医学图像处理-Chapter 2_Basics of Image Processing_092016

二维采样定理（Nyguist 准则）
1/△x,1/△y≥2倍的图象函数上限频带。
一维信号
二维图象
How to choose the spatial resolution
Spatial resolution Original image = Sampling locations
Under sampling, we lost some image details!
2.2 Basic Concepts
目的：便于计算机处理、存储、传输…… 离散化： 空间采样： 512X512 象素 Pixel，体素 (Voxel) 分辨率 Resolution 幅值量化：256级, 28级, 8bit,16bit,24bit 灰度 Gray value 灰度级 Gray level 强(密)度 Intensity 数字图像的矩阵表示与存储
Resolution
Pixel resolution The term resolution is often used for a pixel count in digital imaging. An image of N pixels high by M pixels wide can have any resolution less than N lines per picture height, or N lines.
How about color image?
Digital image = a multidimensional array of numbers (such as intensity image) or vectors (such as color image)
Each component in the image called pixel associates with the pixel value (a single number in the case of intensity images or a vector in the case of color images).
–N= , M = 2m of bits/pixel)
2n
, Q = 2q
(q is the #
– Storage requirements: NxMxQ (e.g., N=M=1024, q=8, 1MB) I=f(x,y) , x,y denote the row and column of the array
Gray value(灰度值)
Gray level(scale) resolution
• 256 gray levels (8bits/pixel) levels (4 bits/pixel) 32 gray levels (5 bits/pixel) 16 gray
•
8 gray levels (3 bits/pixel) levels (1 bit/pixel)
w 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 associated values.
Gray level(scale) resolution
A grayscale or greyscale digital image is an image in which the value of each pixel is a single sample, that is, it carries only intensity information. Grayscale images are often the result of measuring the intensity of light at each pixel in a single band of the electromagnetic spectrum 0-255,0-65535,…
Spectral resolution
Color images distinguish light of different spectra. Multispectral images resolve even finer differences of spectrum or wavelength than is needed to reproduce color. That is, multispectral images have higher spectral resolution than normal color images.
10 10 16 28 70 56 43 9 65 6 26 3756 78 32 99 54 70 96 67 6013902296 15 25 67 21 54 47 42 87853943 32 15 92 85 54 65 65 39 32 65 87 99
Sampled image
How to choose the spatial resolution : Nyquist Rate
Original image Sampled image
2mm
1mm
No detail is lost! Minimum Spatial resolution Nyquist Rate: Period (sampling rate) = Sampling locations
第二章 Basics of Digital Image 数字图象基础
2.1 How to create an image
采样与 量化 一、连续图象 f ( x, y , t ) 照片、电视、录象、电影。 数学表达式： 是一个二维分布函数，t是时间 变量。
Generating a Digital Image
Aliased Frequency
1 0.5 0 -0.5 -1
x1 (t ) sin(2t ),
f 1 f 6
x2 (t ) sin(12t ),
0
0.5
1
1.5
2
1 0.5 0 -0.5 -1
Sampling rate: 5 samples/sec
0
0.5
1
1.5
2
Two different frequencies but the same results !
Spectrum VIS (~0.40µ m to ~0.75µ m) NIR (~0.75µ m to ~1.3µ m) SWIR (~1.3µ m to ~3.0µm)
Temporal resolution
Movie cameras and high-speed cameras can resolve events at different points in time. The time resolution used for movies is usually 15 to 30 frames per second (frames/s)
Spatial resolution must be less or equal half of the minimum period of the image or sampling frequency must be greater or Equal twice of the maximum frequency.
二、数字图象
二维图像用有限数字数值像素的 表示。由数组或矩阵表示，其光照位 置和强度都是离散的。数字图像是由 模拟图像数字化(采样与量化)得到 的、以像素为基本元素的、可以用数 字计算机或数字电路存储和处理的图 像。 三维 数字图象 类似……
Image digitization
• Sampling means measuring the value of an image at a finite number of points. • Quantization is the representation of the measured value at the sampled point by an integer.
f (0,0) f (1,0) ... f ( N 1,0)
f (0,1) f (1,1) ... f ( N 1,1)
ቤተ መጻሕፍቲ ባይዱ
... ... ... ...
f (0, M 1) f (1, M 1) ... f ( N 1, M 1)
x Origin y f(x,y)
Image “After snow storm”
4 gray levels (2 bits/pixel)
2 gray
Intensity(强度)
In physics, intensity is the power transferred per unit area.
2.3 How to represent an image
• An image is represented by a rectangular array of integers. • An integer represents the brightness or darkness of the image at that point. • N: # of rows, M: # of columns, Q: # of gray levels