nishikawa, E. A. Sickles, A. Karellas, and E. M. D’Orsi, “Stereoscopic digital mammography: improved specificity and reduced rate of recall in a prospective clinical trial,” Radiology. 266(1), 81–88 (2013).
[Crossref]

Karlsen, J. S.

A. Abildgaard, A. K. Witwit, J. S. Karlsen, E. A. Jacobson, B. Tennoe, G. Ringstad, and P. D. Tonnessen, “An autostereoscopic 3D display can improve visualization of 3D models from intracranial MR angiography,” International Journal of Computer Assisted Radiology and Surgery 5(5), 549–554 (2010).
[Crossref] [PubMed]

Kay, T. L.

T. L. Kay and J. T. Kajuya, “Ray tracing complex scenes,” ACM SIGGRAPH Computer Graphics,  20(4), 269–278 (1986).
[Crossref]

Khouli, R. H. E.

M. Freed, J. A. D. Zwart, J. T. Loud, R. H. E. Khouli, K. J. Myers, M. H. Greene, J. H. Duyn, and A. Badano, “An anthropomorphic phantom for quantitative evaluation of breast MRI,” Med. Phys. 38(2), 743–753 (2011).
[Crossref] [PubMed]

Kilpelainen, M.

J. Hakkinen, J. Takatalo, M. Kilpelainen, M. Salmimaa, and G. Nyman, “Determining limits to avoid double vision in an autostereoscopic display: disparity and image element width,” J. Soc. Inf. Disp. May,  17(5), 443–444 (2009).
[Crossref]

Kirk, D.

E. Haines, P Hanrahan, R. L. Cook, J. Arva, D. Kirk, P. S. Heckbert, and A. S. Glassner, An overview of ray tracing (Academic Press Inc. I edition 1989).

Kniss, J. M.

K. Engel, M. Hadwinger, J. M. Kniss, C. R. Salama, and D. Weiskopf, Real-Time Volume Graphics (A K Peters1st edition 2006).

Krupinski, E.

E. Samei and E. Krupinski, The Handbook of Medical Image Perception and Techniques (Cambridge University, 1st edition 2010).

Kundel, H. L.

R. L. V. Metter, J. Beutel, and H. L. Kundel, Handbook of medical imaging (SPIE1st edition 2009).

Lacomis, J. M.

X. H. Wang, J. E. Durick, A. Lu, D. L. Herbert, C. R. Fuhrman, J. M. Lacomis, C. A. Britton, D. C. Strollo, S. S. Shang, S. K. Golla, and W. F. Good, “Compare display schemes for lung nodule CT screening,” J. Digital Imaging 24(3), 478–484 (2011).
[Crossref]

Lee, K.

K. C. Huang, J. C. Yang, C. L. Wu, K. Lee, and S. L. Hwang, “System-crosstalk effect on stereopsis human factor study for 3D displays,” SPIE: Stereoscopic Displays and Applications XXI, (2010).

Liang, H.

H. Liang, S. Park, B. D. Gallas, K. J. Myers, and A. Badano, “Image browsing in slow medical liquid crystal displays,” Acad Radiol. 15(3), 370–382 (2008).
[Crossref] [PubMed]

Loud, J. T.

M. Freed, J. A. D. Zwart, J. T. Loud, R. H. E. Khouli, K. J. Myers, M. H. Greene, J. H. Duyn, and A. Badano, “An anthropomorphic phantom for quantitative evaluation of breast MRI,” Med. Phys. 38(2), 743–753 (2011).
[Crossref] [PubMed]

Lu, A.

X. H. Wang, J. E. Durick, A. Lu, D. L. Herbert, C. R. Fuhrman, J. M. Lacomis, C. A. Britton, D. C. Strollo, S. S. Shang, S. K. Golla, and W. F. Good, “Compare display schemes for lung nodule CT screening,” J. Digital Imaging 24(3), 478–484 (2011).
[Crossref]

Lusk, E.

W. Gropp, E. Lusk, and A. Skjellum, Using MPI, Portable Parallel Programming with the Message-Passing Interface (The MIT PressII edition 1999).

Lydick, J. T.

