Introduction to Digital Image Processing

Transcription

1 Introduction to Digital Image Processing Mohammed A. Hasan Department of Electrical & Computer Engineering University of Minnesota-Duluth

2 Related ECE Courses and Software: 1. ECE 2111: Signals and Systems 2. ECE 5741: Digital Signal Processing 3. ECE 8741: Digital Image Processing 4. Matlab Prerequisite: Working knowledge in Statistics, Calculus, and Differential Equations is very helpful in understanding Image Processing. Books: 1. Digital Image Processing 3rd Edition by Gonzalez and Woods. Prentice Hall, Digital Image Processing 6th edition, by Bernd Janhe, Springer Fundamentals of Digital Image Processing, by Anil K. Jain. Prentice Hall, Digital Image Processing 2nd edition by Kenneth R. Castleman. Prentice Hall, 1995.

3 Here are images some of which are real while others are synthetic.

4 .

5 .

6 .

7 Why do we need Image Processing? 1. Human relies very much on our visual system (eyes & brain) to collect visual information about our surrounding. Visual information refers to images and video. In the past, we need visual information mainly for survival. Nowadays, visual information is for survival as well as communication and entertainment. 2. Equipment and software to capture, display, store and process images/video are getting cheaper and having better quality. More & more images/video are used. For example, images/video are common on Internet and mobile phones nowadays. 3. Human visual system is highly non-linear.

8 Optical Illusions

9 .

10 .

11

12 Some History 1. Newspaper Industry s: computers powerful enough + space program

13 : pictures from the Moon (JPL, Pasadena, CA)

14 4. Other fields: (a) Remote Earth resources observation (b) Medical Image processing: 1970 s CAT/CT (Hounsfield, Cormack 1979 Nobel Prize) The Nobel Prize in Physiology or Medicine 1979 for the development of computer assisted tomography (c) Aerial and satellite images (d) Archeology (e) Physics (f) Machine perception: inspection, product assembly, character recognition,... etc

15 .

16 What is Digital Image Processing 1. Basically, we are concerned with the study and the implementation of methods for the (a) (b) (c) (d) Formation Enhancement Analysis Communication/Transmission of digital images in two, three, and four (3 space + 1 time) dimensions

17 2. (Some) places where image processing is needed (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) Optical imaging (cameras, microscopes), Medical imaging (CT, MRI, ultrasound, diffuse optical, advanced microscopes) Astronomical Imaging (telescopes) Geophysical Imaging (seismics, electromagnetics) Radar and hyperspectral imaging (surveillance and remote sensing) Printing (color, dot matrix) Video and Imaging Compression and Transmission (JPEG, MPEG, HDTV,) Computer vision (robots, license plate reader, tracking human motion) Computer graphics: rendering and shading, representation Commercial software (Photoshop) Hardware (FPGA, DSP, cell processor implementation of compute intensive algorithms) Security and Digital Rights Management (watermarking, biometrics)

18 3. (Some) things people need to do All of this in 2D and 3D plus (often) time (a) (b) (c) (d) (e) (f) (g) Form imagery from indirect data i. CAT, MRI, synthetic aperture radar, seismics, Clean up noisy and blurred images i. Removal of blur due to imperfect lenses or noise due to imperfect imaging sensors ii. Balance gray scale due to illumination issues Display images on paper or screen Find things i. Edges, American flags in an image database, tanks vs. schoolbus, tumors, oil pockets, buried landmines, eyes for redeye removal, white matter and gray matter in an MRI Compress images for transmission i. Inherent, PDAs, Cell phones, HDVT, Detect and track motion i. People walking, cells moving and growing Implement all of these things efficiently i. Provably efficient algorithms ii. Hardware options (parallel processing, FPGA, DSP, ASIC, )

