metrology

Journal of Manufacturing Systems 32 (2013) 514 522

Contents lists available at ScienceDirect

Journal of Manufacturing Systems

j ourna l ho me p age : www.elsev ier .com

Technical paper

Perform siosurface

Suresh KDepartment of tte, 9228223, United

a r t i c l

Article history:Received 15 MAccepted 20 MAvailable onlin

Keywords:Multi-sensor dFusion metricsEngineered suSurface metro

eereat difa fusi

to evlogy

typirman

Inten) is t

factu

1. Introduction

A major trend in manufacturing is toward miniaturization whichleads to convergence of the traditional research elds to createinterdisciplinary research areas [1]. For example, a successful lab-on-chip desmicro-uidresearch effscale modethe performsurface anahas also besurfaces, excic purposthe interestscales textand macro-

With theElectro Meca strong nethese surfaarray showaspect ratiowith false c

CorresponE-mail add

a White Light Interferometer (WLI) system (Zygo NV6300 system[2]). The central features on individual lens are resolved much bet-ter compared to the region shown inside the black circled area,under the selected measurement condition (10 objective with a0.5 magnication tube and 100 m scan length). The features are

0278-6125/$ http://dx.doi.oign requires expertise in four domains: micro-biology,ics, micro-tribology and micro-optics. Interdisciplinaryorts have started focusing on the development of multi-ls and development of multi-scale surfaces to optimizeance. Along with the growing demand of multi-scalelysis for development of mathematical models, thereen an increasing development of designer multi-scalehibiting specic properties at different scales for a spe-e. New patterned surfaces are being developed to utilizeing play of surface roughness on friction at differentured surfaces could be used to increase friction in meso-scale, but reduce friction at micro-scale.

rapid evolution of new engineered surfaces for Microhanical Systems (MEMS), micro-uidics etc., there ised for developing tools to measure and characterizeces at different scales. Consider a Fresnel micro lensn in Fig. 1a, where the individual features have varying. The gures show the top view of the 3D surface map,olor spectrum mapped to actual height, obtained using

ding author. Tel.: +1 3207612787.ress: [email protected] (S.K. Ramasamy).

better resolved at a higher magnication using the same 10 objec-tive but with a 2.0 magnication tube, as shown in Fig. 1b. Fromboth the gures, the potential advantage of combining multiplemagnication datasets is evident better capability for characteriz-ing varying aspect ratios. By enabling fusion of data obtained usingdifferent magnications/sampling intervals, the effective space ofthe instrument in the AmplitudeWavelength domain could beexpanded, resulting in better preservation of resolution at differentranges and increased condence on data.

Most technologies tend to overlap in their ability to measurelateral and vertical dimensions of products to cater to some limitedrange of products. So, in order to obtain all meaningful details ofthe surface at various required scales, one is left with the onlyoption of measuring the surface using multiple technologies usinga combination of instruments. Under industrial settings, it becomescumbersome to gure out all possible technologies and to cas-cade those into multiple systems, not to mention the cost burdeninvolved with setting up the bridge type system with the selectedtechnologies. The overlapping systems pose a limitation on thepositioning accuracy of the stages, requiring the stages of an indi-vidual measurement system to be capable to meet positioningrequirement of its successive system. The sensors communicatewith each other, but data is not necessarily merged together. These

see front matter 2013 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.rg/10.1016/j.jmsy.2013.05.013ance evaluation of multi-scale data fu metrology domain

. Ramasamy , Jayaraman RajaMechanical Engineering & Engineering Sciences, University of North Carolina at CharloStates

e i n f o

ay 2013ay 2013e 29 June 2013

ata fusion

rfaceslogy

a b s t r a c t

With the rapid evolution of new enginsure and characterize these surfaces surface at various required scales, datinstruments or technologies. In orderlike Lena are used. But surface metrodata points are in focus, compared toious levels of out-of-focus. So, a perfoand it was shown that Regional Edgeogy datasets, and Regional Energy (REmetrics are considered.

2013 The Society of Manu/ locate / jmansys

n methods for

01 University City Boulevard, Charlotte, NC

d surfaces, there is a strong need for developing tools to mea-ferent scales. In order to obtain all meaningful details of theon can be performed on data obtained from a combination ofaluate the fusion methods, typically, well-recognized images

datasets are distinctly different from those images, as all thecal images with a subject in focus and background with var-ce study was conducted on a wide range of surface samplessity (REI) is the preferred fusion method for surface metrol-he second preferred method, when single-scale performance

ring Engineers. Published by Elsevier Ltd. All rights reserved.