H. P. Chan, M. M. Goodsitt, M. A. Helvie, L. M. Hadjiiski, J. T. Lydick, M. A. Roubidoux, J. E. Bailey, A. Nees, C. E. Blane, and B. Sahiner, “ROC study of the effect of stereoscopic imaging on assessment of breast lesions,” Med Phys. 32(4), 1001–1009 (2005).
[Crossref] [PubMed]

Marschner, S. R.

P. Shirley, M. Ashikhmin, S. R. Marschner, E. r., K. Sung, W. B. Thompson, and P. Willemsen, Fundamentals of Computer Graphics (A K Peters/CRCIInd edition 2005).

Messom, C. H.

C. H. Messom, “Abstract stereo vision controlled humanoid robot tool-kit,” 1st International Conference on Sensing TechnologyNovember, 21–23 (2005).

Metter, R. L. V.

R. L. V. Metter, J. Beutel, and H. L. Kundel, Handbook of medical imaging (SPIE1st edition 2009).

Myers, K.

H. H. Barrett and K. Myers, Foundations of Image Science (John Wiley & Sons, 1st edition, 2004).

Myers, K. J.

M. Freed, J. A. D. Zwart, J. T. Loud, R. H. E. Khouli, K. J. Myers, M. H. Greene, J. H. Duyn, and A. Badano, “An anthropomorphic phantom for quantitative evaluation of breast MRI,” Med. Phys. 38(2), 743–753 (2011).
[Crossref] [PubMed]

M. Freed, J. A. D. Zwart, P. Hariharan, K. J. Myers, and A. Badano, “Development and characterization of a dynamic lesion phantom for the quantitative evaluation of dynamic contrast-enhanced MRI,” Med. Phys. 38(10), 5601–5611 (2011).
[Crossref] [PubMed]

H. Liang, S. Park, B. D. Gallas, K. J. Myers, and A. Badano, “Image browsing in slow medical liquid crystal displays,” Acad Radiol. 15(3), 370–382 (2008).
[Crossref] [PubMed]

K. J. Myers and H. H. Barrett, “Addition of a channel mechanism to the ideal-observer model,” J. Opt. Soc. Am. A 4(12,) 2447–2457 (1987).
[Crossref] [PubMed]

Nees, A.

H. P. Chan, M. M. Goodsitt, M. A. Helvie, L. M. Hadjiiski, J. T. Lydick, M. A. Roubidoux, J. E. Bailey, A. Nees, C. E. Blane, and B. Sahiner, “ROC study of the effect of stereoscopic imaging on assessment of breast lesions,” Med Phys. 32(4), 1001–1009 (2005).
[Crossref] [PubMed]

Newell, M. S.

C. J. D’Orsi, D. J. Getty, R. M. Pickett, I. Sechopoulos, M. S. Newell, K. R. Gundry, S. R. Bates, R. M. Nishikawa, E. A. Sickles, A. Karellas, and E. M. D’Orsi, “Stereoscopic digital mammography: improved specificity and reduced rate of recall in a prospective clinical trial,” Radiology. 266(1), 81–88 (2013).
[Crossref]

Nishikawa, R. M.

C. J. D’Orsi, D. J. Getty, R. M. Pickett, I. Sechopoulos, M. S. Newell, K. R. Gundry, S. R. Bates, R. M. Nishikawa, E. A. Sickles, A. Karellas, and E. M. D’Orsi, “Stereoscopic digital mammography: improved specificity and reduced rate of recall in a prospective clinical trial,” Radiology. 266(1), 81–88 (2013).
[Crossref]

Noo, F.

A. Wunderlich and F. Noo, “New theoretical results on channelized hotelling observer performance estimation with known difference of class means,” IEEE Transactions on Nuclear Science,  60(1), 182–193 (2013).
[Crossref]

A. Wunderlich and F. Noo, “Estimation of channelized hotelling observer performance with known class means or known difference of class means,” IEEE Transactions on Medical Imaging 28(8), 1198–1207 (2009).
[Crossref] [PubMed]

A. Wunderlich, F. Noo, and M. Heilbrun, “Exact confidence intervals for channelized hotelling observer performance,” Proc. of SPIE, Medical Imaging: Image Perception, Observer Performance, and Technology Assessment8673 (2013).
[Crossref]

Nyman, G.

