Chapter 2 - Fundamentals. Comunicação Visual Interactiva

Transcription

1 Chapter - Fundamentals Comunicação Visual Interactiva

2 Structure of the human eye (1) CVI

3 Structure of the human eye () Celular structure of the retina. On the right we can see one cone between two groups of rods. CVI 3

4 Structure of the human eye (3) CVI 4

5 Structure of the human eye (4) CVI 5

6 Photometric model source of light object on the surface sensor (camera) x, y ix, yrx y f, x y x, y 1 f x 0, y i, Amount of illumination that strikes the object 0 r l MIN L MAX Amount of illumination reflected by the object L MIN l L MAX L, Interval variation of the light intensity 0, L where Normalization, where 0 corresponds to black and L-1 to white CVI 6

7 Artificial Systems for Image acquisition (1) Three main configurations of the sensors to transform illumination energy into digital images Cameras CCD (Charge-coupled devices) Typical dimensions: 6.4mm x 4.8mm ½ (640x480 ou 51x51 pixels) For each new image, the electric charges are cleaned and then the received light is integrated in a given time interval (controlled by the shutter) CVI In the final stage, the image plane (array D) is scaned. This process is accomplished line by 7 line.

8 Artificial systems for image acquisition () CCD vs CMOS Established technology; Specific technology; High production costs; High consumption; Higher sensibility; Sequential read; Recent technology; Standard IC technology; Cheaper; Less consumption; Lower sensibility; Pixel amplification; Random acess to pixels; Integration of other components in the same chip; CVI 8

9 Artificial systems for image acquisition (3) CVI 9

10 Bayer Filter (i) An example: CVI 10

11 RGB Filter at different time instants (ii) Original image Imagem chromatic distortion CVI 11

12 Artificial systems for image acquisition (4) CVI 1

13 Artificial systems for image acquisition (5) CVI 13

14 Image formation pin-hole Model perspective projection Dark camera ( câmara escura (século XVI) ) Translucent material CVI 14

15 Perspective effects The apparent size of the object depends on its distance Retina plan (inverted image) The projection of two parallel straight lines seems to converge to a point Virtual plan (non-inverted image) CVI 15

16 Perspective projection Mathematical model x y f f x z y z How to correlate the coordinates of a point in the real world, P, with the corresponding coordinates in the retina, P? ( x, y, z Confirmations: The points P, P and O (optical center) are collinear P ) P ( x, y, z) OP The point is projected on the sensor plan that is located at a distance f (focal distance) of the optical center z OP f CVI 16

17 Perspective Projection (II) When the pin-hole model is used, the relation between the Cartezian coordinates ( x, y, z) of a point in the reference of the camera C and the coordinates of the corresponding projection ( x', y') to the plan of the image is given by x f x z y' f With the assumption that the origin of the reference camera is coincident with the optical center of the camera, and the image origin is the main point From the expressions of x and y', it can be shown that the distance R between two points located in the plane at the distance z to the camera and the distance r, between the projection of these points in the image plan is given as r f R z y z CVI 17

18 Perspective Projection (III) From the expressions of x and y', it can be shown that the distance R between two located points in the plane at the distance z to the camera and the distance r, between the projection of these points in the image plan is given as R r f z CVI 18

19 Image plane Cameras with lenses (1) In practice we need to use lenses It acts as light collector Allows to adjust the focus of objects (changing f) Diffraction phenomena optical axis CVI f f z 19

20 Difraction Example CVI 0

21 Cameras with lenses () Deviations from the model Imperfections in the lens lead to a circle of confusion Sensor with discrete units; spatial integration leads to a blurring effect; limitation of the observed detail. Other problems Chromatic distortion wrap-around blooming Geometric distortion blooming CVI 1

