Motion Correction Structured Light using Pattern Interleaving Technique

Transcription

1 Universit of Kentuk UKnoledge Universit of Kentuk Master's Theses Graduate Shool 28 Motion Corretion Strutured Light using Pattern Interleaving Tehnique Raja Kalan Ra Cavaturu Universit of Kentuk, Clik here to let us kno ho aess to this douent benefits ou. Reoended Citation Cavaturu, Raja Kalan Ra, "Motion Corretion Strutured Light using Pattern Interleaving Tehnique" (28). Universit of Kentuk Master's Theses This Thesis is brought to ou for free and open aess b the Graduate Shool at UKnoledge. It has been aepted for inlusion in Universit of Kentuk Master's Theses b an authorized adinistrator of UKnoledge. For ore inforation, please ontat UKnoledge@lsv.uk.edu.

2 ABSTRACT OF THESIS Motion Corretion Strutured Light using Pattern Interleaving Tehnique Phase Measuring Profiloetr (PMP) is the ost robust sanning tehnique for stati 3D data aquisition. To ake this tehnique robust to the target objets hih are in otion during the san interval a novel algorith alled Pattern Interleaving is used to get a high densit single san iage and aking Phase Measuring Profiloetr insensitive to z otion and prevent otion banding hih is predoinant in 3D reonstrution hen the objet is in otion during the san tie KEYWORDS: Strutured Light Illuination, Phase Measuring Profiloetr, Pattern Interleaving, Motion banding and 3D reonstrution. Raja Kalan Ra Cavaturu Septeber 8 th, 28

3 Motion Corretion Strutured Light using Pattern Interleaving Tehnique B Raja Kalan Ra Cavaturu Dr. Laurene G Hassebrook Diretor of Thesis Dr. YuMing Zhang Diretor of Graduate Studies Septeber 8 th, 28

4 RULES OF THE THESIS Unpublished theses subitted for the Master s degree and deposited in the Universit of Kentuk Librar are as a rule open for inspetion, but are to be used onl ith due regard to the rights of the authors. Bibliographial referenes a be noted, but quotations or suaries of parts a be published onl ith the perission of the author, and ith the usual sholarl aknoledgents. Extensive oping or publiation of the thesis in hole or in part also requires the onsent of the Dean of the Graduate Shool of the Universit of Kentuk. A librar that borros this thesis for use b its patrons is expeted to seure the signature of eah user. Nae Date

5 THESIS Raja Kalan Ra Cavaturu The Graduate Shool Universit of Kentuk 28

6 Title Page Motion Corretion Strutured Light using Pattern Interleaving Tehnique THESIS A thesis subitted in partial fulfillent of the requireents for the degree of Master of Siene in Eletrial Engineering in the College of Engineering at the Universit of Kentuk B Raja Kalan Ra Cavaturu Lexington, Kentuk Diretor: Dr. Laurene G. Hassebrook, Departent of Eletrial Engineering Lexington, Kentuk 28 Copright Raja Kalan Ra Cavaturu 28

7 Dediation Dediated to M fail

8 ACKNOWLEDGEMENTS I ould like to take this opportunit to express sinere heart-felt gratitude to advisor, Dr.Laurene G. Hassebrook for his enourageent, onstant guidane and valuable suggestions and the freedo of thought at ever stage of the researh ork. I ould also like to thank Dr. Kevin Donohue and Dr. Ruigang Yang for serving on defense oittee. I ould like to thank Charles Case and Aksha Pethe for all their ooperation and help. I ould like to thank friends Sandeep Boddapati, Sunil Boddapati, Sudheer Gariella and Vasi Vankadara for their support. Finall, I ould like to thank fail, ithout the I ould never have ade it here. M father, Mr.Madhava Rao Cavaturu for giving e onstant enourageent and otivation at ever step of life. M other, Mrs Vijaa Lakshi Cavaturu for her aring love, enourageent and support, ithout her I ould not be the person as I a toda. M brother, entor, Mr. Kiran Cavaturu for his guidane and onstant support. I a reall fortunate to have a brother like hi. M sister-in-la, Mrs.Aparna Cavaturu for treating e like her son. M friend, Setha Mannepalli for her patiene and onstant enourageent. iii

