Projection-Based Image Registration in the Presence of Fixed-Pattern Noise

Projection-Based Image Registration in the Presence of Fixed-Pattern Noise Stephen C.Cain,Majeed M.Hayat,Senior Member,IEEE,and Ernest E.Armstrong

Abstract—A computationally efficient method for image regis-tration is investigated that can achieve an improved performance over the traditional two-dimensional(2-D)cross-correlation-based techniques in the presence of both fixed-pattern and temporal noise.The method relies on transforming each image in the sequence of frames into two vector projections formed by accu-mulating pixel values along the rows and columns of the image. The vector projections corresponding to successive frames are in turn used to estimate the individual horizontal and vertical components of the shift by means of a one-dimensional(1-D) cross-correlation-based estimator.While gradient-based shift esti-mation techniques are computationally efficient,they often exhibit degraded performance under noisy conditions in comparison to cross-correlators due to the fact that the gradient operation amplifies noise.The projection-based estimator,on the other hand, significantly reduces the computational complexity associated with the2-D operations involved in traditional correlation-based shift estimators while improving the performance in the presence of temporal and spatial noise.To show the noise rejection capability of the projection-based shift estimator relative to the2-D cross correlator,a figure-of-merit is developed and computed reflecting the signal-to-noise ratio(SNR)associated with each estimator.The two methods are also compared by means of computer simulation and tests using real image sequences.

Index Terms—Fixed-pattern noise suppression,image registra-tion,motion estimation,vector projection.

I.I NTRODUCTION

I MAGE registration is commonly used to provide electronic

stabilization of sensors or to facilitate the processing of multiple motion-compensated frames in order to improve image quality(e.g.,by means of temporal averaging).Some new appli-cations of registration also include resolution enhancement from multiple frames of data[1]–[5]and nonuniformity correction in focal-plane arrays[1],[6]–[8].In many situations,the perfor-mance of algorithms that employ image registration information relies heavily on the accuracy of the shift estimates.The accuracy of the shift estimates generated using various registration algo-rithms is,in turn,strongly affected by the temporal and spatial Manuscript received July7,2000;revised August30,2001.This work was supported by the National Science Foundation(CAREER Program MIP-9733308).The associate editor coordinating the review of this manuscript and approving it for publication was Dr.Christoph Stiller.

S.C.Cain is with the Department of Electrical and Computer Engineering, University of Dayton,Dayton,OH45469-0245USA and also with the De-partment of Engineering,Purdue University at Fort Wayne,Fort Wayne,IN 46805-1499USA.

M.M.Hayat is with the Electro-Optics Program and the Electrical and Computer Engineering Department,University of Dayton,Dayton,OH 45469-0245USA and also with the Electrical and Computer Engineering Department,The University of New Mexico,Albuquerque,NM87131-1356 USA(e-mail:hayat@https://www.wendangku.net/doc/3611089350.html,;mhayat@https://www.wendangku.net/doc/3611089350.html,).

E.E.Armstrong is with OptiMetrics,Inc.,AFRL/SNJM,Wright Patterson AFB,OH45433-7700USA(e-mail:ernest.armstrong@https://www.wendangku.net/doc/3611089350.html,). Publisher Item Identifier S1057-7149(01)10571-3.noise inherent in all sensors[9].Temporal noise,which fluctuates randomly from frame to frame,includes photo-detection noise, background or stray light,dark current,read-out noise,etc.In contrast to temporal noise,spatial noise has the characteristic that its realizations do not vary from frame to frame resulting in an ambient spatial pattern which superimposes itself on the true scene[10].This spatial noise is often referred to as fixed-pattern noiseand is duetothe factthateverydetector inthe arrayresponds differently to light.Fixed-pattern noise is especially undesirable in image registration since any pattern that remains stationary in time will tend to bias any shift-estimation algorithm toward solutions that favor no shifts between the frames of image data. Fixed-pattern noise can be reduced by calibrating the sensor by means of imaging target scenes with uniform intensities. Fixed-pattern noise can also be reduced from sequences of video by post-processing algorithms[6],[7],[11].However,some of these methods inherently rely on accurate image registration of the raw video[8].It is therefore very desirable to have a registration algorithm that is tolerant to fixed-pattern noise.