19 4. (Some) tools people use (a) Represent images in various domains i. Space: intensity at every pixel ii. iii. Fourier: waves of varying frequencies Wavelet: Half way between space and Fourier. Pixels of varying size (b) Filtering: i. Convolution in 2D and 3D (space and frequency) ii. Morphology: a form of nonlinear convolution using and, or, & not or rank order stats (min, max, median) (c) Physics-based sensor models i. Cameras and other sensors (MRI and CT) (d) Statistics and probability i. Noise in images or models for images ii. iii. Optimal deblurring or denoising or tracking filters Information theory needed for compression and transmission (e) Linear algebra and optimization

20 Image Formation f :(x, y) R 2 R 1. Intensity proportional to energy radiated by a physical source 2. f(x, y) =i(x, y)r(x, y) 0 f(x, y) < i(x, y) : Incident illumination; 0 i(x, y) < 0 r(x, y) : reflected illumination

21 A Digital Image is obtain from analog image by Sampling and quantization. Representation of Digital Images A 2D image f( x, y) of size: MxN Digitization: M, N, L (# discrete gray levels) L =2 k dynamic range; contrast To store an image: b = MxNxk bits

22 F (x, y) = F (m, n), 0 m M 1, 0 n N 1 A digital image can be written as a matrix x(0, 0) x(0, 1) x(0,n 1) F = x(1, 0). x(1, 1).. x(1,n 1). x(m 1, 0) x(m 1, 1) x(m 1,N 1)

23 Pixels Displays form an image from an array of pixels. Pixel is the smallest addressable area of a display. The word pixel comes from picture element.

24 Resolution The resolution of an image is described as the number of pixels horizontally times the number of pixels vertically.

25 Grayscale Image In a grayscale image, the intensity of a pixel is described by a single number. The high values correspond to bright pixels and the low values correspond to dark pixels.

26 Common types of grayscale images: 1. The intensities of the pixels are integers in the interval [0,255]. We use one byte of memory for each pixel. 2. The intensities of the pixels are integers in the interval [0,65536]. We use two bytes per pixel. 3. The intensities of the pixels are either 0 or 1. Such images are called binary and use only one bit per pixel. 4. The intensity of the image is a real number in the range [0,1]. We will mostly work with images of this type because they are easier to manipulate.

27 The whole image is described by an array of numbers called matrix.

28 Matlab Matlab is a programming language and interactive environment suitable for rapid implementation of image processing algorithms. http : // c enter/tutorials/la Example 1.4: f1 = imread(images/peppers.png) f2 = double(f1) / 255 f3 = 0.33 * f2 imwrite(f3, images/new_peppers.png)

29 Example 1.6: f1 = imread(images/lena.png) f2 = double(f1) / 255 g1 = imread(images/camera.png) g2 = double(g1) / 255 h = 0.5 * f * g2 imwrite(h, images/new_image.png)

30 We can process an image by manipulating the corresponding matrix.

31 We can process an image by manipulating the corresponding matrix. 1 denotes a matrix with the same dimension as A and all its entries equal to 1.

32 .

33 Color Images Color images are usually described in the RGB color space. The RGB is an additive color space. The primary colors red, green and blue are combined to reproduce other colors. In the RGB colour space, a color is represented by a triplet (r,g,b) 1. r gives the intensity of the red component 2. g gives the intensity of the green component 3. b gives the intensity of the blue component Here we assume that r,g,b are real numbers in the interval [0,1]. You will often see the values of r,g,b as integers in the interval [0,255].

34 A color image is described by three matrices

35 In emissive electronic displays, such as TV sets and computer monitors, each pixel consists of three subpixels representing the values of red, green and blue. A typical subpixel arrangement in an LCD display

36

37 Grayscale and Color Images 1. For grayscale image, 256 levels or 8 bits/pixel is sufficient for most applications 2. For color image, each component (R, G, B) needs 256 levels or 8 bits/pixel 3. Storage for typical images (a) , 8 bits grayscale image: 262,144B (b) , 24 bits true color image: 2,359,296B

38 Some Image Processing Functions Why should an image be processed prior to analysis or presentation? 1. It suffers from noise 2. It fails to highlight the particular feature in which we are interested 3. In image processing, we remove noise & unnecessary features while highlighting the required features 4. Filtering

39 Operations 1. Algebraic operations 2. Geometric operations 3. Noise filtering

40 Algebraic operations Include: Intensity transformation functions Gamma correction Contrast increasing functions Intensity transformation functions An intensity transformation function is a function f applied to the intensity of each pixel: Notice that here each pixel is processed by f individually.