S.K. Ramasamy, J. Raja / Journal of Manufacturing Systems 32 (2013) 514 522 515

Fig. 1. Fresnel micro lens array at (a) 5 magnication and (b) 20 magnication.

systems enable the user to obtain different surface maps usingvarious technologies, but user doesnt readily have the ability tocombine all the obtained data into one single dataset. But for effec-tively characterizing the multi-scale surface, all the datasets needto be aligned with respect to each other. It is not sufcient to justperform measurements are multiple scales, but also be capableof characterizing the entire multi-scale surface. The authors [3,4]have previously demonstrated the feasibility of multi-scale/multi-sensor data fusion on surface and dimensional metrology datasetsand discussfused data rversion of loin pixel coomap. The fublack colorea red coloreresolution i

Standardduct perforbut typicalnite focus focus condiin that all thwith a subjof-focus. Somulti-scalethe performmetrology ation resultdata sets.

2. Multi-scale data fusion

Joint Directors of Laboratories [6] denes data fusion as, multi-level, multi-faceted process handling the automatic detection,association, correlation, estimation and combination of data andinformation from several sources. A generic framework for multi-sensor data fusion (MSDF) (based on [7]) is shown in Fig. 4. Thebasic steps involved in MSDF are discussed in detail.

e-con

he dic nocal me is n

squaownl.

arse

r thhly

regil mam utrmaled [5] the method for selection of fusion metrics. Theeplaced into the corresponding location in up sampledw magnication data is shown in Fig. 2. X and Y axis arerdinates and Z axis is in m, shown in spectrum colorsed data location is shown in Fig. 3. The box with dashedd line is used to show the location of the fused data andd box near the fused location is shown to illustrate thessues when low magnication is used.

images like Lena or Lenna are normally used to con-mance study on fusion metrics and fusion methods,

engineered surface datasets are obtained with in-condition, as each individual data point is at the besttion. Surface metrology datasets are distinctly differente data points are in focus, compared to typical images

ect in focus and background with various levels of out-me engineered surfaces are also designed to exhibit

and fractal nature. Hence there is a need to evaluateance of the fusion metrics and methods for the surfacedomain. This paper discusses the performance evalu-s of three data fusion methods on surface metrology

2.1. Pr

If tdynamstatistiIf thera leastval is dinterva

2.2. Co

Afteto rougCoarseduciaprograthe NoFig. 2. Fused data on Fresnel lens.dition

ata is very noisy due to vibration issues or systemsise level, it is recommended to de-noise the data byethods either in the Fourier or wavelet domains [8,9].o reference surface available, the data is leveled usingres plane. The dataset with the higher sampling inter-

sampled to match the dataset with the lower sampling

registration

e datasets have been pre-conditioned, the next step isalign both datasets, which is called coarse registration.stration can be either done manually by locating uniquerkers such as edges in both images, or an automatedilizing the Sum of Absolute Differences (SAD) and/orized Cross Correlation (NCC) [10] could be used to ndFig. 3. Zoomed in view of fused data on Fresnel lens.

516 S.K. Ramasamy, J. Raja / Journal of Manufacturing Systems 32 (2013) 514 522

Fig. 4. Schem(convert all daboth data (F) m

the approxiof two data

SAD(x,y) =P

and the

NCC(x,y) =N1i=0

where, Aence of Gaucompared tWLI systemregistrationatic of generic multi-sensor data fusion (A) original data (B) pre-condition (outlier remota into one domain) (C) coarse registration (D) ne registration after control point deteulti-scale fusion (G) inverse transform on fused sub-datasets to obtain fused data.

mate translation offsets between the two datasets. SADsets A(x,y) and B(x,y) is calculated by:

1

i=0

Q1j=0

A(x + i, y + j) B(i, j) , x = 0, 1, 2, ..., M 1y = 0, 1, 2, ..., N 1

NCC is given by:

M1j=0

A(x + i, y + j) B(i, j)N1i=0

M1j=0 A

2(x + i, y + j)N1

i=0

M1j=0 B

2(i, j)

is of length M N and B of length P Q. In the pres-ssian noise, NCC has been proven to be more accurateo SAD. Typically Gaussian noise would be expected ons, so NCC was chosen as preferred method for coarse

for this study.