J. Hakkinen, J. Takatalo, M. Kilpelainen, M. Salmimaa, and G. Nyman, “Determining limits to avoid double vision in an autostereoscopic display: disparity and image element width,” J. Soc. Inf. Disp. May,  17(5), 443–444 (2009).
[Crossref]

Ogawa, M.

M. Funakoshi, K. Shidoji, and M. Ogawa, “Perception of absolute and relative distances in stereoscopic image,” SPIE: Stereoscopic Displays and Applications XXI, (2010).

Park, S.

L. Platisa, B. Goossens, E. Vanteenkiste, S. Park, B. D. Gallas, A. Badano, and W. Philips, “Channelized hotelling observers for the assessment of volumetric data sets,” J. Opt. Soc. Am. 28(6), 1145–1163 (2011).
[Crossref]

H. Liang, S. Park, B. D. Gallas, K. J. Myers, and A. Badano, “Image browsing in slow medical liquid crystal displays,” Acad Radiol. 15(3), 370–382 (2008).
[Crossref] [PubMed]

Petrick, N.

H. P. Chan, B. Sahiner, R. F. Wagner, and N. Petrick, “Classifier design for computer-aided diagnosis: Effects of finite sample size on the mean performance of classical and neural network classifiers,” Med. Phys. 26(12), 2654–2668 (1999).
[Crossref]

Philips, W.

L. Platisa, B. Goossens, E. Vanteenkiste, S. Park, B. D. Gallas, A. Badano, and W. Philips, “Channelized hotelling observers for the assessment of volumetric data sets,” J. Opt. Soc. Am. 28(6), 1145–1163 (2011).
[Crossref]

Pickett, R. M.

C. J. D’Orsi, D. J. Getty, R. M. Pickett, I. Sechopoulos, M. S. Newell, K. R. Gundry, S. R. Bates, R. M. Nishikawa, E. A. Sickles, A. Karellas, and E. M. D’Orsi, “Stereoscopic digital mammography: improved specificity and reduced rate of recall in a prospective clinical trial,” Radiology. 266(1), 81–88 (2013).
[Crossref]

D. J. Getty, R. M. Pickett, and C. J. D’Orsi, “Stereoscopic digital mammography: improving detection and diagnosis of breast cancer,” International Congress Series,  1230, 74–79 (2001).
[Crossref]

Platisa, L.

L. Platisa, B. Goossens, E. Vanteenkiste, S. Park, B. D. Gallas, A. Badano, and W. Philips, “Channelized hotelling observers for the assessment of volumetric data sets,” J. Opt. Soc. Am. 28(6), 1145–1163 (2011).
[Crossref]

Qu, J. Y.

Ringstad, G.

A. Abildgaard, A. K. Witwit, J. S. Karlsen, E. A. Jacobson, B. Tennoe, G. Ringstad, and P. D. Tonnessen, “An autostereoscopic 3D display can improve visualization of 3D models from intracranial MR angiography,” International Journal of Computer Assisted Radiology and Surgery 5(5), 549–554 (2010).
[Crossref] [PubMed]

Rolland, J. P.

Roubidoux, M. A.

H. P. Chan, M. M. Goodsitt, M. A. Helvie, L. M. Hadjiiski, J. T. Lydick, M. A. Roubidoux, J. E. Bailey, A. Nees, C. E. Blane, and B. Sahiner, “ROC study of the effect of stereoscopic imaging on assessment of breast lesions,” Med Phys. 32(4), 1001–1009 (2005).
[Crossref] [PubMed]

Sahiner, B.

H. P. Chan, M. M. Goodsitt, M. A. Helvie, L. M. Hadjiiski, J. T. Lydick, M. A. Roubidoux, J. E. Bailey, A. Nees, C. E. Blane, and B. Sahiner, “ROC study of the effect of stereoscopic imaging on assessment of breast lesions,” Med Phys. 32(4), 1001–1009 (2005).
[Crossref] [PubMed]

H. P. Chan, B. Sahiner, R. F. Wagner, and N. Petrick, “Classifier design for computer-aided diagnosis: Effects of finite sample size on the mean performance of classical and neural network classifiers,” Med. Phys. 26(12), 2654–2668 (1999).
[Crossref]

Salama, C. R.