A commonly used registration technique is based on max-imizing the two-dimensional(2-D)cross-correlation function between successive frames,in which case,the shift estimate is defined as the maximizing point[12].The2-D cross-corre-lator is generally regarded as a robust estimator in the presence of noise in comparison to more computationally-efficient es-timators.Unfortunately,its implementation involves three dis-crete-Fourier transforms(DFTs)at the size of the image.Gra-dient-based shift estimation techniques[2],[13],on the other hand,have a reduced computational complexity but are sensi-tive to fixed-pattern noise since they may measure false spatial gradients that will be consistently present in successive frames. In this paper,the concept of integral projection is employed to develop a projection-based registration technique that is com-putationally efficient and can achieve improved performance over the traditional2-D cross-correlation-based techniques in the presence of both fixed-pattern and temporal noise.This concept was first conceived from Huang’s observation that the linear phase associated with simple translations is encoded on the Fourier axes[14].Since then the integral projection shift-estimation technique had been introduced to help accom-plish inter-frame image encoding by registering subblocks within an image with subblocks within successive frames in a video sequence[15]–[17].Under the method considered in this paper,each image in a sequence is transformed into two vector projections,formed by accumulating pixel values along the rows and columns of the image,which are subsequently used to estimate the horizontal and vertical components of the shift by means of a one-dimensional(1-D)cross-correlation-based

1057–7149/00$10.00?2001IEEE

estimator.All of the 2-D DFTs associated with the traditional cross-correlator are therefore replaced by 1-D operations.Most importantly,by virtue of the row/column averaging mech-anism involved in the projections and the mutual statistical independence of the response characteristics of the detectors,the effect of fixed-pattern noise can be significantly reduced in many practical situations.Although this 1-D technique for image registration has been used in other similar applications [15]–[17],the notion that the projection operation improves performance over the 2-D correlator in the presence of either temporal or fixed-pattern noise has been either completely unknown or not well understood.It is the goal of this paper to reveal the mechanism by which this improved performance is realized and provide a mathematical framework by which the performance improvement can be understood and quantified.This paper is organized as follows.In Section II,a description of the projection-based estimator is given and an explanation is presented as to why the projections preserve the shift informa-tion.In Section III,a signal-to-noise ratio (SNR)analysis is per-formed that compares the performance of the 2-D cross-correla-tion shift estimator to that of the projection-based shift estimator in the presence of both temporal and fixed-pattern noise.A per-formance figure-of-merit is defined for both shift estimators and evaluated using two image models that reflect scenarios when the image possesses high and low degrees of statistical spatial correlation.In Section IV ,computer simulations are generated demonstrating the performance of the projection technique on simulated image sequences.In Section V ,real image sequences are used to demonstrate the performance of the projection tech-nique.The main conclusions are summarized in Section VI.

II.T HE P ROJECTION -B ASED S HIFT E STIMATOR

Consider observing two successive measurements (frames)of a

scene

matrix whose elements

are

(1)

where

is translated by an

amount

and

and

and

where the shifts are assumed for convenience to be circular.(Border effects resulting from the circular shift become negli-gible as ,

by the

rule

and

(3)

and

and

and

can be written

as

respectively,

where .We now substitute the above projections into the expression for the

projection-based shift estimator given in(3)and apply the con-volution property of the DFT to

obtain

,which is defined

by

,

which implies

that

.

In any real imaging system,the scene does not shift circularly,

which causes new information to enter the field of view.This

new information is similar to noise,which makes the Fourier

arguments for accurate image registration less valid.The pro-

jection-based estimator is sensitive to new information entering

the scene and so the following noncircular correlation estimate

is developed with the projections as opposed to a circular cor-

relation estimate.In order to help the projection-based shift es-

timation algorithm ignore new information entering the scene,

we introduce the window

function that has the following

spatial

structure:

if

and

otherwise.In the

inequality,

,

where

is the average value of this projection.Sim-

ilarly,the projection in the vertical direction is formed in the

following manner.The shift estimate is determined from(3)by

an exhaustive search over all

integers

,we define the SNR at

any

shift as the ratio between the effective signal squared

and the sum of the variance of the noise

at and the vari-

ance of the noise

at

,to de-

fine the

figure-of-merit

(5)