2.3. Fine re

After coathe datasetfusion. Typiducial/coning a transfin both the dest Point (Icalculate th

cos cos

cos sin

sin

0

where, t, , are tval, plane removal, resample and resize) and domain normalizationction (E) multi-scale decomposition on selected same size area from

gistration

rse registration, the next step is ne registration, wheres are precisely aligned to sub-pixel level before datacally ne registration is performed by nding matchingtrol points [11] on both the datasets and then calculat-ormation matrix which would match the control pointsatasets using least squares optimization. Iterative Clos-

CP) algorithms [12] are widely used for alignment, toe transformation matrix T:

cos sin + sin sin cos sin sin cos sin cos tx cos cos sin sin sin sin cos + cos sin sin ty

sin cos cos cos tz0 0 1

x, ty, tz are the translational offsets along x, y and z axis,he angles of rotation with respect to the x, y and z axis.


2.4. Multi-scale decomposition

Multi-scale decomposition deals with representing the givensignal at different resolutions depending on the scale at which it isanalyzed. Tposition meLaplacian Pform (DWT(DWF) or able if the dreduction athat is half tsize, DWF method is decimationPlane methsix level ofwavelet pla

2.5. Data fu

Data fusmeans of sior mean of talso be useddata fusion obtained froscale. For that the indivchoosing thor weighted

2.6. Inverse

Inverse datasets to

3. Weighte

Data fusor average on activity Energy, Regtion, to namlarger than mum or mebased weig

3.1. Region

This mement calledBased on a calculate wsub imagesand VB(x, y)

VA(x, y) =M

VB(x, y) =M

where M, N

The match degree M (x, y) is then computed using the formula,

M(x, y) =2/MN

li=lv

j=vA(x + i, y + j) B(x + i, y + j)VA(x, y) + VB(x, y) ,

,

1,

fusi

(x, y

={

(x, y

={

,

+ 12

[

gion

s meremedingefersw. Th

=x=

1

my=1

wei

=E

new

= W

mbin

s meents

y) s ima

fourj,k(x

nt(W

Kp aution

4 fohe three common methods used for multi-scale decom-thods are the Pyramid Transform (PT) or Generalizedyramid Transform (GLP) [13], Discrete Wavelet Trans-) or Mallat method [14] and Discrete Wavelet FrameTrous method [15]. Multi-scale decomposition is prefer-ata set displays multi-scale nature. DWT requires dyadict each level of decomposition and hence results in imagehe size of the previous level. In order to retain the sameis preferred, where no decimation is performed. Thisalso called Trous (with holes) method as instead of, data is replaced with zeros. Trous Discrete Waveletod with B3 spline as mother wavelet was chosen and

decomposition is performed to obtain two sets of sixnes.

sion

ion is performed at the individual data point level bymple methods like choosing the maximum, minimumhe two data points or weighted averaging methods can. If the multi-scale decomposition was performed, thenis carried out at individual scales. First the sub-datasetsm multi-scale decomposition are matched according toe sub-datasets at each scale, data fusion is performedidual data point level by means of simple methods likee maximum, minimum or mean of the two data points

averaging methods can also be used.

transform

transformation is performed on the fused multi-scaleobtain the fused nal dataset.

d averaging methods

ion could be performed either at pixel level using meanof corresponding planes from both datasets or basedlevel using weighted average approaches Regionalional Edge Intensity and Wavelet Gradient combina-e a few. Since the useful features in the data are usuallyone data point, single data point based maximum, mini-an approach are not recommended and instead, a kernelhted average is generally preferable [16].

al energy based (RE)

thod [17] uses a window based activity level measure- Regional Energy and then a match degree is computed.preset threshold value, the match degree is the used toeighted averages. After n-level of decomposition, two

A(x, y) and B(x, y) are taken and region energies VA(x, y) are calculated.

1N

li=l

vj=v

(A(x + i, y + j))2,

1N

li=l

vj=v

(B(x + i, y + j))2

are the values of local region (3 3, 5 5 etc.)

where

l = M 2

Theby,

If M

F(x, y)

If M

F(x, y)

where

= 12

3.2. Re

Thimeasurespon(x, y) rwindo

EAR(m,n)

where

m =n

x=

The

WB(x,y)

The

F(x, y)

3.3. Co(WGC)

Thisurem

WBj,k

(x,sourceare thecient W

Gradie

whereconvoland p =v = N 12

on rule is given (for a selected threshold of T (T > 0.5))