K. Engel, M. Hadwinger, J. M. Kniss, C. R. Salama, and D. Weiskopf, Real-Time Volume Graphics (A K Peters1st edition 2006).

Salmimaa, M.

J. Hakkinen, J. Takatalo, M. Kilpelainen, M. Salmimaa, and G. Nyman, “Determining limits to avoid double vision in an autostereoscopic display: disparity and image element width,” J. Soc. Inf. Disp. May,  17(5), 443–444 (2009).
[Crossref]

Samei, E.

E. Samei and E. Krupinski, The Handbook of Medical Image Perception and Techniques (Cambridge University, 1st edition 2010).

Sechopoulos, I.

C. J. D’Orsi, D. J. Getty, R. M. Pickett, I. Sechopoulos, M. S. Newell, K. R. Gundry, S. R. Bates, R. M. Nishikawa, E. A. Sickles, A. Karellas, and E. M. D’Orsi, “Stereoscopic digital mammography: improved specificity and reduced rate of recall in a prospective clinical trial,” Radiology. 266(1), 81–88 (2013).
[Crossref]

Shang, S. S.

X. H. Wang, J. E. Durick, A. Lu, D. L. Herbert, C. R. Fuhrman, J. M. Lacomis, C. A. Britton, D. C. Strollo, S. S. Shang, S. K. Golla, and W. F. Good, “Compare display schemes for lung nodule CT screening,” J. Digital Imaging 24(3), 478–484 (2011).
[Crossref]

Shidoji, K.

M. Funakoshi, K. Shidoji, and M. Ogawa, “Perception of absolute and relative distances in stereoscopic image,” SPIE: Stereoscopic Displays and Applications XXI, (2010).

Shirley, P.

P. Shirley, M. Ashikhmin, S. R. Marschner, E. r., K. Sung, W. B. Thompson, and P. Willemsen, Fundamentals of Computer Graphics (A K Peters/CRCIInd edition 2005).

Sickles, E. A.

C. J. D’Orsi, D. J. Getty, R. M. Pickett, I. Sechopoulos, M. S. Newell, K. R. Gundry, S. R. Bates, R. M. Nishikawa, E. A. Sickles, A. Karellas, and E. M. D’Orsi, “Stereoscopic digital mammography: improved specificity and reduced rate of recall in a prospective clinical trial,” Radiology. 266(1), 81–88 (2013).
[Crossref]

Skjellum, A.

W. Gropp, E. Lusk, and A. Skjellum, Using MPI, Portable Parallel Programming with the Message-Passing Interface (The MIT PressII edition 1999).

Strollo, D. C.

X. H. Wang, J. E. Durick, A. Lu, D. L. Herbert, C. R. Fuhrman, J. M. Lacomis, C. A. Britton, D. C. Strollo, S. S. Shang, S. K. Golla, and W. F. Good, “Compare display schemes for lung nodule CT screening,” J. Digital Imaging 24(3), 478–484 (2011).
[Crossref]

Sung, K.

P. Shirley, M. Ashikhmin, S. R. Marschner, E. r., K. Sung, W. B. Thompson, and P. Willemsen, Fundamentals of Computer Graphics (A K Peters/CRCIInd edition 2005).

Takatalo, J.

J. Hakkinen, J. Takatalo, M. Kilpelainen, M. Salmimaa, and G. Nyman, “Determining limits to avoid double vision in an autostereoscopic display: disparity and image element width,” J. Soc. Inf. Disp. May,  17(5), 443–444 (2009).
[Crossref]

Tennoe, B.

A. Abildgaard, A. K. Witwit, J. S. Karlsen, E. A. Jacobson, B. Tennoe, G. Ringstad, and P. D. Tonnessen, “An autostereoscopic 3D display can improve visualization of 3D models from intracranial MR angiography,” International Journal of Computer Assisted Radiology and Surgery 5(5), 549–554 (2010).
[Crossref] [PubMed]

Thompson, W. B.

