数字图像处理-图像的表达

y
2
1
0
x
0 12 3 4
Original Pixel
Row
Column 12 3 4 5
1 0 1 1 1 0 2 1 0 1 0 1 3 1 1 0 1 1
12 3 4 5
x
1
2
3
y
Cartesian co-ordinate system
Matrix co-ordinate system
Pixel co-ordinate system
Sampling and Spatial Resolution
If a continuous-tone image is approximated by a N lines*M pixels digital image, then it requires decisions about values for N and M. In practice, N and M are predetermined due to the limited choice of available cameras and image acquisition hardware and are normally set to integer powers of 2. As N and M are decreased, the number of pixels in a digital image decreased rapidly giving worse approximation of the original image due to lower spatial resolution
Spatial aliasing occurs with the high frequency detail being translated to a low frequency due to some of its transitions are missed
• In the selection of a suitable spatial resolution, the display-observer distance is another factor for consideration. As the distance between an image and observer doubles corresponding to a reduction of the image size by on-half, the spatial resolution can be decreased by on-half without causing any spatial detail loss for the observer.
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Digital Image Representation in Matlab
Matlab uses a rectangular matrix (two-dimensional array) to represent a digital image. There are four basic types of images supported by Matlab, namely, intensity (gray-level) images, binary images, RGB images and indexed images.
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• Like spatial resolution, the brightness resolution also depends on image-observer distance. The smaller the image as it is placed further away from the observer, the lower brightness resolution needs to be.
Image Digitiser
• Consequently, an image digitiser consists of five elements:
(a) Sampling aperture to allow the digitiser to access image elements individually
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Sampling and Spatial Resolution
• However, for a given application, selecting the minimum resolution necessary can significantly reduce storage and processing requirements. According to the classical sampling theorem, an image must be sampled at a rate at least twice as fast as the highest spatial frequency (the frequency at which brightness cycle from dark to light and back to dark) contained in the image.
Brightness Resolution 分辨率
• 電腦顯示器的解析度大約為 72 dpi ，印表機是從150 到1440 dpi (高解析度機種) ，而掃瞄 器的解析度是300dpi 或更高。
• Post scr i pt 的印表機使用一種 解析度衡量方式，稱為每英吋 線數( l pi )，意思是指每一英吋 中可以畫入的線條數量。這種 方式的影用是基於要把半色調 影像，例如相片，分解成點( 或 圖素) 。在過去，這種半色調的
1 (corresponding to white), and it is used for performing mathematical operations.
• uint8(unsigned 8 bit integers): the gray-level values range from 0 (corresponding to black) to 255(corresponding to white), and it is used to save memory as it requires only 1/8 the memory for a double precision array (no mathematical operations are defined for this data type).
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Intensity Images (Gray-Scale Images)
• Matlab uses a single matrix to represent an intensity image with the magnitude value of each element in the matrix corresponding to the gray-level of each pixel in the image.
invisible to the human eye, is normally a continuoustone image with various shades blended together smoothly having no disruptions. Acquisition of a digital image from a continuous-tone image requires digitization of spatial coordinates(Known as sampling) and digitization of brightness(Known as quantisation).
(d) A/D converter to convert the continuous output of the light sensor into an integer value
(e) Memory tபைடு நூலகம் store the gray-level values produced by the A/D converter
顯示是由不同寬度的直線構成。在近年，轉變成以格子的方式來呈現，因此可以把 影像分裂成點，每英吋線數的方式也就不適用了。報紙有 60 lpi的解析度，而雜 誌有133-175 lpi的解析度。高品質的印刷原料可能會超過 200 lpi。
Digital Image Representation
• A digital image is represented mathematically by the function f(x,y), where x and y are independent variables denoting spatial co-ordinates, and the value of f at spatial coordinates (x,y) gives the intensity of the image at that point. However, there are three different spatial co-ordinate systems being used in digital image processing:
(b) Scanning mechanism to move the sampling aperture over the image in s predetermined pattern
(c) Light sensor to measure the brightness of the image at each pixel through the sampling aperture
Correctly Sampled Image Line
Sampled at a rate 2 times the spatial frequency
Original Image Line
Undersampled Image Line
Sampled at a rate less than half the spatial frequency
Quantisation and Brightness Resolution
• If the intensity of a continuous-tone image at a sampling point is quantised to an integer value called the gray-level, then the accuracy of the gray-level assigned depends on the number of bits used to represent the number of gray-levels in an image. As the number of bits are decreased, the image appears coarser due to lower brightness resolution with an insufficient number of gray-levels in smooth areas of the image.
数字图像处理-图像的表达
Sampling&Quantisation 采样和量化
• 采 样 时 要 确 定 好 空 间 分 辨 率 ， 即 DPI • 量化时要确定好灰度分辨率，將采样
影像转换为 数值的过程称为量化。例 如 ， 白 色 是 转 化 为 “1” 和黑色則转化为 “0” 。
• Digital Image Acquisition A physical image, which may be visible or
Two different data types are available in Matlab to represent the gray-level: • double(double precision): the gray-level values rang from 0 (corresponding to black) to