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Chapter 2: Digital Image Fundamentals
Image sampling and quantization Digital image representation Some basic relationships between pixels Linear and nonlinear operation
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2.1 Image sampling and quantization
采 样 子 系 统 成像系统 量 化 器 景物 采样图像 数字图像 图像 图2.1 图像采集系统
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2.1 Image sampling and quantization
digitizing image is to convert a continuous image to digital form. this involves two processes: sampling and quantization
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Image sampling 采样定理 冲激串采样 采样函数 采样周期 T 采样频率
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Image sampling 是频域上的周期函数,它满足 是由一组移位的 叠加而成,但在幅度上有1/T的变化
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Image sampling 采样定理 冲激串采样的频谱
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Image sampling 采样定理 冲激串采样的频谱
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Image sampling 图像采样 空间采样函数 空间采样函数 空间采样频率
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Image sampling 图像采样 空间采样函数
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Image sampling 图像采样 采样后图像
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Image sampling 图像采样 采样图像频谱
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Image sampling digitizing the coordinate is called sampling
sampling space is equal along direction of x- and y-coordinate if sampling space is too small, data capacity is too large, otherwise , information may be overlap, so that detail information can not identified. sampling index
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Sampling example 细节清晰,数据量为100% 细节无法辨认,数据量为1%
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Sampling resolution Spatial resolution
(1) the most smallest number of pixel per unit distance. unit:pixel/inch,pixel/cm (2) a image involves the most smallest number of pixel . unit:pixel × pixel
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quantization Digitizing the amplitude is called quantization
Equal quantization and un-equal quantization Quantization space is too small, otherwise, it may be aliasing and pattern sampling index Gray-level resolution it is the number of gray level of a pixel, which is usually an integer power of 2.the most common number is 8 bit or 16 bit.
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aliasing and pattern
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2.2 Digital image representation
coordinate conventions image as matrices three type of image BITMAP representation reading images displaying images
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coordinate conventions
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image as matrices
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three type of image (1) Binary image Binary image Gray image
Color image (1) Binary image Binary image
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(2) Gray image (3) Color image
A quantity gray is used for image representation, and no color information (3) Color image color image RGB matrix
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File structure 数据区 RGBQUAD 像素的RGB值 像素的调色板索引值 真彩色模式 索引色模式
file-head bITMAPFILEHEADER information-head BITMAPINFOHEADER 数据区 file-head BITMAPFILEHEADER information-head BITMAPINFOHEADER color palette RGBQUAD 数据区 像素的RGB值 像素的调色板索引值 真彩色模式 索引色模式
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file-head BITMAPFILEHEADER
bfType 文件类型标识“BM” bfSize 文件总字节数 bfReserved1 保留字“0” bfReserved2 保留字“0”
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information-head BITMAPINFOHEADER
biSize 信息头结构体长度,为40 biWidth 图像宽度,单位是像素 biHeight 图像高度,单位是像素 biPlanes 必须为1,暂无意义 biCompression 指定位图是否压缩 biSizeImage 实际位图数据所占字节数 biXperlsPerMeter 指定目标设备的水平分辨率 biYperlsPerMeter 指定目标设备的垂直分辨率 biClrImportant 图像中重要的颜色数
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真彩色模式的数据区结构 像素的RGB值 真彩色数据区 :
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索引色模式的调色板 调色板 RGBQUAD 索引值 R G B 1 R1 G1 B1 2 R2 G2 B2 : : N RN GN BN
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索引色模式的数据区 数据区 像素的调色板索引值 索引值 R G B 1 R1 G1 B1 2 R2 G2 B2 : : N RN GN BN
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reading images Syntax : imread( ‘filename’ )
包含图像文件全名的字符串 Syntax : imread( ‘filename’ ) >>f=imread(‘chestxray.jpg’); >>size(f); ans=
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displaying images Syntax : imshow( f,G) or imshow(f,[low high])
显示该图像的灰度级数 Syntax : imshow( f,G) or imshow(f,[low high]) 图像数组 >>f=imread(‘chestxray.jpg’); >>size(f); >>imshow(f,256); >>imshow(f,[ ]);
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2.3 Some basic relationships between pixels
neighbors of a pixel adjacency, connectivity, region, and boundaries distance measure Linear and nonlinear operation
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neighbors of a pixel 1. 4-neighbors of a pixel p at coordinates (x, y)
Their coordinates is respectively (x+1, y), (x-1, y), (x , y+1), (x ,y-1) N4(p) 2. 4 diagonal-neighbors of a pixel p at (x, y) Their coordinates is respectively (x+1, y+1), (x+1, y-1), (x-1 , y+1), (x-1 ,y-1) ND(p)
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neighbors of a pixel 3. 8-neighbors of a pixel p at (x, y)
Their coordinates is respectively (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) N8(p)
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1. adjacency adjacency, connectivity, region, and boundaries
消除采用8-邻接产生的二义性。 (1) 4 - adjacency: if q is in the set N4(p). (2) 8 - adjacency: if q is in the set N8(p). (3)m - adjacency: if q is in N4(p) or q is in ND(p) and N4(p) ∩N4(q) has no pixels whose values are from V. (a) (b) (c) Adjacency of a pixel
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3. connectivity ( p q in set S)
adjacency, connectivity, region, and boundaries 2. path( p(x, y) q(s, t) ) A sequence of distinct pixels with coordinates: ( x0 , y0 ) , ( x1, y1 ) , … , (xn , yn) If ( x0 , y0 ) = (xn , yn) ,the path is a closed path. 3. connectivity ( p q in set S) If there exists a path between them consisting entirely of pixels in S. a connected component of S is the set of pixels that are connected to a pixel in S. if it only has one connected component ,then S is a connected set.
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adjacency, connectivity, region, and boundaries
if R is connected set, R is called a region of the image. 5. boundaries the boundary of a region R is the set of pixels in the region that have one or more neighbors that are not in R.
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Distance measure 1. A distance function or metric
For p(x,y), q(s,t),z(v,w), if (a) D(p,q)≥0 ( D(p,q) = 0 iff p=q ) (b) D(p,q) = D(q, p) (c) D(p,z) ≤ D(p,q) + D(q, z) 2. Euclidean distance
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Distance measure 3. D4 distance city block distance
4. D8 distance chessboard distance 2 D4(p,q)≤2 D8(p,q)≤2
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Linear and nonlinear operation
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