Ulrik Söderström 17 Jan Image Processing. Introduction

Transcription

1 Ulrik Söderström 17 Jan 2017 Image Processing Introduction

2 Image Processsing Typical goals: Improve images for human interpretation Image processing Processing of images for machine perception Image analysis Dealing with images for storage and communication (compression) Image handling 2

3 Image processing steps Low-level Primitive operations (filtering, noise reduction) Both input and output are images Mid-level Segmentation, description, recognition Input. images, output. image attributes High-level Making sense of the recognized objects, (like vision) 3

4 Course outline Lectures Spatial and Frequency domain, Restoration, Compression, Morphological Image Processing, Representation, Description Practical work 3 Labs Project (extensive lab) Written exam 4

5 Grading 3,4,5 Lab exercises ~ 30% Project ~ 30% Written exam ~ 40% 5

6 Images An image is a 2-D function f(x, y) x and y - spatial coordinates f - amplitude (intensity, graylevel) at a point with coordinates (x, y) All values finite and discrete - digital image Digital image processing - computers involved Each value - pixel (picture element) 6

7 Image creation Observation of energy Electromagnetic (EM) radiation most common Human vision is limited to a narrow band Sensors have higher capacities The whole EM spectrum + other energies 7

8 Photons Photon - an amount of energy No mass Travelling at the speed of light Different frequencies v and wavelengths λ c= speed of light, 3x10 8 Energy of a photon h = plancks constant 8

9 The EM spectrum 9

10 Ultraviolet (UV) light Flourescence images of corn UV light from the same star as previous 10

11 Visible light By far the most common 11

12 Visible light Microscopic images of a CD, cholesterol, and a microprocessor 12

13 Infrared light America (north and south) 13

14 Combined spectra Different bands give totally different images of the same object Astronomic images of the same region but in different bands 14

15 Other energies Sound High frequency, ultrasound (1-5 MHz) Medical images 15

16 Other energies Electron microscopy 16

17 Computer generated images No need for a physical energy source Fractals 3-D computer models 17

18 Foundations All imaging systems replicates the human visual system 18

19 Unknown functionalities 19

20 Unknown functionalities 20

21 Image aquisition Sensor to measure energy In digital cameras - CCD arrays Integrate over the sensor, values proportional to the number of photons hitting the surfaces 21

22 Image aquisition 22

23 Image formation An image f(x, y) When generated from a physical process: 0 < f(x, y) < 0 L min f(x, y) L max < (monocromatic image) The interval [L min, L max ] - grayscale of the image 23

24 Image formation Two components - illumination and reflectance f(x, y) = i(x, y) r(x, y) 0 < i(x, y) <, illumination component Determined by illumination source 0 < r(x, y) < 1, reflectance component Determined by object charasteristics Transmissivity is used instead of reflectivity in the case of illumination passing through objects, eg X-rays 24

25 Sampling and quantization The output of a sensor is in most cases a continuous voltage waveform Needs to be digitized Sampling - digitizing the coordinate values Usually M = 2 m steps in x-direction and N = 2 n steps in y-direction Quantization. digitizing the amplitude values L = 2 k gray values Image (storage) size = M N k/8 bytes 25

26 Sampling and quantization 26

27 Sampling and quantization 27

28 Sampling and quantization A square grid is the most common (the only one in the book) 28

29 Image representation Most common convention f(x, y) = Matrix representation of image values 29

30 Image representation Surface color Intensities Gray-level, Color information 30

31 Resolution Spatial resolution - determined by the Sampling Tightness in pixels Sampling distance The human eyes cannot detect resolution higher/lower than a threshold A computer might see more information 31

32 Spatial resolution 32

33 Acceptable resolution? Isopreference subjectively perceived quality of the images Many details- few gray levels needed 33

34 Sampling Sampling theorem If the distance between sampling points is larger than the smallest objects we want to capture, we get problems with aliasing Sampling introduces new frequencies The sampling frequency must be at least twice the highest frequency in the image Blur the image before sampling 34

35 Moiré patterns Moiré pattern effects occurs when periodic patterns break up. E.g. scanned images from printed pages with periodic dots 35

36 Zooming and shrinking Resampling an already digital image Resize the image grid Simplest way to enlarge an image to twice its size - duplicate all pixels (nearest neighbor interpolation) Better results if more neighbors are taken into account (e.g. bilinear interpolation, using the four nearest neighbors) 36

37 Zooming and shrinking 37

38 Zooming 38

39 Pixel relationships Neighbors of a pixel p with coordinates (x, y) Four horizontal and vertical neighbors (x+1, y), (x-1, y), (x, y+1), and (x, y-1) N 4 (p), the 4-neighbors of p Four diagonal neighbors (x+1, y+1), (x+1, y-1), (x-1, y+1), and (x-1, y-1) N D (p) Combined, N 4 (p) N D (p) (union) N 8 (p), the 8-neighbors of p 39

40 Adjacency Two pixels that are neighbors are adjacent 4-adjacency, two pixels p and q with values V are 4-adjacent if q is in the set N 4 (p) 8-adjacency, two pixels p and q with values V are 8-adjacent if q is in the set N 8 (p) 40

41 Distance measures p has coordinates (x, y), q has (s, t) Distances between p and q Euclidean distance (the most natural in R 2 ) D e (p, q) = [(x-s) 2 + (y-t)2] ½ x D 4 distance, - city block distance D 4 (p, q) = x-s + y-t The 4-neighbors of (x, y) have D 4 = x

42 Distance measures D 8 distance, - chessboard distance D 8 (p, q) = max( x-s, y-t ) The 8-neighbors of (x, y) have D 8 = 1 D m distance x The number of jumps between p and q along the path that connects them, depending on the values of the pixels on the path and their neighbors. 42

43 Operations on a pixel basis It is common to carry out arithmetic operations on images E.g. dividing one image by another - not a defined matrix operation Pixel wise operations Images must be of equal size 43

44 Linear and nonlinear operations An operator H whose input and output are images is linear if H(af + bg) = ah(f) + bh(g) for any images f and g and any scalars a and b E.g. summing K images Computing the absolute value of a function is an example of a nonlinear operation 44