Bioimage Informatics Lecture 5 Spring 2012 Fundamentals of Fluorescence Microscopy II Bioimage Data Analysis I Basic Operations Lecture 5 January 25 2012 1 Outline Performance metrics of a microscope Basic image analysis open sources of images Basic image analysis image filtering Basic image analysis image intensity derivative calculation Project assignment 1 2 Performance metrics of a microscope Basic image analysis open sources of images Basic image analysis image filtering Basic image analysis image intensity derivative calculation Project assignment 1 3 Performance Metrics of a Light Microscope Resolution the smallest feature distance that can be resolved Field of view the area of a specimen that can be observed and recorded in an image Depth of field the axial distance depth range in the specimen that appears in focus in an image Light collection power determines image brightness 4 Basic Concept of a Linear System A system is said to be linear if it satisfies the following two conditions Homogeneity Additivity r t S y t A linear system can be characterized in the time domain by its impulse response A properly built and aligned microscope can be accurately modeled as a linear system 5 Microscope as a Linear System A light microscope is a linear system whose impulse response is an Airy disk http micro magnet fsu edu primer java imageformation airydiskformation index html 6 Airy Disk Airy after George Biddell Airy disk is the diffraction pattern of a point feature under a circular aperture It has the following form 2J 1 r I I 0 r 2 J1 x is a Bessel function of the first kind Detailed derivation is given in Born Wolf Principles of Optics 7th ed pp 439 441 7 Microscope Image Formation PSF OTF The impulse response of the microscope is called its point spread function PSF The transfer function of a microscope is called its optical transfer function OTF The PSF of a properly built and aligned microscopy is an Airy Disk 8 Numerical Aperture Numerical aperture NA determines microscope resolution and light collection power NA n sin n refractive index of the medium between the lens and the specimen half of the angular aperture 9 Microscope Image Formation Microscope image formation can be modeled as a convolution with the PSF I x y O x y psf x y F I x y F O x y F psf x y http micro magnet fsu edu primer java mtf airydisksize index html 10 Different Definition of Light Microscopy Resolution Limit Demo Rayleigh limit Sparrow limit 0 61 D NA 0 47 D NA http www microscopy fsu edu primer java imageformation rayleighdisks index html 11 Field of View Demo Field of view the region that is visible under a microscope If characterized in diameter D Field diaphragm diameter M If characterized in area Field diaphragm diameter 2 S M2 http micro magnet fsu edu primer java microscopy diaphragm index html 12 Depth of Field Depth of field the axial distance depth in the specimen that appears in focus in the image dtot n n e 2 NA M NA n refractive index of the medium between the lens and the specimen emission wavelength M magnification NA numerical aperture e smallest resolvable distance in the image plane 13 Example Depth of Field Smaug1 mRNA silencing foci respond to NMDA and modulate synapse formation M Baez et al JCB 195 1141 1157 2011 14 Image Intensity Light Collecting Power For transmitted light 2 NA I M2 For epi fluorescence 4 NA I 2 M http micro magnet fsu edu primer anatomy imagebrightness html 15 Working Distance The distance between the objective lens and the specimen Working distance does not directly influence imaging but may determine how images can be collected 16 Summary High Resolution Microscopy Size of cellular features are typically on the scale of a micron or smaller To resolve such features require 0 61 D NA Shorter wavelength e g electron microscopy High numerical aperture for resolution High magnification for spatial sampling 17 Summary High Resolution Microscopy Higher magnification and higher numerical aperture mean Field diaphragm diameter 2 Smaller field of view S M2 Smaller depth of field dtot Lower light collection power n NA2 n e M NA NA 2 I M2 Smaller working distance 18 Performance metrics of a microscope Basic image analysis open sources of images Basic image analysis image filtering Basic image analysis image intensity derivative calculation Project assignment 1 19 A Few Words about MATLAB There are many excellent tutorials online There are many excellent reference books It is worthwhile to invest some time on learning MATLAB Please bring your questions to our teaching assistant Anuparma Kuruvilla Email anupamak andrew cmu edu Office C119 Hamerschlag Hall 20 Where How to Get Image Data The number of open image repositories is constantly increasing OME open microscopy environment http www openmicroscopy org JCB DataViewer ASCB Cell Image Library 21 Performance metrics of a microscope Basic image analysis open sources of images Basic image analysis image filtering Basic image analysis image intensity derivative calculation Project assignment 1 22 Basic Concept of Image Filtering I Application I noise suppression original noise added 2 10 20 23 Basic Concept of Image Filtering II Application II image conditioning Canny J A Computational Approach To Edge Detection IEEE Trans Pattern Analysis and Machine Intelligence 8 6 679 698 1986 Gonzalez Woods DIP 2 e 24 Basic Concept of Image Filtering III Gonzalez Woods DIP 3 e Basic Concept of Image Filtering IV Image filtering in the spatial domain a b a b w s t f x s y t w s t f x s y t w x y f x y s a t b s a t b f x y w x y g x y g x y w x y f x y G u v W u v F u v http www imageprocessingplace com 26 Gaussian Filter I Gaussian kernel in 1D x 1 G x e 2 2 2 2 G x y x y 1 2 x y e x2 y2 2 x 2 2 y 2 First order derivative x2 2 2 x e 3 2 Second order derivative G x x G x e 3 2 x2 2 2 x2 1 2 27 Gaussian Filters II Some basic properties of a Gaussian filter It is a low pass filter 1 e 2 x2 2 2 F e 2 2 2 2 It is separable G x y x 2 1 y x e y x2 y2 2 x 2 2 y 2 1 2 x e x2 2 x 2 1 2 y e y2 2 y 2 28 Performance metrics of a microscope Basic image analysis open sources of images Basic image analysis image filtering Basic image analysis image intensity derivative calculation Project assignment 1 29 Combination of Noise Suppression and Gradient Estimation I Implementation I x i j I i 1 j I i 1 j 2 I i j 1 I i j 1 I y i j 2 Notation J raw image I filtered image after convolution with Gaussian kernel G A basic property of convolution G J I …