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Chapter 2: Digital Image Fundamentals Fall 2003, 劉震昌
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Outline Elements of Visual Perception Image sensing and acquisition Image sampling and quantization Relationships between pixels
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Understanding visual perception Most image processing operations are based on math. and probability Why understanding visual perception? Human intuition plays an important role in the choice of processing technique
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Structure of the Human eye 角膜 虹膜 網膜 水晶體 Diameter:20mm
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2 class of receptors: cones and rods Distribution of cones and rods 1 cone -> 1 nerve Many rods -> 1 nerve
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Discrete nature of human vision Area of cones 15mm Cone density: 150,000 per mm
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Image formation in the Eye
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Image Sensing and Acquisition
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Images? Illumination source scene reflection
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Image sensors Incoming energy is transformed into a voltage by the combination of input electrical power and sensor material (continuous)
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Single sensor with motion
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Sensor strips Flat-bed scanner aircraft
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Sensor arrays CCD arrays in digital camera
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Image sampling and quantization
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continuous data digital data Sampling: digitize the coordinate values Quantization: digitize the amplitude values Why? Limited representation power in digital computers discretize
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Image sampling and quantization (cont.) Sometimes, the sampling and quantization are done mechanically Limitation on the sensing equipment sensor array
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Sampling rule How to determine the sampling rate? Nyquist sampling theorem If input is a band-limited signal with maximum frequency Ω N The input can be uniquely determined if sampling rate Ω S > 2Ω N Nyquist frequency : Ω N Nyquist rate : Ω S
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Sampling rule (cont.)
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Representing digital images
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Representing digital images (cont.) Matrix form f(0,0) f(0,1) … f(0,N-1) f(1,0) f(0,1) … f(1,N-1) … f(M-1,0) f(M-1,1) … f(M-1,N-1) MxN bits to store the image = M x N x k gray level = 2 k
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Representing digital images (cont.) L = 2 k gray levels, gray scales [0, …,L-1] The dynamic range of an image [min(image) max(image)] If the dynamic range of an image spans a significant portion of the gray scale -> high contrast Otherwise, low dynamic range results in a dull, washed out gray look
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Spatial and gray-level resolution L-level digital image of size MxN = digital image having a spatial resolution MxN pixels a gray-level resolution of L levels Spatial resolution in real-world space line width=W cm space width=W cm Resolution = 1/2W (line/cm)
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Spatial and gray-level resolution (cont.) Resolution of printer or screen dpi(dot per inch) pixel/unit of distance When an digital image of size MxN is to be printed or viewed using devices with resolution k dpi, how large will be the output image?
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Multi-rate image processing Down-sampling Up-sampling neighboring pixel duplication interpolation 2 2
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Down-sampling operations
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See the information loss due to down-sampling
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Gray-level reduction
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false contouring
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Empirical study of resolutions 2 k -level digital image of size NxN How K and N affect the image quality Increased details
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Empirical study of resolutions (cont.) iso-preference curses *shift up and right *A detailed image may need less gray levels
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Zoom and Shrink Operations applied to digital images Zoom: up-sampling Pixel duplication Bi-linear interpolation Shrink: down-sampling
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Zoom and shrink: idea Idea: adjust the grid size over the original image
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Zooming: example pixel duplication bilinear interpolation
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Relationships Between Pixels
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Neighbors of a pixel 4-neighbors of p: N 4 (p) Diagonal neighbors: N D (p) 8-neighbors = 4-neighbors+diagonal neighbors : N 8 (p) p p
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Adjacency, connectivity, regions, and boundaries Connectivity of pixels They are neighbors Their gray levels satisfy a specified criterion of similarity Concept about regions and boundaries Adjacency 4-adjacency: p and q with intensity from V and q is in N 4 (p) 8-adjacency: p and q with intensity from V and q is in N 8 (p)
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Connectivity and adjacency (cont.) m-adjacency(mixed adjacency): p and q having intensity from V and q is in N 4 (p), or q is in N D (p) and N 4 (p) N 4 (q) has no pixels whose values are from V
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Path A path from p: (x,y) to q: (s,t) is a sequence of pixels: Length = n It ’ s a k-path if it is 4-, 8-, and m- adjacency (x,y), (x 1,y 1 ), (x 2,y 2 ), …,, (x n-1,y n-1 ),(s,t) consecutive pixels are adjacency
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Growth of definitions adjacency path connected component connected set (region) S S S boundary
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Summary We need solid mathematical definitions to let the algorithm run on a computer
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Distance measure p: (x,y), q: (s,t) Euclidean distance D e (p,q)=[(x-s) 2 +(y-t) 2 ] 1/2 D 4 distance D 4 (p,q)=|x-s|+|y-t| D 8 distance D 8 (p,q)=max(|x-s|,|y-t|) r 2 2 1 2 2 1 0 1 2 2 1 2 2 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
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Pixel-wise operation For example, how does image I divided by image M? Division is carried out between corresponding pixels in the two images Matlab: Q = I./M
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Linear and non-linear operations H be an operator whose input and output are images H is linear if H(af+bg) = aH(f)+bH(g) Otherwise non-linear We have well-understood theoretical and practical results about linear operators
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Announcement !!! There are solutions to the marked problems in the textbook http://www.imageprocessingbook.com/teaching/problem_sol utions.htm http://www.imageprocessingbook.com/teaching/problem_sol utions.htm HW#1
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