) < T, then

A(x, y) VA(x, y) VB(x, y)B(x, y) VA(x, y) < VB(x, y)

) T, then

A(x, y) + (1 ) B(x, y) VA(x, y) VB(x, y)(1 ) A(x, y) + B(x, y) VA(x, y) < VB(x, y)

1 M(x, y)1 T

]

al edge intensity based (REI)

thod [18] also uses a window based activity levelnt called edge intensity, which is used to calculate cor-

weightage factors. After n-level of decomposition, if A to the data point in a sub image A and R (m, n) a m nen the edge intensity of R (m, n) is dened by,

n

1

my=1

(A(x, y) mm n 1

,

A(x, y)m n

ghts are calculated using the formulae,

EBR(x,y)

AR(x,y) + EBR(x,y)WA(x,y) =

EAR(x,y)EAR(x,y) + EBR(x,y)

pixel value is obtained by,

A(x,y) A(x, y) + WB(x,y) B(x, y)

ation of wavelet coefcients and local gradients

thod [19] uses a combination of two activity level mea-to calculate the weightage factors. Let WA

j,k(x, y) and

tand for wavelet coefcients of source image A andge B, j is the decomposed resolution level and k0,1,2,3

frequency bands. The local gradient of wavelet coef-, y) is dened as below

j,k(x, y)) = max{Kp Wj,k(x, y) , p = 1 4} ,

re the four directional gradient operators. p = 1 is the kernel for 135 direction, p = 2 for the 90, p = 3 for 0

r 45.


The proposed image activity level measurement combines thewavelet coefcient at the sampling point (x, y) and its local waveletcoefcient gradient feature together.

A(Wj,k(x, y)) = Gradient(Wj,k(x, y)) Wj,k(x, y) ,

where A (Wj,k(x, y)) reects the activity level information of thewavelet coefcient Wj,k(x, y). The image fusion scheme is given by,

Woutj,k (x, y) ={

WAj,k

(x, y) A(WAj,k

(x, y)) > A(WBj,k

(x, y))

WBj,k

(x, y) A(WAj,k

(x, y)) A(WAj,k

(x, y))

4. Evaluation of fusion methods

In order to evaluate the performance of the three previouslydescribed fusion methods (RE, REI and WGC), 12 sets of data 4 sets each of structured directional surface (shown in Fig. 5),structured non-directional surface (shown in Fig. 6) and system-atic non-engineered surface (shown in Fig. 7, were measured at 2different magnications on a Zygo NV6300 WLI system.

The datasets were decomposed using a 6-level DWF transfor-mation, coarse registration was performed using NCC, Watershededge detection on single scale was used and the obtained controlpoints were used for ne registration using ICP nite difference

Fig. 5. Structu t (a) 5grid array at (ared directional surface sample datasets (1) beam shaper optical surface measured a) 10 (b) 20, (4) concentric square grid at (a) 10 (b) 20.0 (b) 100, (2) Fresnel micro-lens array at (a) 5 (b) 20, (3) square


Fig. 6. Structugenerator A at

method. BaIndex (UQI)preferred mMulti-scalethe preferre

4.1. Multi-s

The possvalue 1 woucan calculat

MS SSIM(red non-directional surface sample datasets (1) dipole diffuser surface measured at (a) 5 (a) 50 (b) 100, (4) pattern generator B at (a) 50 (b) 100.

sed on recommendations from [5], Universal Quality and Structural Similarity Index (SSIM) were chosen asetrics for single-scale based performance metrics and

Structural Similarity Index (MS-SSIM) was chosen asd metric for multi-scale based performance.

cale Structural Similarity Index (MS-SIM) [20]

ible values for MS-SIM range from 0 to 1 and the bestld be achieved when images x and y are exact. MS-SIMed using the formula,

A, B) = [lj(A, B)]j j

k=1[ck(A, B)]

k

[sk(A, B)]k

where, onetaken and nance comscale M andlarity comp

c(A, B) = 2A

where A =of A and C1 = (K1L)2,of the gray

, , athree factor

= = = 1in universa0 (b) 100, (2) spot array generator at (a) 50 (b) 100, (3) pattern

of the original datasets X and the fused dataset Y areboth are decomposed to M levels. lM(A,B) is the lumi-parison factor, which is computed only at the largest

c(A,B) and s(A,B) are the contrast and structural simi-arison factors computed at all scales.

