Transcript 無投影片標題

影像的定義
• 一般以繪圖、相片或銀幕的顯示，敘述
影像的存在。
• 它代表了空間訊息(information)，有實
質的意義內涵。
•世間有更多視而不見的物體、只因為它
們不具任何意義。
•有時也能看到不存在影像。
•更有主觀性的錯覺。
An image is:
" A non-uniform distribution
of energy or matter“
Types: Aerial
Dose
Latent
Developed
A  A(x, y,s;t)
Normally, CW cases
(time-independent solution) is considered
針孔映像
幻覺影像?
Generalized (cognition)
representation of
Multi-Dimensional information
座
標
• Conventional system
• {x,y} perpendicular
to propagation
direction
• “z” or “s” along
Y
propagation axis
X
Z, S
方
式
• Image description
– Pixels and Field:
– Patterns: ensemble of contiguous non-zero
value pixels
• Image analysis
– Mathematical description
• Information content
– Independent of image carrier (energy,
material)
– Limited by pixel size (Shannon)
Digital Images
• Continuous images A(x,y;s;t) are
sampled on a regular grid
• Size of grid unit cell defines the “pixel”
• Main definitions
– Image size: Nx by Ny (pixels)
– Image resolution: dX by dY (cm)
– Image field: Lx by Ly (cm)
點光源與展體影像
影像的實際定義應該是:
無限組透過光圈的光束聚合
運算？ 描述？
Problems with Pinholes
•Pinhole size (aperture) must be “very small” to obtain
a clear image.
•However, as pinhole size is made smaller, less light is
received by image plane.
•If pinhole is comparable to
wavelength of incoming light,
DIFFRACTION effects blur
the image!
•Sharpest image is obtained
when: pinhole diameter
d 2
f '
Example: If f’ = 50mm,
 = 600nm (red),
d = 0.36mm
全 真 映 像(paraxial)
'
f'
η
z
z'
η'
Inverted
One-to-One
Real & Enlarged
The sinc function
This function’s
information
encoded in the
spatial domain, not
in the frequency
domain.
工
具
The traditional method of describing 3-D imaging
properties of a light microscope is by intensity point
spread function (PSF) or it’s Fourier transform, the optical
transfer function (OTF).
However, the more compact way is to use 2-D generalized
pupil function.
The advantage: the easier way of modification of the
observed PSF to introduce known aberrations.
The disadvantage: it’s not too easy to determine the
complex-valued pupil function from the measured
intensity PSF.
困
擾
Image quality in light microscopy is degraded by
aberrations, causing from:
-sample’s refractive index ( acting like lens)
-the features of the microscope set-up
The result: the image is blurred and not diffraction
limited or specifically speaking:
-we loose resolution
-reduce signal to noise ratio
-get distortions in the collected data.
Microscope Image Formation
and Fourier Optics
Image formation in microscope could be described
as a linear process in which each point of an object
is convolved by the lens PSF to produce a blurred
image
i ( x , y , z )  o ( x , y , z )  s ( x, y , z )
blurred image
original object
lens’s PSF
In the Fourier plane it turns to be:
I ( k , k , k )  O (k , k , k )  S (k , k , k )
x
y
z
x
y
z
x
y
z
S (k x , k y , k z )  OTF  F  PSF 
OTF describes the impulse response of the
microscope in the terms of spatial frequency.
In most microscopy techniques we measure only
light intensities, i.e. :
As a result, all information about the light phase is lost!
Intensity
PSFI  PSFA
complex amplitude
2