9 TABLE OF CONTENTS Aknoledgeents iii List of Figures..v List of Files vii Chapter Introdution.... Thesis Organization...3 Chapter 2 Bakground Strutured Light Illuination Tehnique Multi Frequen Phase Measuring Profiloetr Calibration Lens Distortions: Matheatial Relationship beteen the aera oordinates, orld oordinates and projetor oordinates... Chapter 3 Pattern Interleaving (PIL) tehnique Introdution Desription of Pattern Interleaving (PIL) tehnique PIL Algorith Experients and results Estiating offset beteen the to suessive PIL patterns Interpolating the offset to orret the PMP pattern Result of PIL tehnique Band Ripple Measureent Calulation of Band Energ for an ideal ripple Calulation of Band Energ ithout PIL orretion Calulation of Band Energ after PIL orretion Chapter 4 Lateral Corretion Approah Steps to orret the lateral oveent... 4 Chapter 5 Experients and Results D reonstrution of objets in unifor z otion D reonstrution of objets in non-unifor z otion Chapter 6 Conlusion and Future ork Conlusion Future orks Appendix Assuptions and Liitations of PIL tehnique: Visual C++ ode used to orret the objet otion in z diretion Referenes Vita iv

10 LIST OF FIGURES Figure 2. Strutured Light Illuination (SLI) setup [27]...4 Figure 2.2 Radial Distortion (a) Barrel distortion (b) Pinushion distortion. [9]...8 Figure 2.3 Perspetive distortion of a retangular grid [28]...9 Figure 3. Stati 3D reonstrution of a stati surfae... 8 Figure 3.2 3D reonstrution of a sooth surfae in otion... 9 Figure 3.3 Pattern sequene... 2 Figure 3.4 Pitorial representation of PIL tehnique... 2 Figure 3.5 Flohart of snake detetion Figure 3.6 Snake asked T PIL pattern Figure 3.7 Snake asked T PIL pattern Figure 3.8 Differene iage of the snake asked T PIL pattern and T PIL pattern Figure 3.9 Cropped setion of the differene iage Figure 3. Middle olun intensit of the differene iage Figure 3. d for the pixel loations of the iddle olun at snake loations... 3 Figure 3.2 Need for interpolating the offset beteen the snake regions... 3 Figure 3.3 Figure shoing the offset at the snake loations and the interpolated offset beteen the snake regions Figure 3.4 (a) 3D reonstrution of a sooth surfae using PIL tehnique (b) filtered 3D reonstruted sooth surfae using PIL Figure 3.5 (a)side vie of stati 3D reonstrution of sooth surfae (b) side vie of the 3D reonstruted sooth surfae in otion () side vie of the 3D reonstruted sooth surfae using PIL tehnique Figure 3.6 Ideal ripple Figure 3.7 Measuring Band Energ of a sooth surfae ithout PIL orretion Figure 3.8 Measuring avelength of ripples of a sooth surfae ithout PIL orretion Figure 3.9 Measuring Band Energ of a sooth surfae after PIL orretion Figure 3.2 Measuring avelength of the ripples of a sooth surfae after PIL orretion Figure 4. Setup arrangeent for lateral orretion... 4 Figure 4.2 First aptured PMP pattern... 4 Figure 4.3 Seond aptured PMP pattern... 4 Figure 4.4 Sobel edge enhaneent iage of the first aptured PMP pattern Figure 4.5 Sobel edge enhaned iage of the seond aptured PMP pattern Figure 4.6 3D plot of ross orrelation beteen the to sobel edge enhaned iages Figure 4.7 Correted seond aptured PMP pattern Figure 5. (a) side vie of the 3D reonstruted sooth surfae in stati, (b) side vie of the 3D reonstruted sooth surfae in otion and () side vie of the 3D reonstruted sooth surfae using PIL tehnique Figure 5.2 3D reonstrution of a fae odel Figure 5.3 (a) ropped side vie of the stati 3D reonstruted fae odel (b) ropped side vie of the 3D reonstruted fae odel in otion () ropped side vie of the 3D reonstruted fae odel using PIL tehnique v

11 Figure 5.4 (a) side vie of the stati 3D reonstruted sooth surfae (b) side vie of the 3D reonstruted sooth surfae in z otion aa fro the aera () side vie of the 3D reonstruted sooth surfae using PIL tehnique Figure 5.5 (a) ropped side vie stati 3D reonstrution of a sooth surfae (b) ropped side vie of the 3D reonstrution of the sooth surfae hih is subjeted to non-unifor otion and () ropped side vie of the 3D reonstrution of the sooth surfae using PIL tehnique. 49 Figure 5.6 objet held ith strings to freel osillate during the san tie... 5 Figure 5.7 (a) ropped side vie stati 3D reonstrution of the surfae (b) ropped side vie 3D reonstrution of the surfae hen it is osillating during the san tie and () ropped side vie of the 3D reonstrution of the surfae using PIL tehnique... 5 vi

