Comp putational Imag ging g A Survey of Medical and Scientific Applications Douglas Lanman Lanman presented by Douglas Lanman adapted from slides by Marc Levoy http graphics stanford edu talks 1 Computational Imaging in the Sciences Driving Factors new instruments lead to new discoveries e g Leeuwenhoek microscopy microbiology e g Q most important instrument in last century A the digital computer What is Computational Imagining according to B K P Horn imaging methods in which computation is inherent in image formation digital g p processing g has led to a revolution in medical and scientific data collection e g CT MRI PET remote sensing etc 2 Computational Imaging in the Sciences Medical Imaging transmission tomography CT reflection tomography ultrasound Astronomy coded aperture imaging interferometric imaging Geophysics borehole tomography seismic reflection surveying Remote Sensing multi perspective panoramas synthetic aperture radar Applied Physics diffuse optical tomography diffraction tomography scattering and inverse scattering Optics wavefront coding light field photography holography Biology confocal microscopy deconvolution microscopy 3 Medical Imaging Overview non invasive reconstruction of internal structures of living organisms generally involves solving an inverse problem includes i l d radiology di l endoscopy d thermal h l iimaging i miicroscopy etc Methods tomography includes CT CT MRI MRI PET PET ultrasound electroencephalography EEG and magnetoencephalography MEG Key Issues safety e g ionizing radiation minimally invasive temp poral and sp patial resolution cost to a lesser degree Two brain MRI images removed due to copyright restrictions 4 What is Tomography Definition imaging by sectioning from Greek tomos a section or cutting creates a cross sectional cross sectional image of an object by transmission or reflection data collected by illuminating from many directions Parallllell b beam Tomograph hy Fan b beam Tomograph hy Fig 3 2 and 3 3 in A C Kak and M Slaney Principles of Computerized Tomographic Imaging 1988 Courtesy of A C Kak and Malcolm Slaney Used with permission 5 Simulated Tomograms 0 density function 50 100 Rotation Angle 150 parallel beam projections Radon transform 0 50 100 Rotation Angle 150 fan beam projections 6 Fourier Projection Slice Theorem Image Wikipedia Projection Slice Theorem retrieved on 11 03 2008 public domain A C Kak and M Slaney Principles of Computerized Tomographic Imaging 1988 7 Reconstruction Filtered Backprojection G P t g x y y P t s x Courtesy of A C Kak and Malcolm Slaney Used with permission Fourier Projection Slice Theorem F 1 G P t add slices G into u v at all angles and inverse transform to yield g x y add 2D backprojections P t into x y at all angles fy fx Left Fig 3 6 in A C Kak and M Slaney Principles of Computerized Tomographic Imaging 1988 8 Sampling Requirements and Limitations v 1 u hot spot h Diagrams courtesy of Marc Levoy original density 30 deg spacing correctiion filter fil Ram Lak 5 deg spacing effect of occlusions 1 deg spacing 9 Medical Applications of Tomography Video still removed due to copyright restrictions See Tuttle9955i CT at max speed p March 1 2008 http www youtube com watch v 2CWpZKuy NE Medical images removed due to copyright restrictions Wikimedia Foundation License CC BY SA This content is excluded from our Creative Commons license For more information see http ocw mit edu fairuse bone reconsttructi tion t d vessels l segmented 10 How to Eliminate Moving Parts Prior CT Generations Time Time sequential sequential Projections moving parts synchronization and exposure timing costs up front operating and maintenance dynamic scenes RF interference switching costs for X ray tubes 11 How to Eliminate Moving Parts Our Solution Simultaneous Projections no moving parts no synchronization uses always on sources lower costs simpler mechanical construction and X ray sources well suited for high speed capture of dynamic scenes 12 Shield Fields Si l Simultaneous P Projections j i using i A Attenuating i M Masks k our magic pattern 13 allows spatial heterodyning Shield Fields Si l Simultaneous P Projections j i using i A Attenuating i M Masks k Single shot Photo 14 Geophysical Applications Two diagrams removed due to copyright restrictions Borehole tomography and map of seismosaurus From Reynolds J M An Introduction to Applied and Environmental Geophysics Wiley 1997 mapping a seismosaurus in sandstone using microphones in 4 boreholes and explosions along radial lines Borehole Tomography receivers measure end to end travel time reconstruct to find velocities in intervening cells must use limited angle reconstruction methods e g ART Slide derived from Marc Levoy 15 Geophysical Applications Diagram removed due to copyright restrictions Borehole tomography From Reynolds J M An Introduction to Applied and Environmental Geophysics Wiley 1997 Photo removed due to copyright restrictions Stone map fragment from Stanford Forma Urbis Romae Project http formaurbis stanford edu fra p g gments color mos red uced 010g MOS jpg mapping ancient Rome using explosions in the subways and microphones along the streets Borehole Tomography receivers measure end to end travel time reconstruct to find velocities in intervening cells must use limited angle reconstruction methods e g ART Slide derived from Marc Levoy 16 Optical Diffraction Tomography ODT limit as 0 relative to object size corresponds p to Fourier Slice Theorem Courtesy of A C Kak and Malcolm Slaney Used with permission weakly refractive media using coherent plane wave illumination the amplitude and phase of the forward scattered field can be d described ib d using i tthe h F Fourier i Diff Diffraction ti Th Theorem such h tthat h t F scattered field arc in F object repeat for multiple wavelength use F 1 to reconstruct volume broadband hologram will yield 3D structure i e refraction indices Figures from A C Kak and M Slaney Principles of Computerized Tomographic Imaging 1988 Slide derived from Marc Levoy 17 Optical Diffraction Tomography ODT synthetic ODT reconstruction example P Guo A J Devaney and Optical Society of America This content is excluded from our Creative Commons license For more information see http ocw mit edu fairuse Courtesy of A C Kak and Malcolm Slaney Used with permission weakly refractive media using coherent plane wave illumination the amplitude and phase of the forward scattered field can be d described ib d using i tthe h F Fourier i Diff