AB + C22 + 2B + C2

s(A, B) = AB + C3AB + C3

, l(A, B) = 2AB + C12A + 2B + C1

mean of A, A = standard deviation of A; AB = covarianceB; C1, C2 and C3 are small constants given by;

C2 = (K2L)2 and C3 = C2/2,where L is the dynamic rangescales (255), K1 < < 1 and K2 < < 1.re parameters chosen according to the importance ofsluminance, contrast and structural similarity. When, and C1 = C2 = 0, the Structural Similarity Index resultsl image quality index.


Fig. 7. Systematic non-engineered surface sample datasets (1) line generator measured at (a) 10 (b) 20, (2) surface obtained from turning process at (a) 5 (b) 20, (3)nish honed surface at (a) 5 (b) 20, (4) rough honed surface at (a) 5 (b) 10.

Table 1Performance results based on Universal Quality Index (UQI) and Structural Similarity Index (SSIM) on 12 surface datasets.


Table 2Performance results based on Multi-scale Structural Similarity Index (MS-SIM) on 12 surface.

UniversaUQI calc

effectively tfor UQI ranimages x an

UQI =(2A +

where, A anconverting

B = 1N

Ni=1

B

AB =1

N 1

where N is l Quality Index (UQI) [21]:ulates the amount of salient information that has beenransferred from image x to image y. The possible valuesge from 1 to 1 and the best value 1 would be achievedd y are exact.

4ABAB

2B )[(A)2 + (B)2]

,

d B denotes the reference and test images obtained bythe datasets into gray scale images and

i 2A =

1N 1

Ni=1

(Ai A)2A = 1

N

Ni=1

Ai

Ni=1

(Ai A)(Bi B) 2B =1

N 1

Ni=1

(Bi B)2

the total number of data points in the image.

5. Single-s

Table 1 the low maand high mThe followi

Comparinthat the fudata com

Both RE aWGC.

Using UQand RE pe

6. Multi-sc

The dataresolution abe from onsidered, andcale metrics based analysis

shows two single-scale metrics (UQI and SSIM) whengnication data (Rl) is compared with fused data (F),agnication data (Rh) with fused data (F) respectively.ng observations are made based on Table 1:

g the values between (Rh, F) and (Rh, Rl), it can be seensed data has better similarity to the high magnication

pared to the low magnication data.nd REI methods performance seems to be better than

I or SSIM as the metric, REI performed well on 7 datasetsrformed better on 3 datasets.

ale metrics based analysis

sets were decomposed to 6 levels, L6 being the nestnd L1 being the coarsest. Since the L6 level data wouldly the high magnication data, that level was not con-

the other ve levels of data were used for the analysis.


From some datasets, even L5 and L4 would be from high magni-cation data only. For those data sets, the corresponding levels havebeen grayed out and were not considered for the analysis. Table 2summarizes the MS-SSIM fusion metric results on 12 datasets.

The rst ve column values are obtained by comparing thelow magnication data with the fused data and the next ve col-umn values are obtained by comparing the high magnicationdata with the fused data, at individual resolution levels. For eachdataset, the better performing data fusion method (whichevermethod yields a MS-SIM value closest to 1) is highlighted with yel-low color and bold-face. From this analysis, the following can bededuced:

REI fusion method performed well on 9 datasets, with RE per-forming better on some levels on 3 datasets.

Fused data is able to retain at least 90% of similarity to both highand low magnication data at all levels, which was not demon-strated using the single-scale metrics.

7. Conclusion

The benets of multi-scale data fusion, uniqueness of surfacemetrology datasets and the need for performance evaluation ofmulti-scale data fusion methods were discussed. The basic stepsinvolved in multi-scale data fusion were detailed, followed by thedescription of three multi-scale data fusion methods that were con-sidered for this study.

Based odatasets (4 non-directimeasured asystem), it wmetric, the other two msingle-scaleation, RE mebut overall,

The possTurned andpossible reatributing favariable witures demo

Based on this performance study, it is recommended to use REImethod as the preferred method for multi-scale data fusion for thesurface metrology domain.

References

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[2] Zygo.com [Internet]. ZYGO Metrology Services Division; [cited February 2,2013]. http://www.zygo.com/?/met/prolers/

[3] Ramasamy SK. Multi-scale data fusion for surface metrology. Charlotte, NC:University of North Carolina at Charlotte; 2011 [PhD thesis].

[4] Ramasamy SK, Raja J, Boudreau BD. Multi-Sensor Data Fusion in Surface andDimensional Metrology Domains. In: Proceedings of the 40th North AmericanManufacturing Research Conference. 2012.