P. Shirley, M. Ashikhmin, S. R. Marschner, E. r., K. Sung, W. B. Thompson, and P. Willemsen, Fundamentals of Computer Graphics (A K Peters/CRCIInd edition 2005).

Tonnessen, P. D.

A. Abildgaard, A. K. Witwit, J. S. Karlsen, E. A. Jacobson, B. Tennoe, G. Ringstad, and P. D. Tonnessen, “An autostereoscopic 3D display can improve visualization of 3D models from intracranial MR angiography,” International Journal of Computer Assisted Radiology and Surgery 5(5), 549–554 (2010).
[Crossref] [PubMed]

Vanteenkiste, E.

L. Platisa, B. Goossens, E. Vanteenkiste, S. Park, B. D. Gallas, A. Badano, and W. Philips, “Channelized hotelling observers for the assessment of volumetric data sets,” J. Opt. Soc. Am. 28(6), 1145–1163 (2011).
[Crossref]

Wagner, R. F.

H. P. Chan, B. Sahiner, R. F. Wagner, and N. Petrick, “Classifier design for computer-aided diagnosis: Effects of finite sample size on the mean performance of classical and neural network classifiers,” Med. Phys. 26(12), 2654–2668 (1999).
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R. F. Wagner and D. G. Brown, “Unified SNR analysis of medical imaging system,” Phys. Med. Biol. 30(6), 489–518 (1985).
[Crossref]

Wang, X. H.

X. H. Wang, J. E. Durick, A. Lu, D. L. Herbert, C. R. Fuhrman, J. M. Lacomis, C. A. Britton, D. C. Strollo, S. S. Shang, S. K. Golla, and W. F. Good, “Compare display schemes for lung nodule CT screening,” J. Digital Imaging 24(3), 478–484 (2011).
[Crossref]

Weiskopf, D.

K. Engel, M. Hadwinger, J. M. Kniss, C. R. Salama, and D. Weiskopf, Real-Time Volume Graphics (A K Peters1st edition 2006).

Willemsen, P.

P. Shirley, M. Ashikhmin, S. R. Marschner, E. r., K. Sung, W. B. Thompson, and P. Willemsen, Fundamentals of Computer Graphics (A K Peters/CRCIInd edition 2005).

Witwit, A. K.

A. Abildgaard, A. K. Witwit, J. S. Karlsen, E. A. Jacobson, B. Tennoe, G. Ringstad, and P. D. Tonnessen, “An autostereoscopic 3D display can improve visualization of 3D models from intracranial MR angiography,” International Journal of Computer Assisted Radiology and Surgery 5(5), 549–554 (2010).
[Crossref] [PubMed]

Wu, C. L.

K. C. Huang, J. C. Yang, C. L. Wu, K. Lee, and S. L. Hwang, “System-crosstalk effect on stereopsis human factor study for 3D displays,” SPIE: Stereoscopic Displays and Applications XXI, (2010).

Wu, T. T.

Wunderlich, A.

A. Wunderlich and F. Noo, “New theoretical results on channelized hotelling observer performance estimation with known difference of class means,” IEEE Transactions on Nuclear Science,  60(1), 182–193 (2013).
[Crossref]

A. Wunderlich and F. Noo, “Estimation of channelized hotelling observer performance with known class means or known difference of class means,” IEEE Transactions on Medical Imaging 28(8), 1198–1207 (2009).
[Crossref] [PubMed]

A. Wunderlich, F. Noo, and M. Heilbrun, “Exact confidence intervals for channelized hotelling observer performance,” Proc. of SPIE, Medical Imaging: Image Perception, Observer Performance, and Technology Assessment8673 (2013).
[Crossref]

Yang, J. C.

K. C. Huang, J. C. Yang, C. L. Wu, K. Lee, and S. L. Hwang, “System-crosstalk effect on stereopsis human factor study for 3D displays,” SPIE: Stereoscopic Displays and Applications XXI, (2010).

Yaroslavsky, L. P.

Zafar, F.