22 Focal distance of the lens (1) Magnification factor m f z ' x x y y m Field of view space of the scene projected by the sensor It depends not only the focal distânce, f, but also of the sensor dimensions (usually 1/4, 1/3 ou 1/ ) When is large, the lens is said a wide angle lens When small the lens is telescopic H Sensor area L H H L 1 tan 1 tan H f L f CVI

23 Image plane Focal distance of the lens () Depth-of-field (profundidade de campo) P P optical axis p p' f f z CVI 3

24 CVI 4

25 Image plane Focal distance of the lens (3) Change of the depth-of-field Distance change between the lens and the image plan Deformation of the lens P P optical axis p p' f f z CVI 5

26 Sampling and quantization (1) CVI 6

27 Sampling and quantization () CVI 7

28 Representation of the digital images (1) f x, y f f f 0,0 f 0,1 f 0, N 1 1,0 f 1,1 f 1, N 1 M 1,0 f M 1,1 f M 1, N 1 CVI 8

29 Representation of the digital images () Gray level or number of colors k L Number of bits b M N k CVI 9

30 Spatial and gray level resolution CVI 30

31 Number of quantification levels CVI 31

32 Image interpolation (1)? Nearest neighbor Bilinear interpolation???? Bicubic interpolation v x y ax by cxy d, vx, y CVI 3 3 i0 3 j0 a ij x i y j

33 Image interpolation () CVI 33

34 Relationships between pixels (1) Neighborhood of a pixel Neighborhood 4 x y X X? X X N 4 x 1, y, x 1, y, x, y 1, x, y 1 Neighborhood 8 X X X X? X X X X N 8 x 1, y 1, x 1, y 1, x 1, y 1, x 1, y 1 CVI 34

35 Relationships between pixels () Path between x y e q s, t p, x 0, y0, x1, y1,, x n, y n where x 0, y0 x, y, xn, yn s, t x y, x y i 1,,, and i, i i1, i1 are neighbors, for n Connectivity Two pixels are connected if there exists a path that links them Region Set of connected pixels. CVI 35

36 Relationships between pixels(3) Euclidian distance City-block or D4 distance Chessboard or D8 distance y x p, t s q, w v z, 0, q p D p D q q p D,, z D q q p D z p D,,, Distance metrics for pixels, t y s x q p D e t y s x q p D, 4 t y s x q p D, max, CVI

37 Arithmetic operations (1) Operations that are performed between corresponding pixels pairs (point-by-point operations) x, y f x, y gx y s, x, y f x, y gx y d, x, y f x, y gx y p, x, y f x, y gx y v, CVI 37

38 Arithmetic operations () CVI 38

39 Arithmetic operations (3) CVI 39

40 Arithmetic operations (4) CVI 40

41 Logical operations and sets (1) CVI 41

42 Logical operations and sets () CVI 4

43 Spatial operations (1) 1. Operation based on one pxel s T z. Operation based on neighbors S Neighbors of the pixel p x, y xy 3. Geometric transformations x, y T v, w CVI 43

44 Spatial operations Examples (1) Negative image CVI 44

45 Spatial operations Examples () Mean CVI 45

46 Spatial operations Examples (3) Afine transform x y 1 v w1t v w1 t t t t t t CVI 46

47 Types of Images Definition: a monochromatic image (gray level), I[r,c], assigns for each pixel one scalar value (intensity) Definition: a multiespectral imagem, M[r,c], assigns for each pixel one N-dimensional vector. In the case of color images, we have N=3 (RGB) Definition: a binary image, B[r,c], assigns each pixel the values of 0 or 1 Definition a label image (classes), L[r,c], assigns each pixel to a given label, that is chosen from a pre-defined alphabet of labels CVI 47

48 Image formats Header Data Use (or not) data compression algorithms. Compression without losses (lossless) or with losses (lossy) Example of a format CVI 48

49 Readings Chapter 1 e de R. Gonzalez, R. Woods, Digital Image Processing, 3ª edição, 008. Chapter de L. Shapiro, G. Stockman, Computer Vision, 001. CVI 49