41 Gamma Correction The gamma correction is an intensity transformation function f(x) =x γ where γ is a constant. 1. If γ<1 the image is weighted toward higher (brighter) output values. 2. If γ>1 the image is weighted toward lower (darker) output values. 3. If γ = 1 the transformation has no effect on the image.

42 Contrast-stretching transformations The contrast stretching function E>2), in- 1 f(x) = 1+(0.5)/x) E where E is a relatively large constant (e.g. creases the contrast of the image. Pixel values below 0.5 are pushed nearer to 0. Pixel values above 0.5 are pushed nearer to 1.

43

44 Geometric operations 1. Change the spatial relationships between objects within an image E.g.: (a) Spatial transformation (b) Geometric decalibration (c) Pixel transfer (d) Image format conversion

45 Examples Zooming

46 Shrinking

47 Rotation and transformation

48 Histograms The histogram function is defined over all possible intensity levels. For each intensity level, its value is equal to the number of the pixels with that intensity.

49 Histogram Equalization We can use the normalised histogram function to compute an intensity transformation function giving a more uniform distribution of the intensities.

50 Histogram Equalization of Color Images

51 Sharpening and Edge Detection (based on first- and second- order derivatives) 1. highlight fine detail 2. enhance detail that has been blurred common applications 1. medical imaging 2. industrial inspection 3. electronic printing

52 Derivatives of digital functions: differences First-order derivatives: f = f(x +1,y) f(x, y) x f = f(x,, y +1) f(x, y) y Second-order derivatives: 2 f = f(x +1,y)+f(x 1,y) 2f(x, y) x2 2 f = f(x, y +1)+f(x, y 1) 2f(x, y) y2 Laplacian : 2 f(x, y) = 2 f x f y 2 2 f(x, y) =f(x +1,y)+f(x 1,y) 2f(x, y) + f(x, y +1)+f(x, y 1) 2f(x, y) = f(x+1,y)+f(x 1,y)+f(x, y+1)+f(x, y 1) 4f(x, y)

53 Sharpening filter example using the Laplacian The Laplacian is a derivative operator 1. highlights gray-level discontinuities in an image deemphasizes regions with slowly varying gray levels

54 .

55 Edge Detection The Gradient of f(x, y) is defined as f(x, y) = [ f ] x f y or The magnitude of gradient: f(x, y) = ( f x )2 +( f y )2 f(x, y) = f ) + f x y Gradient of digital image f(x, y) f(x, y) = [ ] f(x +1,y) f(x, y) f(x, y +1) f(x, y) filter mask: f(x, y) z 7 +2z 8 + z 9 ) (z 1 +2z 2 + z 3 ) + (z 4 +2z 5 + z 6 ) (z 1 +2z 2 + z 3 )

56 ..

57 .

58 .

59 Elementary noise reduction 1. Averaging 2. Median filtering Basic Assumptions: 1. Noise is random 2. Appear as spikes 3. Image data are not random 4. pixel near a given pixel (probably) has the same or close gray levels Smoothing or Averaging Filter: Take the average of the pixels in the neighborhood including/excluding pixel P Let this average be the new value at P This has to be repeated for all the pixels in the image Example 1. Replace pixels in a square window surrounding this pixel as follows:

60 2. Trade-off between noise removal and detail preserving: 3. Larger window = can remove noise more effectively, but also blur the details/edges

61 Median Filtering 1. Replaces the value of a pixel by the median of intensities in the neighborhood of that pixel. 2. Is very effective against the salt-and-pepper noise.

62 .

63 Periodic Noise 1. From electrical or electromechanical interference during image acquisition 2. Spatially dependent 3. E. g. sinusoidal noise