F. Zafar, J. Dorband, and A. Badano, “Computational observer approach for the assessment of stereoscopic visualizations for 3D medical images,” Proc. SPIE, Medical Imaging: Image Perception, Observer Performance, and Technology Assessment, 2012.
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Zwart, J. A. D.

M. Freed, J. A. D. Zwart, J. T. Loud, R. H. E. Khouli, K. J. Myers, M. H. Greene, J. H. Duyn, and A. Badano, “An anthropomorphic phantom for quantitative evaluation of breast MRI,” Med. Phys. 38(2), 743–753 (2011).
[Crossref] [PubMed]

M. Freed, J. A. D. Zwart, P. Hariharan, K. J. Myers, and A. Badano, “Development and characterization of a dynamic lesion phantom for the quantitative evaluation of dynamic contrast-enhanced MRI,” Med. Phys. 38(10), 5601–5611 (2011).
[Crossref] [PubMed]

Acad Radiol. (1)

H. Liang, S. Park, B. D. Gallas, K. J. Myers, and A. Badano, “Image browsing in slow medical liquid crystal displays,” Acad Radiol. 15(3), 370–382 (2008).
[Crossref] [PubMed]

ACM SIGGRAPH Computer Graphics (1)

T. L. Kay and J. T. Kajuya, “Ray tracing complex scenes,” ACM SIGGRAPH Computer Graphics,  20(4), 269–278 (1986).
[Crossref]

IEEE Transactions on Medical Imaging (1)

A. Wunderlich and F. Noo, “Estimation of channelized hotelling observer performance with known class means or known difference of class means,” IEEE Transactions on Medical Imaging 28(8), 1198–1207 (2009).
[Crossref] [PubMed]

IEEE Transactions on Nuclear Science (1)

A. Wunderlich and F. Noo, “New theoretical results on channelized hotelling observer performance estimation with known difference of class means,” IEEE Transactions on Nuclear Science,  60(1), 182–193 (2013).
[Crossref]

International Congress Series (1)

D. J. Getty, R. M. Pickett, and C. J. D’Orsi, “Stereoscopic digital mammography: improving detection and diagnosis of breast cancer,” International Congress Series,  1230, 74–79 (2001).
[Crossref]

International Journal of Computer Assisted Radiology and Surgery (1)

A. Abildgaard, A. K. Witwit, J. S. Karlsen, E. A. Jacobson, B. Tennoe, G. Ringstad, and P. D. Tonnessen, “An autostereoscopic 3D display can improve visualization of 3D models from intracranial MR angiography,” International Journal of Computer Assisted Radiology and Surgery 5(5), 549–554 (2010).
[Crossref] [PubMed]

J. Digital Imaging (1)

X. H. Wang, J. E. Durick, A. Lu, D. L. Herbert, C. R. Fuhrman, J. M. Lacomis, C. A. Britton, D. C. Strollo, S. S. Shang, S. K. Golla, and W. F. Good, “Compare display schemes for lung nodule CT screening,” J. Digital Imaging 24(3), 478–484 (2011).
[Crossref]

J. Opt. Soc. Am. (1)

L. Platisa, B. Goossens, E. Vanteenkiste, S. Park, B. D. Gallas, A. Badano, and W. Philips, “Channelized hotelling observers for the assessment of volumetric data sets,” J. Opt. Soc. Am. 28(6), 1145–1163 (2011).
[Crossref]

J. Opt. Soc. Am. A (2)

J. Soc. Inf. Disp. (1)

J. Hakkinen, J. Takatalo, M. Kilpelainen, M. Salmimaa, and G. Nyman, “Determining limits to avoid double vision in an autostereoscopic display: disparity and image element width,” J. Soc. Inf. Disp. May,  17(5), 443–444 (2009).
[Crossref]

Med Phys. (1)

H. P. Chan, M. M. Goodsitt, M. A. Helvie, L. M. Hadjiiski, J. T. Lydick, M. A. Roubidoux, J. E. Bailey, A. Nees, C. E. Blane, and B. Sahiner, “ROC study of the effect of stereoscopic imaging on assessment of breast lesions,” Med Phys. 32(4), 1001–1009 (2005).
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Med. Phys. (3)

