Lecture 3 Digital image processing.

Transcription

1 Lecture 3 Digital image processing. MI_L3 1

2 Analog image digital image 2D image matrix of pixels scanner reflection mode analog-to-digital converter (ADC) digital image MI_L3 2

3 The process of converting a continuous physical image into digital image MI_L3 3

4 Concept of blurring The blur of on individual object point Intensity distribution of the Gaussian spot MI_L3 4

5 Blur distribution patterns I C = 1 I I 1 2 MI_L3 5

6 Overlap between adjacent Gaussian spots How to quantify the blur? MI_L3 6

7 Mathematical description Fourier Analysis Trigonometric functions are periodic functions sin(x + 2π) = sin(x) Periodic phenomenon is a function of time and is characterize by the period (T) or the frequency (f = 1/T) Trigonometric function period = 2π angle Recalculation sin(angle) = sin(2π*t/t) = sin(2π*f*t) A(t) = A0*sin(2π*f*t) = A0*sin(ω*t) ω angular (circular) frequency ω = 2π*f A0 amplitude (maximum value) MI_L3 7

8 Time domain representation and frequency domain presentation Amplitude [a.u.] Amplitude [a.u.] y 1 =2sin(2πx) time [s] y 2 =3sin(4πx) time [s] 10 Amplirude [a.u.] Amplitude [a.u] frequency [Hz] frequncy [Hz] Amplitude [a.u.] Amplitude [a.u.] y 3 =4sin(6πx) time [s] y 4 =y 1 +y 2 +y time [s] Amplitude [a.u.] Amplitude [a.u.] frequnecy [Hz] frequency [Hz] Summation of waves A(t) = A1(t) + A2(t) + A2(t) The identification of the frequency components is called spectral (Fourier, harmonic) analysis. Fourier (harmonic) analysis of this pattern can be performed without previous knowledge of these individualized components and yields the frequency spectrum. The magnitude at each frequency describes the relative contribution of that frequency to the original waveform. MI_L3 8

9 Fourier (harmonic) analysis mathematical formula f(t) = 1 2 A 0 + N A sin(2π * n * f * t) n n 1 = N B n = B1 + B2 + B3 + + BN n= 1 f1 = 1*f fundamental frequency (1 st harmonic) f2 = 2*f 2 nd harmonic f3 = 3*f 3 rd harmonic fn = n*f n th harmonic 20 Amplitude [a.u.] ,500 1,505 1,510 1,515 1,520 time [s] Amplitude [a.u.] "A" frequency [Hz] MI_L3 9

10 Fourier analysis on an image t (time) x (position = n* x) T (period) size of the image L = N* x x = L/N Fundamental frequency (1 st harmonic) Time f1 = 1/T Image f1 = 1/L fn (time frequency) = n/t sn (spatial frequency) = n/l Units [t] = s [f] = 1/s = Hz [x] = mm, cm [s] = cycles(periods)/mm, lp/mm, lp/cm MI_L3 10

11 Jean Baptiste Fourier and his Fourier transform MI_L3 11

12 Modulation Transfer Function (MTF) of Contrast Transfer Function (CTF) Sampling pixel size MI_L3 12

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16 Effect of blur on the contrast of objects of different size MI_L3 16

17 File Format DICOM Digital Imaging and Communications in Medicine is a standard for handling, storing, printing, and transmitting information in medical imaging Image 1024*1024 pixels 256 grey scale levels 8 bits/pixels 1 MB grey scale levels 14 bits/pixel 2 MB 1 Byte = 8 bits Digital camera ~3000*3000 = 9*10 6 pixels Color image x3 *.TIF Tagged Image File (graphic artist) *.GIF Graphical Interchange Format (internet - 8*3 bits) *.BMP Bip-Mapped (Microsoft) *.JPEG Joint Photographics Experts Group (compression) MI_L3 17

18 JPEG compression - 16:1 or 40:1 BMP 8 bits/pixel, GIF 4.96 bits/pixel, TIF 8.08 bits/pixel MI_L3 18

19 Histogram An image and its gray-level histogram MI_L3 19

20 Point operation single input image into a single output image Effect of the point operation on the histogram Gray-scale transformation function - f(d) MI_L3 20

21 Histogram equalization Corresponding histogram (red) and cumulative histogram (black) MI_L3 21

22 Histogram equalization MI_L3 22

23 Photometric calibration Image digitizer has a nonlinear relationship between its input film density and output gray level Image before calibration Image after calibration MI_L3 23

24 Algebraic Operations Background subtraction MI_L3 24

25 Geometric Operations Chromosome map Original After straightened MI_L3 25

26 Filtering of the image Removal of small blobs Extraction and grouping of linear objects MI_L3 26

27 Correction of uneven illumination Noise filtering Edge enhancement MI_L3 27

28 Segmentation of images Separation of connected blobs Segmentation of digital elevation model MI_L3 28

29 Histogram based classification Feature space clustering MI_L3 29

30 Extraction of grid lines MI_L3 30

31 Quantitative measurements Pattern spectrum or Analysis of directions MI_L3 31

32 Texture analysis MI_L3 32