12 LIST OF FILES Thesis.pdf (Arobat Reader file).7 MB (File Size) vii

13 Chapter Introdution 3D data aquisition tehniques are broadl lassified into to tpes: ative and passive. The neessar ondition for both ative and passive 3D data aquisition tehniques is optial triangulation. The ost proinent sanning feature tehnique in the passive 3D data aquisition is Stereo Vision (StV). In stereo vision tehnique, the optial triangulation is established beteen the target objet and an arra of aeras. In stereo vision tehniques, the 3D reonstrution of the target objet is ahieved b finding the orrespondene beteen the iages vieed fro to or ore points of vie (POV). Hoever, the ain proble assoiated ith the stereo vision is the one relating to the feature orrespondene. This orrespondene proble in the stereo vision tehnique is solved b using ative ethods [] but is ver dependent on the objet having distintive features. The ost idel used sanning feature tehnique in ative ethods is strutured light illuination (SLI). It has its appliations in different fields like bioedial topolog [2], qualit ontrol [3] and teleollaboration [4]. In the Strutured Light Illuination (SLI) tehnique optial triangulation is established b replaing one of the aeras in the stereo vision tehnique ith a projetor. Thus, a geoetri relationship beteen the aeras, projetor and the target objet is established. In a SLI tehnique, a oded light pattern is projeted b the projetor on to the target objet hih is aptured b the aera. Depth inforation an be obtained b easuring the distortion ourred beteen the aptured iage and the refleted iage. Various oded light patterns like binar, single spot, stripe or a oplex pattern an be used. A oonl used SLI sanning tehnique is Phase Measuring Profiloetr (PMP). The SLI ethodolog overoes the feature orrespondene proble assoiated ith the StV b projeting strutured patterns. The advantages of using ultiple patterns are [6]. Depth resolution is deterined b nuber of patterns 2. Non abiguous depth easureent over long ranges 3. Insensitive to abient light interferene 4. Insensitive to surfae shading or olor 5. Spatial resolution is deterined b aera resolution.

14 The ain drabak of using ulti pattern SLI is that it takes ore tie to san the target objet and thus not suitable for the target objets hih are in otion during the san tie. To overoe this drabak, a single pattern tehnique [7] is used for the dnai senes but this tehnique is not as aurate as the ulti pattern tehnique. B using ulti frequen PMP tehnique higher aura and preision of 3D data an be obtained for a stati target objet []. Chun Guan et al introdued a ne tehnique alled oposite pattern (CP) b using the ulti frequen PMP patterns for sanning dnai senes [2]. In this tehnique, ultiple PMP patterns are obined to for a single pattern b using ouniation theor onepts. Hoever, this tehnique suffers fro lo depth resolution and also arrier frequen detetion in the aptured pattern. Hassebrook et al [6] proposed a ne ethod, Lok and Hold strateg to trak the objet otion. In this tehnique, a lok state an be obtained b using ethods like ultiple patterns PMP or single pattern or suessive boundar subdivision to deterine the snake identit. The phase value of eah snake is obtained, thereb getting the phase value of the aera oordinates. In the hold state a single ulti frequen sine ave is used and the snake proess is used to trak the hold state. Hoever it is diffiult for ertain target objets like huan hand to be in standstill state in the lok state. Song Zhang [29] proposed a novel algorith alled Fast three step phase shift algorith hih ust have a high speed projetor and a aera. Hall-Holt [8] proposed a ne ethod for opensating otion. In this tehnique otion opensation is ahieved b traking the stripe boundaries. Wiese [9] presented a 3D sanning sste hih uses both strutured light and stereo vision and proposed a stereo phase shift ethod for otion opensation. In this ethod, the otion opensation is perfored on eah pixel b analzing the otion error. Soren Konig [] proposed a novel otion opensation tehnique here to additional patterns (on and off patterns) are introdued beteen the strutured light patterns to trak the otion. The ain ai of the researh ork is to opensate for the error that ourred in 3D reonstrution due to the otion of the target objet during the san tie. In our ethod, e interleave a single pattern in beteen eah SLI pattern. We then trak otion of these 2