where the factors appearing in the denominator are condi-

tional variances

(e.g.,

)and the expectation in the denominator of(5)

represents ensemble averaging of the image

.If noise were

not present in the

system,

correlation is not always dependent on these differences,the figure-of-merit is a function

over

(6)

and

(8)

and

is assumed to be temporally fixed between the two observed

frames and its entries are assumed to be independent and

identically distributed random variables each with a variance

of

and

and

,appearing as the auto-correla-

tion

function

,An example of images

that possess this property include astronomical images of

unresolvable stars.With the above auto-correlation model,the

expression

for

that

minimizes

which can be maximized

over to yield the upper

bound

).In this special case,the

figures-of-merit

within and obtain a version

of only.This assumption does not

affect the computation

of

from which it follows

that

in the expression

for

that minimizes the

ratio

,the

ratio

and

Fig.2.Images showing a star in the presence of temporal noise at two different times.

shift estimator will have a higher SNR than the 2-D cross-cor-relation shift estimator

whenever

.IV .S IMULATION R ESULTS

In this section,a set of simulations is generated to demon-strate the validity of the conclusions established in the previous

section.The first set of simulations feature an image of a simu-lated star field.This image exhibits no spatial correlation (ap-proximating the uncorrelated image model considered in the previous section)and is corrupted with temporal Poissonian noise.(We use the Poisson model as a convenient approximation that captures the signal-dependent nature of temporal noise es-pecially in cases when shot noise dominates the sensor read-out noise.)These images are shown in Fig.2.The operation of generating two circularly shifted versions of the scene is re-peated 100times and shift estimates are generated using both the projection-based and 2-D correlation methods.These shift estimation algorithms are implemented exactly as described in Section II with a search range of seven pixels.The registra-tion

parameters

are integers as are the shifts gener-ated in the simulation.The cross-correlations are computed and the maximum is chosen over the entire range of shifts for both algorithms.Although real sequences of data generally possess noninteger and noncircular shifts,these assumptions are ade-

quate for comparing the performance of the shift estimation techniques.

The shift estimates are compared with the known synthetic shifts for accuracy.The shift estimation error in pixels is com-puted by squaring the difference between the known synthetic shifts and the estimated shifts and summing this squared error over all frames.The result of this summation is then divided by the number of frames used in the test and the square root of this result is taken as the average error with units of pixels.The 100trials are used to establish the statistical behavior of the shift estimation techniques.The results are shown in Table I.The performance of the two shift estimators are shown as a func-tion of the SNR.The SNR is defined as the amplitude of the signal divided by the standard deviation of the noise.The peak signal-to-noise ratio (PSNR)in an image is then the highest SNR achieved within the frame.These results verify that in-deed the 2-D cross-correlation shift estimator outperforms the projection-based shift estimator when the scene is spatially un-correlated.

Next,a fixed-pattern noise is added to each frame and the standard deviation of the fixed-pattern

noise

Fig.3.Example of star images with fixed-pattern noise added to them.

PSNR of the data is fixed at ten and the ratio of fixed-pattern noise variance to temporal noise variance is varied.These re-sults again verify that the lack of correlation in the scene causes the2-D cross-correlation shift estimator to outperform the pro-jection-based shift estimator.In general,we have observed that the performance of the two estimators becomes comparable as the fixed-pattern noise variance increases.The next set of data is generated in the same manner as in the previous simulations using the scene shown in Fig.4,which possesses strong spa-tial correlation.This scene was chosen because its auto-correla-tion is similar to the linear auto-correlation model used in Sec-tion III.The auto-correlation function of the scene is shown in Fig.5.The results,shown in Table III demonstrate that the pro-jection-based shift estimator outperforms the2-D cross-corre-lation shift estimator.Finally,Table IV shows the performance of the two estimators in the presence of fixed-pattern noise.The PSNR is fixed at26when the fixed-pattern noise is small with respect to the temporal noise.The fixed-pattern noise variance is adjusted to be a fraction of the temporal noise variance to produce the various ratios of fixed-pattern to temporal noise variance shown in Table IV.These results show that the perfor-mance improvement achieved using the projection-based shift estimator is more significant when fixed-pattern noise is a se-rious

concern.Fig.4.Cloud scene used to generate the data used to analyze the behavior of the shift estimators in the presence of high spatial correlation.

