# Bioimage Informatics

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1 Bioimage Informatics Lecture 5, Spring 01 Fundamentals of Fluorescence Microscopy (II) Bioimage Data Analysis (I): Basic Operations Lecture 5 January 5, 01 1

2 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

3 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

4 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

5 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

6 Microscope as a Linear System A light microscope is a linear system whose impulse response is an Airy disk. 6

7 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 I I J r 1 0 r J 1 (x) is a Bessel function of the first kind. Detailed derivation is given in Born & Wolf, Principles of Optics, 7th ed., pp

8 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

9 Numerical aperture (NA) determines microscope resolution and light collection power. Numerical Aperture NA n sin n: refractive index of the medium between the lens and the specimen : half of the angular aperture 9

10 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 10

11 Different Definition of Light Microscopy Resolution Limit (Demo) Rayleigh limit D 061. NA Sparrow limit D 047. NA 11

12 Field of View (Demo) Field of view: the region that is visible under a microscope If characterized in diameter D If characterized in area S Field diaphragm diameter M Field diaphragm diameter M 1

13 Depth-of-Field Depth-of-field: the axial distance (depth) in the specimen that appears in focus in the image. d tot n NA n M NA e 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

14 Example: Depth-of-Field Smaug1 mrna-silencing foci respond to NMDA and modulate synapse formation, M. Baez, et al, JCB, 195: ,

15 Image Intensity: Light Collecting Power For transmitted light I NA M For epi-fluorescence I NA M

16 The distance between the objective lens and the specimen. Working Distance Working distance does not directly influence imaging but may determine how images can be collected. 16

17 Summary: High Resolution Microscopy Size of cellular features are typically on the scale of a micron or smaller. To resolve such features require - Shorter wavelength (e.g. electron microscopy) - High numerical aperture (for resolution) - High magnification (for spatial sampling) D 061. NA 17

18 Summary: High Resolution Microscopy Higher magnification and higher numerical aperture mean - Smaller field of view S Field diaphragm diameter M - Smaller depth of field d tot n NA n e M NA - Lower light collection power I NA M - Smaller working distance 18

19 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

20 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 Office: C119 Hamerschlag Hall 0

21 Where & How to Get Image Data The number of open image repositories is constantly increasing. OME: open microscopy environment JCB DataViewer ASCB Cell Image Library 1

22 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

23 Basic Concept of Image Filtering (I) Application I: noise suppression original noise added σ= σ=10 σ=0 3

24 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): , Gonzalez & Woods, DIP /e 4

25 Basic Concept of Image Filtering (III) Gonzalez & Woods, DIP 3/e

26 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 sa tb sa tb 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 6

27 Gaussian kernel in 1D x 1 Gx; e First order derivative x Gx; e 3 Second order derivative Gaussian Filter (I) x x x x G x; e Gx,y ; x, y e x y x y x y 7

28 Gaussian Filters (II) Some basic properties of a Gaussian filter - It is a low pass filter - It is separable x 1 F e e x y y x Gx,y ; x, y e e e x y x y x y x y 8

29 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 9

30 Combination of Noise Suppression and Gradient Estimation (I) Implementation I x i,j 1 1 I i,j I i,j Ii,j1Ii,j1 Iy i,j Notation: J: raw image; I: filtered image after convolution with Gaussian kernel G. A basic property of convolution G J G J I G I G Ix J Iy J x x x y y y 30

31 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 31

32 Basic Image Operations Reading an imaging Accessing individual pixels Setting a region of interest (ROI) Writing an image 3

33 Questions? 33

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