F  PSFI   F  PSFA   F

 PSFA 
In Fourier space the intensity OTF is the autocorrelation
of the amplitude OTF.
The benefits of acquiring phase information for a
microscope system are:
-quantification of the aberrations/features of an optical
system for use in deconvolution of collected data.
- using as a means to adjust, correct or compensate for
optical problems in the optical system or in the sample
using adjustable elements in the optical path.
The pupil function is a powerful way to understand image
formation. A phase retrieved pupil function can be used to
calculate PSFs that contain key features observed in the
measured PSF’s that are not represented in simulated PSFs.
光學系統解像率
Δx = 0.61 λ/N.A.
鑑
別
率
測
試
靶
Johnson 鑑別定義
關鍵次元
Johnson 實驗數據
TARGET
RESOL. / MIN. DIMEN. IN LINE PAIRS
SIDE VIEW DETEC. ORIENT. RECOG. IDENTIF.
TRUCK
0.90
1.25
4.5
8.0
M-48 TANK
0.75
1.20
3.5
7.0
STALIN TANK 0.75
1.20
3.3
6.0
CENTURION 0.75
1.20
3.5
6.0
HALF-TRACK 1.00
1.50
4.0
5.0
JEEP
1.20
1.50
4.5
5.5
COMMAND 車 1.20
1.50
4.3
5.5
SOLDIER(站立) .50
1.80
3.8
8.0
105 砲
1.00
1.50
4.8
6.5
AVERAGE 1.0.25 1.4 .35 4.0 .8
6.4  1.5
Fourier image
Signals are functions of time. There are two ways by which we can
represent the signal.
Time Domain
Representation
Signal
Frequency Domain
Representation
Why Use Frequency Representations When We Can Represent
Any Signal With Time Functions?
Advantages of Frequency response methods
Gives a different kind of insight into a system.
It focuses on how signals of different frequencies are represented
in a signal. We think in terms of the spectrum of the signal
Most of us would rather do algebra than solve differential equations
Gives more insight into how to process a signal to remove noise
Easier to characterize the frequency content of a noise signal than
it is to give a time description of the noise.
Different treatment of different parts of the electromagnetic
spectrum means that you can separate out different signals.
“So, give it a shot and try learning about frequency response
methods. They can save you time and money in the long run”
Objective
Be able to compute the frequency components
of the signal.
Be able to predict how the signal will interact
with linear systems and circuits using frequency
response methods.
The Fourier Series
Fourier, doing heat transfer work,
demonstrated that any periodic
signal can be viewed as a linear
composition of sine waves
“A periodic signal can always be represented as a sum of sinusoids,
This representation is now called a Fourier Series ”
How a signal can be built from a sum of sinusoids?
Example:Here is a single sine signal
The expression for this signal is
Sig(t) = 1 * sin(2пt/T)
+ (1/3)sin(6пt/T)
+ (1/5)sin(10пt/T)
79th
49th
Multiple
Multiple
In fact, the way we are building this signal we are using Fourier's results.
We know the formula for the series that converges to a square wave.
Here's the formula. For a perfectly accurate representation, let N go to infinity.
Calculating
The Fourier Series Coefficients
At this point there are a few questions
that we need to address.
What kind of functions can be represented using
these types of series?
Actually, most periodic signals can be represented with a series
composed of sines and cosines. Even discontinuities (like in the
square wave function or the saw tooth function in the simulations).
practical implications
Functions can be composed of sines and cosines at different frequencies,
Various linear systems process sinusoidal signals is frequency dependent,
The response of a system with a periodic input can be predicted using
frequency response methods.
Signals can be analyzed using frequency component concepts.
Special computational techniques (FFT) have been developed to calculate
frequency components quickly for various signals.
Examples:
Sound signals in
earthquakes
Bridge vibrations
Stress vibrations in
buildings and aircraft
The series for a given function
Periodic signal can be represented as a sum of both sines
and cosines
Also, since sines and cosines have no average term, periodic
signals that have a non-zero average can have a constant
component
This series can be used to represent many periodic functions
The coefficients, an and bn, are what you need to know to generate the signal
Formulas to find all the coefficients
in a Fourier Series expansion:-
Fourier Transforms
The Fourier transform (FT) is a generalization of the Fourier series.
Instead of sines and cosines, as in a Fourier series, the Fourier
transform uses exponentials and complex numbers.
i
e  cos   i sin 
For a signal or function f(t), the Fourier transform is defined as
Inverse Fourier transform is defined as
Digital implementation
M
N
g (i, j )   f (m, n) PSF (i  m, j  n)
m 1 n 1
M
N
r (i, j )   f1 (m, n) f 2 (i  m, j  n)
m1 n1
M
N
F (k , l )   f (m, n)e
m 1 n 1
i 2  km / M  ln/ N 
影 像 處 理
• Why should an image be
processed prior to analysis?
– It suffers from noise
– It fails to highlight the particular
feature in which we are interested
• In image processing, we
remove noise & unnecessary
features while highlighting the
required features
– Filtering
Optical image
Ronchi (1961):
Ethereal – physical nature
Calculated – mathematical
representation
(resolution, PSF,.., etc.,), it is noise
free!
Detected – practice image , source
energy
& sensitivity included.
Resolution is limited by systematic &
random errors due to inadequacy of
description.
Linear system
描述影像的兩條途徑
傅氏轉換
物體
影像頻譜
點
展
包
容
積
分
乘
傳
遞
函
數
影像
調幅頻譜
傅氏返轉換
Two points resolution
• PSF behavior:
0.8 overlape ; ¼ λRayleigh criteria.
A rule conveniently to define resolution.
• Depends nothing more than size & shapes
of aperture + wavelength of light.
The radius of the Airy disk: 1.22λF/#
The measurement can never be S/N
free.
Imaging formation
Intensity function
C=
Optical Transfer function
OTF = MTF + PTF
Neglect in general
系統性能解讀
映像品質規格
• For photographic films, namely
modulation transfer function (MTF),
ISO speed, granularity, and D-plot,
which users can relate to certain
image qualities
• For digital sensors, signal-to-noise
ratio (SNR), dark current, fill factor,
full-well capacity, and sensitivity
interact with image quality
Mathematical representation
of an image
Functional dependence of f in x (position vector) :
f = f （x）
General distortion function:
h = h (x,ξ)
Implied that f at ξis spread out according to the formula
h (x,ξ).
For linear distortion system, the blurred information:

b(x) =
 f

(ξ) h (x,ξ) d (ξ)
2D, all information, over area d, i.e.
Fourier Transformation
Power
spectrum
amplitude
Phase
change
Temporal coherence
Spatial coherence
Infinitive
coherence
finite
coherence
Pin-hole
Out-of focus imaging
Cylindrical
Function
F-T
Blurred spot
( disk )
Amplitude filter
shape?
Correction and deblurring
Spatial filtering
Coherent
light
transparency
Shaded area
blocked
Improve the image
TV
image
Blurred
image
processed
Overdeveloped
linear
( optical spectrum)
Improve Astigmatism
Amplitude Transfer Function
Combined = add + shift
Phase Transfer Function
Spatial masks
Low-pass filters eliminate or attenuate high
frequency components in the frequency
domain (sharp image details), and result in
image blurring.
High-pass filters attenuate or eliminate lowfrequency components (resulting in
sharpening edges and other sharp details).
Band-pass filters remove selected frequency
regions between low and high frequencies
(image restoration).
Filters and their
effects
High-pass
Band-pass
BLIND DECONVOLUTION
Some applications
• Image sorting
• Remote sensing
• Pattern (character)
recognition
• Target tracking
• Biological imaging
• Intelligence communication
光纖與光纜
將許多根光纖綑在一起，外圍再包一層
塑膠，便可形成光纜，可傳送更多資訊
光纖通訊所用的零組件
光纖在內視鏡中的應用
• 各種醫療用內視鏡如胃鏡、大腸鏡等，都使用
光纖傳輸訊號
• 內視鏡的基本結構─以胃鏡為例(左圖) ，前端
為一個迷你攝影機，而所拍攝到的胃內部影像
訊號透過光纖傳送到外部螢幕上(右圖)
各種顯示器的應用
軟性電子材料顯示器
數位和傳統相機的差別
• 傳統相機是利用光線讓底片感光，而將影像記錄在底
片上，無法直接連接電腦作處理
• 數位相機是利用電荷耦合元件(Charge Coupled Device ,
CCD)或是互補式氧化物金屬半導體(Complementary
Metal Oxide Semiconductor, CMOS)的影像感應功能，
將光線轉換為數位訊號，這些訊號可儲存於內建的記
憶體晶片上，並且可直接連上電腦作影像處理
追蹤熱源之響尾蛇飛彈
• 響尾蛇飛彈於1953年由美國試射成功，它使用紅
外線感測器追蹤敵機，可鎖定敵機引擎的位置，因
為飛機引擎的溫度最高，會輻射大量紅外線
• 1958年(民國47年)台海「八二三砲戰」期間，我國
空軍F-86「軍刀式」戰鬥機發射AIM-9B型響尾蛇
飛彈，擊落中共空軍 10 架以上米格15戰鬥機
紅外線防盜器
• 人的體溫與周圍環境不同，會發射特定波長範
圍的紅外線，因此可用紅外線感測器來製作防
盜器，只要感測器偵測到有人靠近，即可發出
警訊
• 紅外線防盜器只能偵測是否有人靠近，但無法
分辨是「好人」還是「壞人」，必須要配合其
他影像處理方法
Conclusion
Filters -- Linear and nonlinear
Source -- coherent and incoherent
H. H. Hopkins (1955)
B & W: partial coherent !!
Mutual intensity included
meaning:
Precision computation