To demonstrate the correlation between the simulations and the analytic expressions for the figures-of-merit,the magnitudes

of

and

Fig.5.Auto-correlation function of the scene used to test the performance of shift estimation in the presence of high spatial correlation.

TABLE II

P ERFORMANCE OF THE P ROJECTION -B ASED E STIMATOR (1-D)V ERSUS THE 2-D C ROSS -C ORRELATION E STIMATOR (2-D)IN THE P RESENCE OF B OTH F IXED -P ATTERN AND T EMPORAL N OISE .N OTE T HAT THE I MAGE P OSSESSES

N O S PATIAL C ORRELATION IN T HIS E

XAMPLE

and

m wavelengths).

TABLE III

P ERFORMANCE OF THE P ROJECTION -B ASED E STIMATOR (1-D)V ERSUS THE 2-D C ROSS -C ORRELATION E STIMATOR (2-D)W HEN S PATIAL C ORRELATION I S

P RESENT IN THE I

MAGE

TABLE IV

P ERFORMANCE OF THE P ROJECTION -B ASED E STIMATOR (1-D)AND THE 2-D C ROSS -C ORRELATION E STIMATOR (2-D)A GAINST

T EMPORAL AND F IXED -P ATTERN N OISE W HEN S PATIAL C ORRELATION I S

P RESENT IN THE I

MAGE

Fig.6.

Plot showing the value of the figures-of-merit

F and F

=100; =10; =

0;w = =0;and z =1.

Two sample frames from this 80-frame sequence are shown in Fig.7.The 2-D cross-correlator is used to measure the shifts between frames of the sequence in integer amounts.This set of shifts is used as the true shifts for purposes of measuring the registration error when noise is added to the

Fig.7.Two sample frames from a sequence of infrared video data(top).Frame one of the sequence at a PSNR of2(bottom left)and PSNR of20(bottom right).

video sequence.In the first test,fixed-pattern noise is added to the sequence in varying amounts to produce19sequences each possessing a different PSNR between2and20.Fig.7 shows frame one of the sequence at a SNR of2and20. Fig.8shows the error performance of the projection-based technique(dotted line)and the2-D cross-correlator(solid line) plotted as a function of the PSNR in the data.The error metric used in this study is the root mean-squared error in units of pixels.Finally,Fig.9shows the performance of the algorithms as a function of the PSNR when the noise is temporal in nature(changes from frame to frame in the sequence).In both cases it is clear that the projection-based technique produces consistently lower registration root mean-squared error. The second sequence of video is taken with a visible camera of the planet Jupiter through severe atmospheric turbulence.This type of turbulence changes the impulse response of the imaging system between observations,which will cause the image to change in its appearance from frame to frame.Two sample frames from this40-frame sequence are shown in Fig.10.The2-D cross-correlator is again used to measure the shifts between frames of the sequence in integer amounts.In the first test,temporal noise is added to the sequence in varying amounts to produce ten video sequences each possessing a different PSNR between1and10.Fig.10shows frame one of the sequence at a SNR of1and10.Fig.11shows the error performance of the projection-based technique(dotted line) and the2-D cross-correlator(solid line)plotted as a function of the peak temporal SNR in the data.Finally,Fig.12shows the performance of the algorithms as a function of the PSNR when fixed-pattern noise is added to the data.In both cases it is

Fig.8.Root mean-squared registration error performance of the

projection-based technique (dotted line)and the 2-D cross-correlator (solid line)as a function of peak fixed-pattern SNR for the infrared data sequence.This demonstrates the improved noise-rejection capability of the projection-based

technique.

Fig.9.Root mean-squared registration error performance of the projection-based technique (dotted line)and the 2-D cross-correlator (solid line)as a function of peak temporal SNR for the infrared data sequence.

clear that the projection-based technique produces consistently lower root mean-squared registration error.

