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Compputational Imaggingg: A Survey of Medical and Scientific Applications Douglas Lanman*Douglas Lanman * presented by Douglas Lanman, adapted from slides by Marc Levoy: http://graphics.stanford.edu/talks/ 1Computational Imaging in the Sciences Driving Factors:  new instruments lead to new discoveries (e g Leeuwenhoek + microscopy Æ microbiology)(e.g., Leeuwenhoek + microscopy Æ microbiology)  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 processing has led to a revolution in medical g p g and scientific data collection (e.g., CT, MRI, PET, remote sensing, etc.) 2Computational Imaging in the Sciences Medical Imaging:  transmission tomography (CT)  reflection tomography (ultrasound) Geophysics:  borehole tomography  seismic reflection surveying seismic reflection surveying Applied Physics:  diffuse optical tomography diffuse optical tomography  diffraction tomography  scattering and inverse scattering Biology:  confocal microscopy  deconvolution microscopy Astronomy:  coded-aperture imaging  interferometric imaging Remote Sensing:  multi-perspective panoramas  synthetic aperture radar synthetic aperture radar Optics:  wavefront coding wavefront coding  light field photography  holography 3Medical Imaging Overview:  (non-invasive) reconstruction of internal structures of living organisms  generally involves solving an inverse problem  ild di l d h li iincludes: radiology, endoscopy, thermal imaging, miicroscopy, etc. Methods:  tomography (includes: CT MRI PET ultrasound)tomography (includes: CT, MRI, PET, ultrasound)  electroencephalography (EEG) and magnetoencephalography (MEG) Key Issues:Key Issues:  safety (e.g., ionizing radiation)  minimally invasive  tempporal and sppatial 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 image of an object by transmission or creates a cross sectional image of an object by transmission or reflection data collected by illuminating from many directions PParall llell-bbeam TTomographhy FFan-bbeam TTomographhy * Fig 3.2 and 3.3 in A.C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging, 1988 5 Courtesy of A. C. Kak and Malcolm Slaney. Used with permission.Simulated Tomograms 0 50 100 150 0 50 100 150 Rotation Angle Rotation Angle density function parallel-beam projections fan-beam projections (Radon transform) 6Fourier 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 7Reconstruction: Filtered Backprojection P (t) Gθ(ω) Pθ(t) g(x,y) x y Pθ(t,s) Fourier Projection-Slice Theorem:  F-1{{Gθθ((ω)})} = Pθθ(()t)  add slices Gθ(ω) into {u,v} at all angles θ and inverse transform to yield g(x,y)  add 2D backprojections Pθ(t) into {x,y} at all angles θangles θ fy fx * Left: Fig. 3.6 in A.C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging, 1988 8 Courtesy of A. C. Kak and Malcolm Slaney. Used with permission.Sampling Requirements and Limitations v 1/ω |ω| u ω ω correctiion filter (Ram-Lak) effect of occlusions “h“hot spot”” fil Diagrams courtesy of Marc Levoy. original density 30 deg. spacing 5 deg. spacing 1 deg. spacing 9Medical Applications of Tomography Video still removed due to copyright restrictions. See Tuttle9955i. “CT at max speed.” March 1, 2008.p , http://www.youtube.com/watch?v=2CWpZKuy-NE Medical images removed due to copyright restrictions. bbone reconsttructiti on td lsegmented vessels 10 © Wikimedia Foundation License CC BY-SA. Thiscontent is excluded from our Creative Commons license.For more information, see http://ocw.mit.edu/fairuse.How to Eliminate Moving Parts? Prior CT Generations: Time-sequential Projections Prior CT Generations: Time sequential Projections  moving parts  synchronization and exposure timing  costs (up-front, operating, and maintenance)  dynamic scenes (RF interference, switching costs for X-ray tubes) 11How to Eliminate Moving Parts? Our Solution: Simultaneous ProjectionsOur Solution: Simultaneous Projections  no moving parts  no synchronization Æ uses “always-on” sources  lower costs (simpler mechanical construction and X-ray sources)  well-suited for high-speed capture of dynamic scenes 12Shield Fields: Si l P j i i A i M k Simultaneous Projections using Attenuating Masks allows spatial heterodyning 13 our “magic” pattern:Single-shot PhotoShield Fields: Si l Pji iA iMk Simultaneous Projections using Attenuating Masks 14Geophysical Applications Two diagrams removed due to copyright restrictions.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 15Geophysical Applications Diagram removed due to copyright restrictions. Borehole tomography. From Reynolds, J.M., An Introduction to Applied and Environmental 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/frap gments/color_mos_red g uced/010g_MOS.jpg mapping ancient Rome using explosions in the subways and 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 16t t t tOptical Diffraction Tomography (ODT) limit as λ→0 (relative to object size) corresponds to Fourier Slice Theorem p weakly-refractive


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MIT MAS 531 - Computational Imaging

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