15 interleaved patterns and orret the SLI pattern set for objet otion during the san. We all this Pattern Interleaving (PIL) This tehnique uses the traditional PMP tehnique, a robust algorith for stati 3D sanning, thereb aking the traditional PMP insensitive to otion.. Thesis Organization This thesis is organized into six hapters, hapter one gives the introdution to the researh ork and the objetive of the researh ork. Chapter to gives the desription of SLI tehnique, desription of ulti frequen Phase Measuring Profiloetr (PMP) is presented, the iportane of the alibration and a atheatial relationship beteen the aera oordinates and the orld oordinates is presented. Chapter three introdues a ne tehnique, Pattern Interleaving (PIL), hih is used to opensate the z otion during the san tie. Chapter four presents an approah to opensate the lateral oveent of the objet during the san tie. Chapter five explains the experiental results of the 3D reonstrution of the objets obtained b using PIL tehnique. Chapter six is a onluding hapter ith a fe insights of further researh. 3

16 Chapter 2 Bakground We disuss the strutured light illuination tehnique and its advantages. The oonl used SLI tehnique, Phase Measuring Profiloetr, is disussed folloed b advantages of alibrating the sste and the different alibration tehniques used that take distortion odels into aount and atheatial relationship beteen the aera oordinates and orld oordinates and the projetor oordinates is presented. 2. Strutured Light Illuination Tehnique One of the ost iportant sanning ethodologies used in the ative ethods for 3D shape easureent is SLI. Unlike the passive sanning ethods like stereovision, SLI overoes the fundaental abiguities [2] and it is also sipler and has high preision. And another advantage is the ost of using SLI tehniques is lo and e an ahieve high speeds. A SLI tehnique onsists of a aera and a projetor as shon in the Figure 2. Figure 2. Strutured Light Illuination (SLI) setup [27] 4

17 The projetor projets oded light patterns suh as stripes, binar odes and gra odes et. on to the target objet and the defored patterns are aptured b the aera. As shon in the Figure 2., the aera, the projetor and the target objet have to for a triangle to detet the deforation. As the aptured iages are enoded ith projetor oordinates, b deoding the aptured iages the orrespondene athing an be obtained. 2.2 Multi Frequen Phase Measuring Profiloetr Phase Measuring Profiloetr (PMP) is one of the ost aurate and robust sanning SLI tehniques used for 3D reonstrution. In a SLI PMP tehnique, the projetor projets the shifted sinusoidal patterns on to the target objet hih are expressed as [5] I n p p p p p ( x, ) A + B os( 2πf 2πn ) p p here ( ) = (2.) N x, are the projetor oordinates, p A and p B are the onstants of the projetor, f is the frequen of the sine ave and n is the phase shift index and N represents the total nuber of sine ave patterns. The defored projeted iages are aptured b the aera, hih is expressed as ( φ 2πn ) I n ( x, ) A( x, ) + B( x, ) os ( x, ) here ( x, ) are the aera o-ordinates and ( x, ) loation ( x, ) and an be alulated as = (2.2) N ( x, ) φ is the phase of the pixel N 2πn I n sin n= ( ) N φ x, = artan N n I ( ) (2.3) 2π n x, os n= N The projetor o-ordinate an be alulated fro the phase obtained in the Eq (2.3) as p ( x, ) = φ (2.4) 2πf Hene ith the help of p and ( x, ) φ 3D orld oordinates an be obtained. 5