VI.C ONCLUSION

Image registration of adjacent frames in a video sequence is often desired in order to take advantage of temporal correlation in images.This process can be very computationally intensive relative to the scale dictated by real time processing.The pro-jection-based algorithm reported here has the potential of al-leviating much of the computational burden of image registra-tion by operating only on vectors as opposed to images.The proposed technique also has the benefit of being more robust against temporal and especially fixed-pattern noise,which can be a great impediment to achieving accurate image registration.

In this paper,the performance of the projection-based shift es-timator is compared to the performance of the 2-D cross-corre-lation shift estimator.A significant conclusion drawn from this work is that the relative performance of the two estimators varies depending on the auto-correlation function of the scene.

The two auto-correlation models considered in the analysis show the diverse dependence of these algorithms on the degree of spatial correlation in the image.Scenes that possess signifi-cant neighbor-to-neighbor correlation over large neighborhoods will allow the projection-based shift estimator to perform better than the 2-D cross-correlator,while scenes whose pixels are un-correlated allow the 2-D cross-correlator to produce superior re-sults.Both estimators work well when the standard deviation of the noise is small with respect to the contrast in the scene.The decision of which estimator to use would be a simple one at high SNRs because the projection-based technique,as described in Section II,operates

on pixels in comparison

to

.With this

auto-correlation model,the expression

for

that

minimizes

is minimized

if

1870IEEE TRANSACTIONS ON IMAGE PROCESSING,VOL.10,NO.12,DECEMBER

2001

Fig.10.(Top)Two sample frames from a sequence of video of the planet Jupiter,(bottom left)frame one of the sequence at a PSNR of 1,and (bottom right)PSNR of 10.

the numerator gives rise to the following

inequality:

Next,we wish to maximize the denominator or determine an upper bound for it.Because all the terms in the denominator are

strictly positive,if we choose them to be as large as possible,this will serve as an upper bound for the denominator.If all the impulse functions take on their maximum value,then the following inequality

results:

CAIN et al.:PROJECTION-BASED IMAGE REGISTRATION IN PRESENCE OF FIXED-PATTERN NOISE

1871

Fig.11.Root mean-squared registration error performance of the projection-based technique (dotted line)and the 2-D cross-correlator (solid line)as a function of peak temporal SNR for the Jupiter data

sequence.

Fig.12.Root mean-squared registration error performance of the projection-based technique (dotted line)and the 2-D cross-correlator (solid line)as a function of peak fixed-pattern SNR for the Jupiter data sequence.

For the projection-based estimator,the vertical-direction figure-of-merit can be computed and expressed

as

,re-sults

in

and ,then the numerator is

minimized.Because all the terms in the denominator are non-negative,if we choose the impulse functions to be equal to zero,then this will serve as a lower bound for the value of the de-nominator.Now that the numerator is as large as possible and

the denominator is as small as possible,the figure-of-merit is bounded above in the following

inequality:

.This means that

the inequality can be reduced to the following

expression:

If the ratio of the figures-of-merit is greater than one then the denominator subtracted from the numerator should be greater than

zero

,

if

1872IEEE TRANSACTIONS ON IMAGE PROCESSING,VOL.10,NO.12,DECEMBER2001 [13] A.Schaum and M.McHugh,“Analytic methods of image registration:

Displacement estimation and resampling,”,Naval Res.Rep.9298,Feb.

1992.

[14]T.S.Huang,Image Sequence Analysis.Berlin,Germany:Springer-

Verlag,1981.

[15]S.C.Cain and K.D.Sauer,“Fast block motion estimation using integral

projections,”presented at the IEEE Workshop Visual Communications

and Signal Processing,Raleigh,NC,1992.

[16]K.Sauer and B.Schwartz,“Efficient block motion estimation using in-

tegral projections,”IEEE Trans.Circuits Syst.Video Technol.,vol.6,pp.

513–518,Oct.1996.

[17]J.S.Kim and R.H.Park,“A fast feature-based block matching algorithm

using integral projections,”IEEE J.Select.Areas Commun.,vol.10,pp.

968–971,June1992.

[18] A.R.Hambley,Introduction to Communication Systems.Rockville,

MD:Computer Science,1990.