[5] Ramasamy SK, Raja J. Performance Evaluation of Data Fusion Metrics. In:Proceedings of the 27th ASPE Annual Meeting, October. 2012.

[6] Data fusion lexicon. Data Fusion Subpanel of the Joint Directors of Laboratories,Technical Panel for C3. U.S. Department of Defense; 1991.

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[8] Donoho DL. De-noising by soft-thresholding. IEEE Trans Inform Theory1995;41(May (3)):61327.

[9] Krim H, Tucker D, Mallat S, Donoho DL. On denoising and best signal represen-tation. IEEE Trans Inform Theory 1999;45(November (7)):22538.

[10] Raol JR. Multi-Sensor Data Fusion with MATLAB, Ch. 11: performance evalua-tion of image based data fusion systems. CRC Press; 2009.

[11] Wang MY, Fitzpatrick JM, Maurer CR. Design of ducials for accurate regis-tration of CT and MR volume images. In: Jr., Medical Imaging 1995: ImageProcessing Proc. SPIE, vol. 2434. 1995. p. 96108.

[12] Besl PJ, McKay ND. A method for registration of 3-D shapes. IEEE Trans PatternAnal Mach Intell 1992;14(February (2)):23956.

[13] Burt PJ, Adelson AE. The Laplacian pyramid as a compact image code. IEEE Transmun

llat S. entatinsa Mms. IE, Guoltisenlicatin H, Lsformi Y, Zompornatio953g Y, Li

its arnationg Z, lity atems ng Z, ters 20n a comparison study on twelve different types ofsets each of structured directional surface, structuredonal surface and systematic non-engineered surface,t 2 different magnications on a Zygo NV6300 WLIas shown that with MS-SIM as the chosen performance

Regional Edge Intensity (REI) method outperforms theethods RE and WGC. It was also shown that when

performance metrics were also taken into consider-thods performance seems to improve marginally well,

REI method outperforms both the methods.ible reasons for inconsistencies on Fresnel micro lens,

nish honed surfaces need further investigation. Oneson could be that the activity window size be a con-ctor. In order to validate this, another study usingndow size needs to be conducted on samples with fea-nstrating different spectral distributions.

Com[14] Ma

res[15] She

rith[16] Li H

MuApp

[17] Chetran

[18] ChadecInte404

[19] SonandInte

[20] WaquaSys

[21] WaLet 1983;31:53240.A theory for multi resolution signal decomposition: the wavelet rep-on. IEEE Trans Pattern Anal Machine Intell 1989;11:67493.J. Discrete wavelet transforms: wedding the trous and Mallat algo-EE Trans Signal Process 1992;40:246482.

L, Liu H. Current research on wavelet-based image fusion algorithms,sor, Multisource Information Fusion: Architectures, Algorithms, andons 2005. In: Proceedings of the SPIE, vol. 5813. 2005. p. 3607.iu Y, Wang Y. A novel image fusion method based on wavelet packet. IEEE Int Symp Knowledge Acquis Model 2008:4626.hao R, Ren J. Self-adaptive image fusion based on multi-resolutionsition using wavelet packet analysis. In: Proceedings of the Thirdnal Conference on Machine Learning and Cybernetics. 2004. p.

. M, Li Q, Sun L. A new wavelet based multi-focus image fusion schemepplication on optical microscopy. In: Proceedings of the 2006 IEEEnal Conference on Robotics and Biomimetics. 2006. p. 4015.Simoncelli EP, Bovik AC. Multi-scale structural similarity for imagessessment. In: Invited Paper, IEEE Asilomar Conference on Signals,and Computers, November. 2003.Bovik AC. A universal image quality index. IEEE Signal processing02;9:814.

Performance evaluation of multi-scale data fusion methods for surface metrology domain1 Introduction2 Multi-scale data fusion2.1 Pre-condition2.2 Coarse registration2.3 Fine registration2.4 Multi-scale decomposition2.5 Data fusion2.6 Inverse transform

3 Weighted averaging methods3.1 Regional energy based (RE)3.2 Regional edge intensity based (REI)3.3 Combination of wavelet coefficients and local gradients (WGC)

4 Evaluation of fusion methods4.1 Multi-scale Structural Similarity Index (MS-SIM) [20]

5 Single-scale metrics based analysis6 Multi-scale metrics based analysis7 ConclusionReferences

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