18 In the single frequen PMP, the aura of the depth easureent is diretl proportional to the nuber of the shifted sine ave patterns used and the spatial frequen. Hoever, as the spatial frequen inreases the abiguit error inreases. To solve this, Chun and Yalla et al proposed ulti frequen PMP [5] [2] hih is an extension of the single frequen PMP. In the ulti frequen PMP, N nuber of frequenies an be used and the total nuber of shifted sine ave patterns projeted is onstant. The ulti frequen PMP algorith is desribed belo. Projet the base frequen PMP and apture it 2. Calulate the phase at eah pixel of the aptured iage using Eq. (2.3). This serves as the base frequen for the higher frequenies 3. Repeat the folloing steps until all the higher frequenies are projeted 3. apture the higher frequen defored patterns 3.2 alulate the phase using Eq. (2.3) and the phase value lies in the range of -2π 3.3 unrap the phase obtained above using the base frequen obtained in step 2 and 4. Calulate subtrat π to bring it in the range of (-π, π]. This ne phase is used to unrap the phase for the next higher frequen. p fro the phase obtained above and find the 3D orld oordinates 2.3 Calibration Caera alibration plas a proinent role in 3D data aquisition proess. With the help of aera alibration 3D depth inforation an be extrated. The ain ai of the aera alibration is to for a relationship beteen the target objet, projetor and the aera. Thus, a atheatial relationship beteen the orld oordinates, projetor oordinates and the aera oordinates have to be established. This atheatial relationship is affeted b to paraeters intrinsi paraeters and the extrinsi paraeters. Intrinsi paraeters are ainl related to the aera harateristis like foal length, optial enter, pixel sale fators and the distortion paraeters. Extrinsi paraeters are those hih desribe the position of aera oordinate sste ith respet to the orld oordinate sste. Thus, aera alibration is the proess of estiating the above said 6

19 paraeters. In general, if the aera is alibrated auratel, the error in 3D reonstrution is inial Lens Distortions: Lens distortions, hih are ourred b optial aberrations, pla a proinent role in the 3D reonstrution so it is ver iportant to take these distortions into onsideration hen perforing alibration. Lens distortions are of to tpes. Radial distortion 2. Perspetive distortion. Radial distortion: Radial distortion ours hen the iage points are distorted in the radial diretion fro the optial enter. Depending upon the radial diretion fro the optial enter, radial distortion is lassified into to tpes. Barrel distortion 2. Pinushion distortion When the iage points ove toards the optial enter along the radial diretion then that distortion is alled Barrel distortion. If the iage points ove aa fro the optial enter along the radial diretion then that distortion is alled Pinushion distortion. The barrel distortion and the pinushion distortion of a retangular grid are shon in Figure 2.2.The solid line is the original retangular objet and dotted lines represent the distortion of the retangular objet. 7

20 Figure 2.2 Radial Distortion (a) Barrel distortion (b) Pinushion distortion. [9] Perspetive Distortion: Perspetive distortion in an iage ours hen the distane beteen the objet and the lens is hanged. The perspetive distortion of a retangular grid is shon in Figure 2.3 8

21 Figure 2.3 Perspetive distortion of a retangular grid [28] As alread entioned, higher the aura of the alibration of aera paraeters the better is the 3D reonstrution. So these distortion paraeters pla a huge role in 3D reonstrution. Hall [4] proposed a aera alibration tehnique, in hih the transforation atrix is ahieved b using linear tehniques. O.D.Faugeras and G.Tosani [5] proposed a solution to estiate the aera paraeters b onsidering to ases, ith and ithout the knoledge of 3D orld oordinates. In the first ase, aera paraeters are obtained b using linear least squares approah. In the seond ase, the aera paraeters are obtained b athing features and reursivel perforing kalan filtering to estiate the paraeters. Hoever, the ain disadvantage of using these linear tehniques is higher aura an t be ahieved hen the distortion paraeters are taken into onsideration. Bron [6] proposed the plub line ethod to alibrate the lens distortions (radial and tangential). Salvi[7] proposed a non linear optiization tehnique to alibrate the aera b onsidering the distortion paraeters. Higher aura an be ahieved b using this tehnique but the initial guess for the iterative algorith to ahieve 9