[19]H.Stark and J.W.Woods,Probability,Random Processes,and Estima-

tion Theory for Engineers.Englewood Cliffs,NJ:Prentice-Hall,1994.

[20]M.C.Roggemann and B.Welsh,Imaging Through Turbulence.Boca

Raton,FL:CRC,

1996.

Stephen C.Cain was born in Pontiac,MI,in 1969.He received the B.S.E.E.degree from the University of Notre Dame,Notre Dame,IN,in1992, the M.S.E.E.degree from Michigan Technological University,Houghton,in1994,and the Ph.D.degree in electrical engineering from the University of Dayton,Dayton,OH,in2001.

From1994to1997,he served as an Officer in the United States Air Force.From1997to1998,he was with Wyle Laboratories and from1998to2000,he was with ITT A/CD.In2000,he began teaching as

an Visiting Assistant Professor in the Department of Engineering,Purdue Uni-versity at Fort Wayne,Fort Wayne,IN,where he now teaches as an Assistant

Professor.

Majeed M.Hayat(S’89-M’92-SM’00)was born

in Kuwait in1963.He received the B.S.degree

(summa cum laude)in electrical engineering from

the University of the Pacific,Stockton,CA,in1985,

and the M.S.degree in electrical engineering and

the Ph.D.degree in computer engineering,from the

University of Wisconsin-Madison in1988and1992,

respectively.

From1993to1996,he was with the University

of Wisconsin-Madison as a Research Associate and

Co-Principal Investigator of a project on statistical minefield modeling and detection,which was funded by the Office of Naval Research.In1996,he joined the faculty of the Electro-Optics Graduate Pro-gram and the Department of Electrical and Computer Engineering,University of Dayton,Dayton,OH,where he was granted early tenure and promotion to As-sociate Professor in2000.He is currently an Associate Professor in the Depart-ment of Electrical and Computer Engineering at the University of New Mexico, Albuquerque.His research interests include modeling and design of high-per-formance photodetectors,optical communication systems,statistical communi-cation theory,communication networks,infrared imaging,and statistical signal and image processing.

Dr.Hayat is a recipient of a1998National Science Foundation Early Faculty Career Award.He is a member of SPIE and

OSA.

Ernest E.Armstrong received the B.S.degree

in computer science and the M.S.degree in X-ray

crystallography from Wright State University,

Dayton,OH,in1977and1980,respectively,and

received the Ph.D.degree in material analysis from

Case Western Reserve University,Cleveland,OH.

He is currently a Senior Scientist(image pro-

cessing)for OptiMetrics,Inc.,a defense contractor

at Wright Patterson AFB,OH.He previously held

positions with Exxon Production Research and

British Petroleum Research,where his research was primarily concerned with the application of signal and image processing techniques in materials analysis.He has authored and coauthored a number of publications in image processing,specializing in the area of image registration, resolution enhancement,and nonuniformity correction.

JPEG图像的编解码实现

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导数与函数图像

导数与函数图像问题
1.函数 y ? f (x) 的图像如右图,那么导函数 y ? f , (x) 的图像可能是（ ）
2．函数 f (x) 的定义域为开区间 (a, b) ，导函数 f ?(x) 在 (a, b) 内的图象如图所示，则函数 f (x) 在开区间 (a, b)
内有极小值点（ ）
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a
3 ． 设 f ?(x) 是 函 数 f (x) 的 导 函 数 ， 将 y ? f (x) 和
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5.设 函 数 f（ x） 在 R 上 可 导 ， 其 导 函 数 为 f′ （ x）， 且 函 数 f（ x） 在 x=-2处 取 得 极 小 值，则函数 y=xf′（x）的图象可能是（ ）
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1