H. P. Chan, B. Sahiner, R. F. Wagner, and N. Petrick, “Classifier design for computer-aided diagnosis: Effects of finite sample size on the mean performance of classical and neural network classifiers,” Med. Phys. 26(12), 2654–2668 (1999).
[Crossref]

M. Freed, J. A. D. Zwart, J. T. Loud, R. H. E. Khouli, K. J. Myers, M. H. Greene, J. H. Duyn, and A. Badano, “An anthropomorphic phantom for quantitative evaluation of breast MRI,” Med. Phys. 38(2), 743–753 (2011).
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M. Freed, J. A. D. Zwart, P. Hariharan, K. J. Myers, and A. Badano, “Development and characterization of a dynamic lesion phantom for the quantitative evaluation of dynamic contrast-enhanced MRI,” Med. Phys. 38(10), 5601–5611 (2011).
[Crossref] [PubMed]

Opt. Express (2)

Perceptual and Motor Skills (1)

A. Badano, “Predicting perceived image quality: a critique of Lin and Kuo,” Perceptual and Motor Skills 114(1), 236–238 (2012).
[Crossref] [PubMed]

Phys. Med. Biol. (1)

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Radiology. (1)

C. J. D’Orsi, D. J. Getty, R. M. Pickett, I. Sechopoulos, M. S. Newell, K. R. Gundry, S. R. Bates, R. M. Nishikawa, E. A. Sickles, A. Karellas, and E. M. D’Orsi, “Stereoscopic digital mammography: improved specificity and reduced rate of recall in a prospective clinical trial,” Radiology. 266(1), 81–88 (2013).
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[Crossref]

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A. Wunderlich, F. Noo, and M. Heilbrun, “Exact confidence intervals for channelized hotelling observer performance,” Proc. of SPIE, Medical Imaging: Image Perception, Observer Performance, and Technology Assessment8673 (2013).
[Crossref]

A. Wunderlich, “Statistical Software for Image Quality Assessment with Model Observers,” https://code.google.com/p/iqmodelo/ .

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Figures (11)

Fig. 1
Fig. 1 Visual representation of how existing Ideal 2D and 3D model observers can be modeled using our approach. Images have been contrast-enhanced for improved visibility.
Fig. 2
Fig. 2 Stereoscopic image generation for our Stereo V differs from existing 2D and 3D model observer approaches. The additional step includes the volume rendering stage. Output image data is dependent on the visualization models and projection matrices used for rendering. Images have been contrast-enhanced for improved visibility.
Fig. 3
Fig. 3 Voxelized rendering of white noise background using S(g){R0{xAbs, worthographic}, {Ω1 > 1, Ω2 = 1, Ω3 = ∅, Ω4 = [1,1,0]}} where α=0.01. Voxels have been deliberately set larger than pixels to demonstrate that when voxels do not align with the rendering plane, blurring artifacts are added to the output image which is a consequence of rendering algorithms and added perspective.
Fig. 4
Fig. 4 Four stages of observer performance calculation.
Fig. 5
Fig. 5 Two backgrounds used during the study generated using Maximum Intensity Projection technique. (Top row) 5 samples of the Gaussian white noise background. (Bottom row) 5 samples of the lumpy background with 800 lumps, 0.03 lump amplitude and 3 lump variance. These images are generated at 320 × 320 resolution and contrast enhanced for improved visibility.
Fig. 6
Fig. 6 Ideal 2D T vs. Ideal 2D E with different dataset sizes for white noise background. We show that using 160,000 images for calculating Ideal 2D E provides a reasonably close SNR estimate for 32×32 image size. Same data plotted differently to highlight the asymptotic relationship [32] converging towards the truth value as number of samples are increased.
Fig. 7
Fig. 7 Schematic visualization of the two covariance matrices for the stereoscopic image dataset. For K, we can visualize that the bottom left and top right quadrants show correlations between the stereo pairs. In case of K′, it’s better to think in terms of directions and how the pixels in the image relate to neighboring pixels. Some example covariance matrices are presented in Fig. (11).
Fig. 8
Fig. 8 Top left tile-section of the empirical covariance for Stereo2D(β = 0) used to calculate empirical SNR is presented (left image). It should be noted that Stereo2D(β = 0) is equivalent to the Ideal 2D T case. Ideal 2D T dataset image size is set to 32×32 while the Stereo2D(β = 0) dataset image size is 32×64.
Fig. 9
Fig. 9 White noise vs. lumpy backgrounds stereoscopic images (β = 30, size = 32 × 64) with embedded Gaussian signal of the specified amplitude(a′) rendered using MIP for white noise and lumpy backgrounds.
Fig. 10
Fig. 10 SNR results for Stereo V (β) using two different backgrounds using xMIP. The results show progressive gain in Ideal Linear Stereoscopic Observer performance as the stereoscopic angle is increased. The uncertainty intervals are smaller than 4 × 10−2 due to the large number of images used for each trial.
Fig. 11
Fig. 11 K′ covariance matrix for white noise (1 st and 2 nd row) and lumpy (3 rd and 4 th row) backgrounds at different stereo angles (β) using xMIP. The peak in the center represents the average of correlations in or nearby the diagonal elements in K, and the neighboring correlations along that entire diagonal in every direction. Since K′ is symmetric, the top and bottom peaks both represent correlations between the left and the right images. Increasing β shifts the perspective to add unique information in each of the images resulting in reduced intensity of the correlation between the stereo pair while the correlation spreads to a larger neighborhood of pixels. As β increases, the correlation decrease can be noticed in the color values, while the spread of correlation is represented by the spread of the top and bottom peaks.

