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1、Digital Image ProcessingChapter 2: Digital Image Fundamental6 June 2007 What is Digital Image Processing ?Processing of a multidimensional pictures by a digital computerWhy we need Digital Image Processing ?1. To record and store images2. To enhance images using mathematics3. To analysis images4. To
2、 synthesize images5. To create computer vision systems Digital Image Digital image = a multidimensionalarray of numbers (such as intensity image) or vectors (such as color image) Each component in the imagecalled pixel associates withthe pixel value (a single number in the case of intensity images o
3、r a vector in the case of color images). 39871532 22132515 372669 28161010 39656554 42475421 67965432 43567065 99876532 92438585 67969060 78567099 Visual Perception: Human Eye (Picture from Microsoft Encarta 2000) Cross Section of the Human Eye (Images from Rafael C. Gonzalez and Richard E. Wood, Di
4、gital Image Processing, 2nd Edition. 1. The lens contains 60-70% water, 6% of fat.2. The iris diaphragm controls amount of light that enters the eye.3. Light receptors in the retina- About 6-7 millions cones for bright light vision called photopic - Density of cones is about 150,000 elements/mm2.- C
5、ones involve in color vision.- Cones are concentrated in fovea about 1.5x1.5 mm2.- About 75-150 millions rods for dim light vision called scotopic- Rods are sensitive to low level of light and are not involved color vision.4. Blind spot is the region of emergence of the optic nerve from the eye. Vis
6、ual Perception: Human Eye (cont.) Range of Relative Brightness SensationSimutaneous range is smaller thanTotal adaptation range (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition. Distribution of Rods and Cones in the Retina (Images from Rafael C. Gonzalez and
7、 Richard E. Wood, Digital Image Processing, 2nd Edition. Image Formation in the Human Eye (Picture from Microsoft Encarta 2000) (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition. PositionIntensity Brightness Adaptation of Human Eye : Mach Band Effect Mach Ban
8、d Effect Intensities of surrounding points effect perceived brightness at each point.In this image, edges between bars appear brighter on the right side and darker on the left side. (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition. In area A, brightness perc
9、eived is darker while in area B isbrighter. This phenomenon is called Mach Band Effect. PositionIntensity AB Mach Band Effect (Cont) Simultaneous contrast. All small squares have exactly the same intensitybut they appear progressively darker as background becomes lighter. Brightness Adaptation of Hu
10、man Eye : Simultaneous Contrast Simultaneous Contrast (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition. Optical illusion (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition. Visible Spectrum (Images from Rafael C. Gonza
11、lez and Richard E. Wood, Digital Image Processing, 2nd Edition. Image Sensors Single sensorLine sensorArray sensor (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition. Image Sensors : Single Sensor (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Im
12、age Processing, 2nd Edition. Image Sensors : Line Sensor Fingerprint sweep sensor Computerized Axial Tomography (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition. CCD KAF-3200E from Kodak.(2184 x 1472 pixels, Pixel size 6.8 microns2)Charge-Coupled Device (CCD
13、)w Used for convert a continuous image into a digital imagew Contains an array of light sensorsw Converts photon into electric chargesaccumulated in each sensor unitImage Sensors : Array Sensor Horizontal Transportation Register Output GateAmplifierVertical Transport RegisterGate Vertical Transport
14、RegisterGate Vertical Transport RegisterGate Photosites Output Image Sensor: Inside Charge-Coupled Device Image Sensor: How CCD worksabc ghi def abc ghi def abc ghi defVertical shift Horizontal shiftImage pixelHorizontal transportregister Output Image “After snow storm”Fundamentals of Digital Images
15、 f(x,y)xyw An image: a multidimensional function of spatial coordinates.w Spatial coordinate: (x,y) for 2D case such as photograph, (x,y,z) for 3D case such as CT scan images (x,y,t) for movies w The function f may represent intensity (for monochrome images) or color (for color images) or other asso
16、ciated values.Origin Digital ImagesDigital image: an image that has been discretized both inSpatial coordinates and associated value.w Consist of 2 sets:(1) a point set and (2) a value setw Can be represented in the formI = (x,a(x): x X, a(x) F where X and F are a point set and value set, respective
17、ly.w An element of the image, (x,a(x) is called a pixel where- x is called the pixel location and - a(x) is the pixel value at the location x Conventional Coordinate for Image Representation (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition. Digital Image Typ
18、es : Intensity ImageIntensity image or monochrome image each pixel corresponds to light intensitynormally represented in gray scale (gray level). 39871532 22132515 372669 28161010Gray scale values 39871532 22132515 372669 28161010 39656554 42475421 67965432 43567065 99876532 92438585 67969060 785670
19、99 Digital Image Types : RGB ImageColor image or RG B image:each pixel contains a vectorrepresenting red, green andblue components.RGB components Image Types : Binary ImageBinary image or black and white imageEach pixel contains one bit :1 represent white0 represents black 1111 1111 0000 0000Binary