6． 设 函 数 f（ x） =ax2+bx+c（ a， b， c∈ R）， 若 x=-1为 函 数 y=f（ x） ex 的 一 个 极 值 点 ， 则下列图象不可能为 y=f（x）的图象是（ ）
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7.若函数 y=f（x）的导函数在区间[a，b]上是增函数，则函数 y=f（x）在区间[a，b] 上的图象可能是（ ）
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8．已 知 函 数 y=xf′（ x）的 图 象 如 上 中 图 所 示（ 其 中 f′（ x）是 函 数 f（ x）的 导 函 数 ），
下面四个图象中 y=f（x）的图象大致是（ ）
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9.设函数 f（x）在 R 上可导，其导函数为 f′（x），且函数 y=（1-x）f′（x）的图象如上
右图所示，则下列结论中一定成立的是（ ）
A．函数 f（x）有极大值 f（2）和极小值 f（1） 值 f（1） C．函数 f（x）有极大值 f（2）和极小值 f（-2） 值 f（2）
B．函数 f（x）有极大值 f（-2）和极小 D．函数 f（x）有极大值 f（-2）和极小
2

图像处理技术及其应用

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图像编解码技术及应用 1．图像编解码技术概论： 在当前的图像压缩领域中常用的技术有： BMP、EPS、GIF、JPG、PDF、PIC、PNG、PSD、TIF。上述技术间的差异主要存在于图像编解码的算法不同，通过对算法的研究可以使我们更加容易的理解图像压缩的原理。 位图格式（BMP）是在DOS时代就出现的一种元老级文件格式，因此它是DOS和WINDOWS操作系统上的标准的WINGDOWS点阵图像格式，以此文件格式存储时，采用一种非破坏性的RLE压缩,不会省略任何图像的细部信息。 EPS是最常见的线条稿共享文件格式，它是以PostScript语言为开发基础，所以EPS文件能够同时兼容矢量和点阵图形，所有的排版或图像处理软件如PageMaker或Illustrator等，都提供了读入或置入EPS格式文件的能力，而且RGB和CMYK对象也可以保有各自的原始的色彩模式。 GIF应该是在网络上最常见的一种压缩文件格式，它的英文全名Graphic Interchange format，当初研发的目的是为了最小化电缆上的传输，因此能采用LZW方式进行压缩，但可显示的颜色范围只局限于256索引色，目前所采用 的GIF图形共有两种格式：87a和89a，常见于网页上建议的小动画制作，其中GIF89a还可提供透明色效果，点阵图形，灰度图形或者索引颜色模式皆可存储为此种文件格式 JPG跟GIF一样为网络上最常见道的图像格式，其英文正式名称为Joint Photographic Experts Group，它是以全彩模式进行显示色彩，是目前最有效率的一种压缩格式，常用于照片或连续色调的显示，而且没有GIF去掉图像细 部信息的缺点，但需要注意的是此类图像需要自行设置压缩程度，在打开时JPG 图像会自动解压缩，不过要注意的是JPG采用的压缩是破坏性的压缩，因此会在一定程度上减损图像本身的品质。

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导 数 1. 导数（导函数的简称）的定义：设0x 是函数)(x f y =定义域的一点，如果自变量x 在0x 处有增量x ?，则函数值y 也引起相应的增量)()(00x f x x f y -?+=?；比值x x f x x f x y ?-?+= ??) ()(00称为函数)(x f y =在点0x 到x x ?+0之间的平均变化率；如果极限x x f x x f x y x x ?-?+=??→?→?)()(lim lim 0000存在，则称函数)(x f y =在点0x 处可导，并把这个极限叫做)(x f y =在0x 处的导数，记作)(0'x f 或0|'x x y =，即 )(0'x f =x x f x x f x y x x ?-?+=??→?→?)()(lim lim 0000. 注：①x ?是增量，我们也称为“改变量”，因为x ?可正，可负，但不为零. ②以知函数)(x f y =定义域为A ，)('x f y =的定义域为B ，则A 与B 关系为B A ?. 2. 函数)(x f y =在点0x 处连续与点0x 处可导的关系： ⑴函数)(x f y =在点0x 处连续是)(x f y =在点0x 处可导的必要不充分条件. 可以证明，如果)(x f y =在点0x 处可导，那么)(x f y =点0x 处连续. 事实上，令x x x ?+=0，则0x x →相当于0→?x . 于是)]()()([lim )(lim )(lim 0000 00 x f x f x x f x x f x f x x x x +-+=?+=→?→?→ ). ()(0)()(lim lim ) ()(lim )]()()([ lim 000'0000000000x f x f x f x f x x f x x f x f x x x f x x f x x x x =+?=+??-?+=+???-?+=→?→?→?→?⑵如果)(x f y =点0x 处连续，那么)(x f y =在点0x 处可导，是不成立的. 例：||)(x x f =在点00=x 处连续，但在点00=x 处不可导，因为x x x y ??= ??| |，当x ?＞0时，1=??x y ；当x ?＜0时， 1-=??x y ，故x y x ??→?0lim 不存在. 注：①可导的奇函数函数其导函数为偶函数.②可导的偶函数函数其导函数为奇函数. 3. 导数的几何意义： 函数)(x f y =在点0x 处的导数的几何意义就是曲线)(x f y =在点))(,(0x f x 处的切线的斜率，也就是说，曲线)(x f y =在点P ))(,(0x f x 处的切线的斜率是)(0'x f ，切线方程为).)((0'0x x x f y y -=- 4. 求导数的四则运算法则：

