Digital image basics

1. Digital image basics • Human vision perception system • Image formation • Human vision property and model • Image acquisition • Image transform • Image quality • Connected components • Image sensing • Image formats

2. 1. Human vision

3. 1. Human vision (cont’d) • Two types of receptors • -- Cones (fovea): sensitive to brightness and color • - 7M • - Cone-vision (photopic, bright-light vision) • -- Rod (cell): sensitive to low-level illumination • - 100M • - Rod-vision (scopotic, dim-light vision)

4. 2. Image perception and formation

5. 3. Vision property

6. 3. Vision property (cont’d) • Brightness adaptation • -- There are a range of intensity levels that human eye can adapt • - photopic: 10^(-3) (mL) – 10^(3) (mL) • - scopotic: 10^(-3) (mL) – 10^(-1) (mL) • -- Human eyes have brightness adaptation level, • they cannot adapt the whole range • simultaneously

7. 3. Vision property (cont’d) • Brightness discrimination • -- The ability to discriminate different intensity level • - Weber ratio: just noticeable difference of intensity versus the background intensity • -- The intensity defined in the digital image is not the real intensity. It is a contrast scale (e.g., gray scale)

8. 3. Vision property (cont’d) • Contrast • -- Absolute contrast • C = Bmax / Bmin • whereBmax is the maximum brightness intensity • Bmin is the minimum brightness intensity • -- Relative contrast • Cr = (B – B0) / B0 • B is the brightness of object; B0 is the background brightness • -- Mach Band: over-shooting effect

10. theta eye d L 3. Vision property (cont’d) • Spatial discrimination (SD) • -- minimum view angle which can discriminate two points on the object to be viewed • d/(2 * Pi * L) = theta / 360

11. 3. Vision property (cont’d) • Spatial discrimination (SD) • -- low illumination (SD decreases) • -- low contrast (SD decreases) • -- too high illumination (SD does not increase too much) • -- SD of color is weaker than SD of brightness • -- projection on fovea (SD increases)

12. Optical system H(u,v) ~ h(x,y) Input image f(x,y) Output image g(x,y) 3. Vision property (cont’d) • Human vision model • -- g(x, y) = T [ f(x, y)] • -- T: transform input optical scene to output image • - linear or non-linear transform • - H(u,v) low pass filter (e.g., limited discrimination, linear) • - log response to the brightness (e.g., non-linear) • - time-delay effect (e.g., “image-remain” effect)

13. 4. Image acquisition • Wavelength • -- electromagnetic spectrum

14. 4. Image acquisition (cont’d) • Principle of imaging sensor • -- transform illumination energy into digital image • -- output voltage waveform is proportional to light • -- e.g., single sensor, group sensors (one-strip, CT/MRI), group sensors (2D array CCD)

15. 4. Image acquisition (cont’d) • Image digitizing • -- Sampling: digitizing the coordinate values (spatially) • - Nyquest rate: 2*F(max) • - limited by the number of sensors • - spatial sampling: uniform and non-uniform • (e.g., fovea-based, fish-eye based) • -- Quantization: digitizing the amplitude values • - uniform • - non-uniform (based on image characteristics)

16. 4. Image acquisition (cont’d) • Image digitizing • -- f(x, y) is the gray level at pixel location (x, y) • -- Gray level is not real illumination intensity (it is an • index of the gray scale) • -- f(x, y) is in the range of [0, 255] for 8-bit image • -- the image with size of M*N and k bits per pixel, • has the total bits: M*N*k

17. 4. Image acquisition (cont’d) • Spatial resolution • -- number of pixels with respect to the image size • -- line pair: smallest discernible detail per unit • distance in an image • - e.g., 100 lp/mm.

18. 4. Image acquisition (cont’d) • Relationship between spatial resolution N and gray level resolution K • -- N  and K   quality  • -- N  and K   contrast  • -- N (detail)   K (number of gray level) can be  • (e.g., half-tone image)

19. 4. Image acquisition (cont’d) • Aliasing problem • -- JigJag or staircase effect. • -- occurs in image acquisition (e.g., image processing) • -- occurs in display (e.g., computer graphics) • -- Reasons: • The sampling or displaying resolution is lower than the • minimum rate 2*F(max), which is the Nyquest rate. • -- Possible solution: • - Smooth image before sampling to reduce the F(max) • - side-effect: image blurred, quality 

20. 5. Image transform • Size change • -- Zoom-in • -- Zoom-out • -- pixel replication • -- pixel interpolation • -- super-resolution • Shape change • -- geometric transformation

21. 6. Image quality • Subjective • -- Rating (e.g., R=1, 2,…, 5) • where N is the number of evaluators; JiR • -- application in image enhancement, restoration, compression, etc.

22. 6. Image quality • Objective • -- Mean square error • -- dB value: -10Log(E) • -- f(x,y) is the image to be evaluated. • f^(x,y) is the reference image to be compared with. • -- application in image coding, etc.

