DigitalImageProcessing2-ImageProcessingFundamentals.ppt

courseware download: /digitalimageprocessing/ username: download password: download digital image processing: digital imaging fundamentals dr. guangming lu l 3 of 58 contents main purpose: introduce several concepts related to dip and some of the notation used throughout the course. this lecture will cover: human vision system light and electromagnetic spectrum image acquisition sampling and quantization resolution basic relationships between pixels 4 of 58 human visual system uthe best vision model we have! uknowledge of how images form in the eye can help us with processing digital images uwe will take just a whirlwind tour of the human visual system 5 of 58 structure of the human eye nthe lens focuses light from objects onto the retina nthe retina is covered with light receptors called cones (6-7 million) and rods (75-150 million) ncones are concentrated around the fovea and are very sensitive to colour nrods are more spread out and are sensitive to low levels of illumination 6 of 58 structure of the human eye 7 of 58 blind-spot experiment draw an image similar to that below on a piece of paper (the dot and cross are about 6 inches apart) close your right eye and focus on the cross with your left eye hold the image about 20 inches away from your face and move it slowly towards you the dot should disappear! 8 of 58 brightness adaptation & discrimination n because digital images are displayed as a discrete set of intensities, the eyes ability to discriminate between different intensity levels is an important consideration in dip results. n the human visual system can perceive approximately 1010 different light intensity levels n subjective brightness is a logarithm function of the light intensity incident on the eye. n however, at any one time we can only discriminate between a much smaller number brightness adaptation 9 of 58 nfor a given set of conditions, the current sensitivity level of the visual system is called the brightness adaptation level. brightness adaptation & discrimination 10 of 58 brightness adaptation & discrimination (cont) perceived brightness is not a simple function of intensity： mach bands(1865) seeing is believing? 11 of 58 brightness adaptation & discrimination (cont) nsimilarly, the perceived intensity of a region is related to the light intensities of the regions surrounding it 12 of 58 brightness adaptation & discrimination (cont) another experiment: a piece of paper on a desk is always white, but can appear totally black when used to shield the eyes while looking directly at a bright sky optical illusions our visual systems play lots of interesting tricks on us 14 of 58 optical illusions (cont) 15 of 58 light and the electromagnetic spectrum newton, 1666 violet, blue, green, yellow, orange, and red blends smoothly into the next. light is just a particular part of the electromagnetic spectrum that can be sensed by the human eye light and the electromagnetic spectrum 17 of 58 light and the electromagnetic spectrum nvisible light: 0.430.79um nthe electromagnetic spectrum is split up according to the wavelengths of different forms of energy where c is the speed of the light, v is the frequency, and h is the plancks constant light and the electromagnetic spectrum la stream of massless particles 19 of 58 light and the electromagnetic spectrum nthe colours that we perceive are determined by the nature of the light reflected from an object nfor example, if white light is shone onto a green object most wavelengths are absorbed, while green light is reflected from the object white light colours absorbed green light 20 of 58 light reflectance properties a body that reflects light and is relatively balanced in all visible wavelengths appears white to the observer. a body that favors reflectance in a limited range of the visible spectrum exhibits some shades of color. achromatic or monochromatic light: the only attribute is intensity-gray-level black to gray to white light and the electromagnetic spectrum 21 of 58 chromatic light light and the electromagnetic spectrum 22 of 58 light and the electromagnetic spectrum nin principle, if a sensor can be developed that is capable of detecting energy radiated by a band of the electromagnetic spectrum, we can image events of interest in that band. nhowever, the wavelength of an electromagnetic wave require to “see” an object must be of the same size as or smaller than the object. nelectromagnetic waves is not the only method for image generation. such as sound reflection-ultrasonic images nnote there is an error in the reference book in this section, far infrared should be far ultraviolet. page 35. 23 of 58 other em spectrum: short-wavelength end gamma rays medical imaging astronomical imaging radiation in nuclear environments hard x rays industrial applications soft x rays chest x-ray (shorter wavelength end) dental x-ray (lower energy end) ultraviolet microscopy imaging infrared region: near-infrared far-infrared microwave microwave ovens, communication, radar radio wave am, fm, tv, and medical imaging stellar bodies observation light and the electromagnetic spectrum tumour infrared visible 24 of 58 image acquisition images are typically generated by illuminating a scene and absorbing the energy reflected by the objects in that scene. 