Tables (1)

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Table 1 A description of symbols used in defining the model observer and its components.

Equations (28)

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H 1 : g = b + s ,
H 2 : g = b ,
Δ ( g ) = pr ( g | H 2 ) pr ( g | H 1 ) ,
SNR ^ = s t K L 1 s ,
L = L 1 L 2 L J ,
g = H f + noise .
g 1 M S ( g 1 a 1 , g 1 a 2 , , g 1 a b ) T ( L 1 a 1 , L 1 a 2 , , L 1 a b ) ,
g = S ( g ) { R 0 ( x , w ) , Ω } ,
Ω = { Ω 1 , Ω 2 , Ω 3 , } .
R 0 ( x , w , λ , t ) = R e ( x , w , λ , t ) + Γ ,
R 0 ( x , w ) = R e ( x , w ) .
w u , v Perspective = ( u ( u 2 + v 2 + 1 ) 2 , v ( u 2 + v 2 + 1 ) 2 , 1 ( u 2 + v 2 + 1 ) 2 ) ,
w u , v Orthographic = ( 0 , 0 , 1 ) ,
x MIP ( w ) = max { Color ( x 1 w ) , Color ( x 2 w ) , Color ( x n w ) } ,
x Abs ( w ) = ψ { ψ { ψ { x 1 w , x 2 w } , x 3 w } , x n w } ,
ψ ( x i w , x i + 1 w ) = Color ( x 1 w ) * α x i w + Color ( x i + 1 w ) * ( 1 α x i + 1 w ) ,
L i = T ( g i ) = g i .
g Ideal 2 D E = S ( g ) { R 0 { x Abs , w orthographic } , { Ω 1 = 1 , Ω 2 = 1 } } ,
L g = L n / 2 ,
g Stereo V = S ( g ) { R 0 { x MIP , w orthographic } , { Ω 1 = 1 , Ω 2 = 2 , Ω 3 = β , Ω 4 = [ 0 , 1 , 0 ] } } ,
L = L l L r ,
SNR = γ 2 SNR ^ ,
γ 2 = 2 π N H 2 + N H 1 1 B ( N H 2 + N H 1 p 1 2 , 1 2 ) ,
K L ( x , y ) = i = 0 n ( L x i L x i ¯ ) ( L y i L y i ¯ ) n 1 ,
K p , q = 0 i N K i + p , i + q n count ( K i + p , i + q n ) ,
0 mod ( i , n ) + p < n ,
0 j / n + q < m ,
g Stereo 2 D = S ( g ) { R 0 { x Abs , w orthographic } , { Ω 1 = 1 , Ω 2 = 2 , Ω 3 = β , Ω 4 = [ 0 , 0 , 0 ] } } .

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