23. P P 7. Connected components • Relationship of pixels • -- Four neighbors of pixel P • - N4(P) (strong neighbors) • - ND(P) (weak neighbors) • -- Eight neighbors of pixel P • - N8(P) = N4(P) + ND(P) P Strong weak 8-neighbor

24. P 7. Connected components (cont’d) • Adjacency • -- 4-adjacency • -- 8-adjacency • -- m-adjacency (mixed-adjacency) q P q P q 4-connected pq is not m-connected 8-connected m-adjacent: if q is N4(p), or q is Nd(p) and N4(p) N4(q) = 

25. P q P q 7. Connected components (cont’d) • Path • -- If p and q is connected, there is a path between p and q. • -- m path: the path between p and q based on m-connected pixels. • -- closed path: starting p and ending q are connected

26. 7. Connected components (cont’d) • Connected component • -- set of pixels which are connected • -- The set is also called connected set • Concept • -- R is a region if R is a connected set • -- boundary of R is “closed path” • -- edge: gray-level discontinuity at a point • - link edge points  edge segment

27. 7. Connected components (cont’d) • Distance • -- D(p, q) is defined as the distance between p and q. • D(p, q) >=0 • D(p, q) = D(q, p) • D(p, q) <= D(p,z) + D(q,z) • -- Euclidean distance (disk shape) • De(p,q) = sqrt[(xp – xq)^(2) + (yp – yq)^(2)]

28. 7. Connected components (cont’d) • Distance • -- D4 distance (city-block distance) (diamond shape) • D4(p,q) = |(xp – xq)|+ |(yp – yq)| • 2 • 2 1 2 • 2 1 0 1 2 • 2 1 2 • 2

29. 7. Connected components (cont’d) • Distance • -- D8 distance (chessboard distance) (square shape) • D8(p,q) = max(|(xp – xq)|, |(yp – yq)|) • 2 2 2 2 2 • 2 1 1 1 2 • 2 1 0 1 2 • 2 1 1 1 2 • 2 2 2 2 2

30. 7. Connected components (cont’d) • Distance • -- Dm distance (shortest m-path between two points) • 1 - 1 • | • 1 - 1 • | • 1 • Dm = 4

31. 8. Pixel operation • Point-wise operation • -- M*N image bound matrix t r (r,t): coordinates of upper-left component; each component is either defined (which is represented by a certain intensity value), or undefined (which is represented by “*”).

32. 8. Pixel operation (Cont’d) • Arithmetic operation • (1) ADD[f, g](I,j) • = f(I,j) + g(I,j) IF f(I,j)   and g(I,j)   (C1) • =  otherwise • (2) Mult[f,g](I,j) • = f(I,j) • g(I,j) IF C1 • =  otherwise • (3) SCALAR[t; f](I,j) • = t • f(I,j) IF f(I,j)   • =  otherwise

33. 8. Pixel operation (Cont’d) • Arithmetic operation • (4) Max[f,g](I,j) • = max[f(I,j), g(I,j)] IF C1 • =  otherwise • (5) Min[f,g](I,j) • = min[f(I,j), g(I,j)] IF C1 • =  otherwise • (6) Sub[f](I,j) • = -f(I,j) IF f(I,j)   • =  otherwise • (6) SCALAR[t; f](I,j) • = t • f(I,j) IF C1 • =  otherwise

34. 8. Pixel operation (Cont’d) • Arithmetic operation • (7) EXTEND[f,g](I,j) • = f(I,j) IF f(I,j)   • = g(I,j) otherwise • (8) EXTADD[f,g](I,j) • = ADD[f,g](I,j) IF C1 • = f(I,j) IF f(I,j)   and g(I,j) =  • = g(I,j) IF g(I,j)   and f(I,j) =  • = * both g and f on undefined domain

35. 8. Pixel operation (Cont’d) • Arithmetic operation • (9) THRESH[f,t](I,j) • = 1 IF f(I,j)  t • = 0 IF f(I,j) < t • =  IF f(I,j) =  • (10) TRUNC[f,t](I,j) • = f(I,j) IF f(I,j)  t • = 0 IF f(I,j) < t • =  IF f(I,j) =  • TRUNC[f,g](I,j) = Mult[f, THRESH(f, t)]

36. 8. Pixel operation (Cont’d) • Arithmetic operation • (11) EQUAL[f,t](I,j) • = 1 IF f(I,j) = t • = 0 otherwise • = * on the undefined domain • (12) similar definition for • GREATER[f,t](I,j) • BETWEEN[f, t1, t2](I,j) • (13) operation with masking: • AND, OR, NOT.

37. 8. Pixel operation (Cont’d) • Arithmetic operation • (14) PIXSUM(f) is the summation of all pixels on the • defined domain • (15) DOT(f,g) = SUM[f(I,j)  g(I,j)] on the common domain • (16) Norm(f) = [SUM[f(I,j)^2]]^(1/2) • Norm(f) = (DOT(f,f))^(1/2)

38. 8. Pixel operation (Cont’d) • Arithmetic operation • (17) REST[f,g](I,j) • = f(I,j) IF g(I,j)   • =  IF g(I,j) =  • (18) Note: • Linear operation: H(af + bg) = aH(f) + bH(g) • otherwise: non-linear operation (e.g., |f-g| operation) • H: operator • f, g: images • a, b: scale values

39. Image Sensing • Single Image Sensor • Line Sensor (Sensor strip) • Array Sensor

40. Image Sensing • Linear motion • Rotation • Sensing Ring for CT (x-ray) to create cross-sectional images

41. Image Format • TIF (LZW – lossless coding) • GIF • JPEG • BMP

42. Image Format • TIF (LZW – lossless coding) • Tagged image file format • Image head: • field = tags + values • image size • compression • color depth • location of data • bits per sample • …….

43. Image Format • JPEG • 8*8 blocks  DCT  Coefficient quantization  Huffman coding  zig-zag run-length coding

44. Demo

45. Image Format • BMP • PBM - portable bitmap file format (binary) • PGM – portable greymap (grey scale) • PPM – portable pixmap (color)