20、data Image Types : Index ImageIndex imageEach pixel contains index numberpointing to a color in a color table 256 746 941Index value Index No. Redcomponent Greencomponent Bluecomponent1 0.1 0.5 0.32 1.0 0.0 0.03 0.0 1.0 0.04 0.5 0.5 0.55 0.2 0.8 0.9 Color Table Digital Image Acquisition Process (Ima
21、ges from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition. Generating a Digital Image (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition. Image Sampling and QuantizationImage sampling: discretize an image in the spatial domain Spat
22、ial resolution / image resolution: pixel size or number of pixels(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition. How to choose the spatial resolution = Sampling locationsOriginal image Sampled image Under sampling, we lost some image details!Spatial resolu
23、tion How to choose the spatial resolution : Nyquist RateOriginal image = Sampling locationsMinimumPeriod Spatial resolution(sampling rate) Sampled imageNo detail is lost!Nyquist Rate: Spatial resolution must be less or equalhalf of the minimum period of the imageor sampling frequency must be greater
24、 orEqual twice of the maximum frequency.2mm 1mm 0 0.5 1 1.5 2-1 -0.5 0 0.5 1 0 0.5 1 1.5 2-1 -0.5 0 0.5 1 1 ),2sin()(1 fttx 6 ),12sin()(2 fttx Sampling rate: 5 samples/secAliased Frequency Two different frequencies but the same results ! Effect of Spatial Resolution256x256 pixels 64x64 pixels 128x12
25、8 pixels32x32 pixels Effect of Spatial Resolution (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition. Moire Pattern Effect : Special Case of SamplingMoire patterns occur when frequencies of two superimposed periodic patterns are close to each other. (Images fr
26、om Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition. Effect of Spatial Resolution (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition. Can we increase spatial resolution by interpolation ? Down sampling is an irreversible process.(I
27、mages from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition. Image QuantizationImage quantization: discretize continuous pixel values into discrete numbersColor resolution/ color depth/ levels: - No. of colors or gray levels or- No. of bits representing each pixel value-
28、 No. of colors or gray levels N c is given bybcN 2where b = no. of bits Quantization function Light intensityQuantization level 012Nc-1Nc-2Darkest Brightest Effect of Quantization Levels256 levels 128 levels 32 levels64 levels Effect of Quantization Levels (cont.)16 levels 8 levels 2 levels4 levels
29、In this image,it is easy to seefalse contour. How to select the suitable size and pixel depth of images Low detail image Medium detail image High detail imageLena image Cameraman image To satisfy human mind1. For images of the same size, the low detail image may need more pixel depth.2. As an image
30、size increase, fewer gray levels may be needed. The word “suitable” is subjective: depending on “subject”.(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition. Basic Relationship of Pixels xy(0,0) Conventional indexing method(x,y) (x+1,y)(x-1,y) (x,y-1)(x,y+1) (
31、x+1,y-1)(x-1,y-1)(x-1,y+1) (x+1,y+1) Neighbors of a Pixelp (x+1,y)(x-1,y) (x,y-1) (x,y+1) 4-neighbors of p:N4(p) = (x-1,y)(x+1,y)(x,y-1)(x,y+1) Neighborhood relation is used to tell adjacent pixels. It is useful for analyzing regions. Note: q N4(p) implies p N4(q) 4-neighborhood relation considers o
32、nly vertical and horizontal neighbors. p (x+1,y)(x-1,y) (x,y-1)(x,y+1) (x+1,y-1)(x-1,y-1)(x-1,y+1) (x+1,y+1)Neighbors of a Pixel (cont.) 8-neighbors of p:(x-1,y-1)(x,y-1)(x+1,y-1)(x-1,y)(x+1,y)(x-1,y+1)(x,y+1)(x+1,y+1)N8(p) = 8-neighborhood relation considers all neighbor pixels. p (x+1,y-1)(x-1,y-1
33、)(x-1,y+1) (x+1,y+1) Diagonal neighbors of p:ND(p) = (x-1,y-1)(x+1,y-1)(x-1,y+1)(x+1,y+1)Neighbors of a Pixel (cont.) Diagonal -neighborhood relation considers only diagonalneighbor pixels. ConnectivityConnectivity is adapted from neighborhood relation. Two pixels are connected if they are in the sa
34、me class (i.e. the same color or the same range of intensity) and they are neighbors of one another. For p and q from the same classw 4-connectivity: p and q are 4-connected if q N4(p)w 8-connectivity: p and q are 8-connected if q N 8(p)w mixed-connectivity (m-connectivity): p and q are m-connected
35、if q N4(p) or q ND(p) and N4(p) N4(q) = Adjacency A pixel p is adjacent to pixel q is they are connected.Two image subsets S1 and S2 are adjacent if some pixelin S1 is adjacent to some pixel in S2S 1 S2We can define type of adjacency: 4-adjacency, 8-adjacencyor m-adjacency depending on type of conne
36、ctivity. Path A path from pixel p at (x,y) to pixel q at (s,t) is a sequenceof distinct pixels:(x0,y0), (x1,y1), (x2,y2), (xn,yn)such that (x0,y0) = (x,y) and (xn,yn) = (s,t)and (xi,yi) is adjacent to (xi-1,yi-1), i = 1,np q We can define type of path: 4-path, 8-path or m-pathdepending on type of ad
37、jacency. Path (cont.) pq pqpq 8-path from p to qresults in some ambiguity m-path from p to qsolves this ambiguity8-path m-path Distance For pixel p, q, and z with coordinates (x,y), (s,t) and (u,v),D is a distance function or metric ifw D(p,q) 0 (D(p,q) = 0 if and only if p = q)w D(p,q) = D(q,p) w D
38、(p,z) D(p,q) + D(q,z) Example: Euclidean distance 22 )()(),( tysxqpDe -+- Distance (cont.)D4-distance (city-block distance) is defined astysxqpD -+-),(4 1 2101 2122 2 222 Pixels with D4(p) = 1 is 4-neighbors of p. Distance (cont.)D8-distance (chessboard distance) is defined as),max(),(8 tysxqpD - 12 1012122 2 222 Pixels with D8(p) = 1 is 8-neighbors of p.222 22222 111 1
數(shù)字圖像處理-岡薩雷斯-課件(英文)Chapter02Eng 數(shù)字圖像基礎(chǔ)