25 of 58 imaging sensors uimage acquisition sensors usingle sensor ustrip sensor usensor array 26 of 58 nincoming energy lands on a sensor material responsive to that type of energy and this generates a continuous voltage nto create a digital image, we need to convert the continuous sensed data into digital form. nthis involves two steps: sampling and quantization. image sampling and quantization 27 of 58 image sampling and quantization 28 of 58 image sampling and quantization ndigitizing the coordinate values is called sampling, and digitizing the amplitude values is called quantization. nquantisation is the process of converting a continuous analogue signal into a digital representation of this signal 29 of 58 mathematical statement let z be the set of real integers r the set of real numbers sampling: partition the xy plane into a grid. the coordinates of the center of each grid being a pair of elements from the cartesian product z2. the set of all ordered pairs of elements (zi, zj). with zi and zj being integers from z. quantization: f is a function that assigns a gray-level value (a real number in r) to each distinct pair of coordinate (x, y). image sampling and quantization 30 of 58 representation 31 of 58 both spatial and gray level resolutions determine the storage size of an image (bytes) e.g. spatial resolution: 40 x 40 gray level resolution: 64 (log264 = 6 bits/pixel) the number of pixels: 40 x 40 = 1600 pixels the storage size (no compression, no overhead): 1600 x 6 = 9600 bits = 1200 bytes 1.17 kb representation usually, the m and n are positive integers, and the number of gray levels is an integer power of 2: 32 of 58 representation 33 of 58 spatial & intensity level resolution uthe spatial resolution of an image is determined by how sampling was carried out. uspatial resolution simply refers to the smallest discernable detail in an image vision specialists will often talk about pixel size graphic designers will talk about dots per inch (dpi) 5.1 megapixels 34 of 58 intensity level resolution refers to the number of intensity levels used to represent the image the more intensity levels used, the finer the level of detail discernable in an image intensity level resolution is usually given in terms of the number of bits used to store each intensity level number of bits number of intensity levels examples 120, 1 2400, 01, 10, 11 4160000, 0101, 1111 825600110011, 01010101 1665,5361010101010101010 spatial & intensity level resolution 35 of 58 spatial & intensity level resolution 36 of 58 1024 * 1024512 * 512256 * 256 128 * 12864 * 6432 * 32 spatial & intensity level resolution 37 of 58 128 grey levels (7 bpp) 64 grey levels (6 bpp)32 grey levels (5 bpp) 16 grey levels (4 bpp)8 grey levels (3 bpp) 4 grey levels (2 bpp)2 grey levels (1 bpp) 256 grey levels (8 bits per pixel) spatial & intensity level resolution 38 of 58 spatial resolution: m*n gray level resolution：l how many samples and gray levels are required for a good approximation? resolution (the degree of discernible detail) of an image depends on sample number and gray level number. i.e. the more these parameters are increased, the closer the digitized array approximates the original image. but: storage & processing requirements increase rapidly as a function of n, m, and k spatial & intensity level resolution 39 of 58 the big question with resolution is always: “how much is enough?” this all depends on what is in the image and what you would like to do with it key questions include does the image look aesthetically pleasing? can you see what you need to see within the image? spatial & intensity level resolution 40 of 58 the picture on the right is fine for counting the number of cars, but not for reading the number plate spatial & intensity level resolution 41 of 58 zooming oversampling shrinking subsampling zooming and shrinking digital images 42 of 58 zooming: the creation of new pixel locations the assignment of gray levels to those new locations nearest neighbor interpolation (nn) pixel replication: a special case of nn nn produces checkerboard effect zooming and shrinking digital images nngray level 43 of 58 zooming: bilinear interpolation using the four nns of a point. g(a), g(b), g(c), g(d) are the gray levels of pint a, b, c, d. zooming and shrinking digital images 44 of 58 zooming and shrinking digital images 45 of 58 shrinking: similar manner as just described for zooming. delete expand the grid: nearest neighbor interpolation bilinear interpolation zooming and shrinking digital images 46 of 58 basic relationships between pixels a pixel p at (x,y) has 2 horizontal and 2 vertical neighbors: (x+1,y), (x-1,y), (x,y+1), (x,y-1) this set of pixels is called the 4-neighbors of p: n4(p) the 4 diagonal neighbors of p are: (nd(p) - (x+1,y+1), (x+1,y-1), (x-1,y+1), (x-1,y-1) - n4(p) + nd(p) n8(p): the 8-neighbors of p definitions: f(x,y): digital image pixels: q, p n4 n4pn4 n4 ndnd p ndnd n8n8n8 n8pn8 n8n8n8 47 of 58 basic relationships between pixels 000000000000 000110000000 001111100000 011111110000 011111110000 001111110000 001111111000 001111111110 000001111110 000000000000 s n4(p) qn8(p)pnd(p) 48 of 58 connectivity connectivity between pixels is important: because it is used in establishing boundaries of objects and components of regions in an image two pixels are connected if: uthey are neighbors (i.e. adjacent in some sense - e.g. n4(p), n8(p), ) utheir gray levels satisfy a specified criterion of similarity (e.g. equality, ) v is the set of gray-level values used to define adjacency (e.g. v=1 for adjacency of pixels of value 1) 49 of 58 adjacency we consider three types of adjacency: 4-adjacency: two pixels p and q with values from v are 4-adjacent if q is in the set n4(p) 8-adjacency : p & q are 8- adjacent if q is in the set n8(p) m-adjacency: p & q with values from v are m-adjacent if q is in n4(p) or q is in nd(p) and the set n4(p)n4(q) has no pixels with values from v 50 of 58 adjacency mixed adjacency is a modification of 8- adjacency and is used to eliminate the multiple path connections that often arise when 8-adjacency is used. v=1 8-adjacencym-adjacency 51 of 58 path(通路) u a sequence of adjacent pixels. u for example: a path from pixel p with coordinate (x, y) to pixel q with coordinate (s, t) is defined (x0, y0)，(x1, y1)，(xn, yn) where (x0, y0) = (x, y)，(xn, yn) = (s, t), (xi, yi) and (xi-1, yi- 1) are adjacent, 1 i n, n is called the length of the path. uif (x0, y0) = (xn, yn), the path is a closed path(闭闭合通路 ). uwe can define 4-, 8-, and m-path depending on the type of adjacency. path 52 of 58 path 4-path m-path8-path 53 of 58 definitions: ulet s represent a subset of pixels in an image. two pixel p and q are said to be connected (连连通) in s if there exists a path between them. ufor any pixel p in s, the set of pixels that are connected to it in s is called a connected component（连连通分量） of s. uif it only has one connected component, then set s is called a connected set(连连通集). ulet r be a subset of pixels in an image. we also called r a region(区域) of the image is r is a connected set. uthe