图像处理技术的应用论文

图像处理技术的应用先展示一下自己用Photoshop处理的图片（做的不好望见谅）

摘要：图像处理技术的研究和应用越来越收到社会发展的影响，并以自身的技术特点反过来影响整个社会技术的进步。本文主要简单概括了数字图像处理技术近期的发展及应用现状，列举了数字图像处理技术的主要优点和制约其发展的因素，同时设想了图像处理技术在未来的应用和发展。 关键字：图像处理发展技术应用 1.概述 1.1图像的概念 图像包含了它所表达的物体的描述信息。我们生活在一个信息时代，科学研究和统计表明，人类从外界获得的信息约有百分之七十来自视觉系统，也就是从图像中获得，即我们平常所熟知的照片，绘画，动画。视像等。 1.2图像处理技术 图像处理技术着重强调在图像之间进行的变换，主要目标是要对图像进行各种加工以改善图像的视觉效果并为其后的目标自动识别打基础，或对图像进行压缩编码以减少图像存储所需要的空间或图像传输所需的时间。图像处理是比较低层的操作，它主要在图像像素级上进行处理，处理的数据量非常大。 1.3优点分析 1．再现性好。数字图像处理与模拟图像处理的根本不同在于，它不会因图像的存储、传输或复制等一系列变换操作而导致图像质量的退化。 2．处理精度高。按目前的技术，几乎可将一幅模拟图像数字化为任意大小的二维数组，这主要取决于图像数字化设备的能力。现代扫描仪可以把每个像素的灰度等级量化为16位甚至更高，这意味着图像的数字化精度可以达到满足任一应用需求。 3．适用面宽。图像可以来自多种信息源，它们可以是可见光图像，也可以是不可见的波谱图像（例如X射线图像、射线图像、超声波图像或红外图像等）。从图像反映的客观实体尺度看，可以小到电子显微镜图像，大到航空照片、遥感图像甚至天文望远镜图像。即只要针对不同的图像信息源，采取相应的图像信息采集措施，图像的数字处理方法适用于任何一种图像。 4．灵活性高。图像处理大体上可分为图像的像质改善、图像分析和图像重建三大部分，每一部分均包含丰富的内容。而数字图像处理不仅能完成线性运算，而且能实现非线性处理，即凡是可以用数学公式或逻辑关系来表达的一切运算均可用数字图像处理实现。 2.应用领域 2.1图像技术应用领域

图像处理英文翻译

数字图像处理英文翻译 （Matlab帮助信息简介） xxxxxxxxx xxx Introduction MATLAB is a high-level technical computing language and interactive environment for algorithm development, data visualization, data analysis, and numeric computation. Using the MATLAB product, you can solve technical computing problems faster than with traditional programming languages, such as C, C++, and Fortran. You can use MATLAB in a wide range of applications, including signal and image processing, communications, control design, test and measurement, financial modeling and analysis, and computational biology. Add-on toolboxes (collections of special-purpose MATLAB functions, available separately) extend the MATLAB environment to solve particular classes of problems in these application areas. The MATLAB system consists of these main parts: Desktop Tools and Development Environment This part of MATLAB is the set of tools and facilities that help you use and become more productive with MATLAB functions and files. Many of these tools are graphical user interfaces. It includes: the