22 onvergene is the ain liitation to this tehnique. Tsai [8] proposed a ne alibration tehnique that onsiders the lens distortion. In this ethod, aera paraeters (intrinsi and extrinsi) are estiated b single vie of oplanar and non-oplanar points. Weng et al [9] proposed a to-step alibration tehnique, in the first step aera paraeters are estiated b using linear ethods ithout onsidering the distortion and in the seond step these estiated aera paraeters are iterated through non linear optiized tehniques b onsidering distortion paraeters. The initial guess for the seond step is obtained fro the step one. Zhang [3] presented a ne alibration tehnique, the aera paraeters are estiated b observing a planar pattern at different orientations and using a losed for solution. The nonlinear refineent, b onsidering radial distortion, of the aera paraeters is done b axiu likelihood riteria. Wang et al [2] proposed a ne alibration odel for lens distortion. The basi idea of this odel lies in atheatiall expressing the deentering and tilt distortion in a transfor onsisting of rotation and translation. Thus, this transfor is desribed as to angular paraeters and to linear paraeters. The to angular paraeters desribe the pose of the sensor arra plane ith respet to ideal iage plane and the to linear paraeters desribe loation of the sensor arra ith respet to optial axis. Guangjun Zhang et al [2] proposed a ne alibration algorith for radial distortion based on ross ratio invariabilit of the perspetive projetion. De Xu et al[22] proposed a ne alibration ethod to orret the large lens distortions using a planar grid pattern. In this ethod, an iterative algorith is used initiall to adjust the distortion paraeters and later the aera paraeters are estiated hen the distortion paraeters are adjusted. Zhengou Zhang [23] presented a ne alibration tehnique b onsidering the epipolar geoetr beteen the to iages having lens distortion. This ethod is based on the idea that a point in one iage and the orresponding point in another iage should lie on an epipolar urve instead of straight lines (hih is the ase for distortionless odels). Basing on this epipolar onstraint the distortion paraeters and the aera paraeters are estiated. Lili Ma et al[24] presented a piee ise radial distortion odel orretion for the aera alibration. In this tehnique the distortion paraeters are solved analtiall. Sione Graf and Tobias Hanning [25] also presented a ethod here the aera paraeters an be solved analtiall.

23 Frederi Deverna and Faugeras [26] proposed an autoati alibration for the distortion. This ethod is based on the idea, that a projetion of ever line in a spae on to the aera is a line if the aera is odeled as a pin hole odel. This ethod doesn t require an alibration objet and it requires iages of senes ontaining 3D segents. Edge extration is perfored initiall on the distorted video sequene folloed b a polgonal approxiation to extrat lines and then finding the distortion paraeters that transfers edges to segents Matheatial Relationship beteen the aera oordinates, orld oordinates and projetor oordinates As alread explained, aera alibration is the proess of establishing relationship beteen the aera oordinates and the orld oordinates and also establishing the relationship beteen the orld oordinates and projetor oordinates. Caera alibration is ahieved b estiating intrinsi and extrinsi paraeters. Extrinsi paraeters are ainl dependent on the aera position and aera orientation ith respet to the orld frae and intrinsi paraeters are ainl dependent on the aera internal harateristis suh as foal length, sale fators et. The transforation of the orld oordinates and the aera oordinates is ahieved b the folloing four steps [5] [5] [8][27]. Rigid bod transforation 2. Projetive transforation 3. Lens Distortion 4. Mapping fro the aera oordinates to iage pixel loation Let ( x, ) be the aera iage oordinates, ( X Y, Z ) ( X, Y, Z ) be the 3D aera oordinates. Rigid bod transforation: The rigid bod transforation is given as, be the orld oordinates and X Y Z = R X Z 3 3 Y + T3 (2.6)

24 here R 3 3 is the rotation atrix and T3 is the translation atrix are the extrinsi paraeters given as R 3 3 r = r r 2 3 r r r r r r T 3 t = t t 2 3 Perspetive projetion: Let us onsider ( X u, Y u ) is the undistorted iage oordinates and f is the foal length of the aera. B onsidering the aera as a pin-hole odel, the perspetive projetion is u X X = f (2.7a) Z Y u Y f Z = Lens Distortion: (2.7b) Let ( X d, Y d ) be the undistorted iage oordinates, b onsidering the radial distortion into aount e get u d X = X + u d Y = Y + D D Y X D X is the distortion in x diretion defined as 2 4 ( k r + k + ) (2.8a) (2.8b) d DX = X 2r (2.9a) D Y is the distortion in diretion defined as 2 4 ( k r + k + ) d DY = Y 2r (2.9b) here k and k2 are the radial paraeters and r is given as 2

25 3 ( ) ( ) ( ) 2 2 d d Y X r + = (2.) Mapping fro the aera oordinates to iage pixel loation: Finall the aera oordinates easured are apped to the aera iage oordinates in the frae buffer as + = d d Y X x Y X S S x (2.) here x, are the onstant offsets in x and diretions respetivel, X S and S are the sale fators in x and diretions respetivel These paraeters, foal length, radial paraeters, sale fators and onstant offsets, are intrinsi paraeters. Thus, the transforation of orld oordinates to the aera oordinates is expressed as = Y X Z Y X t r r r t r r r t r r r S x S s s x s (2.2) here s is the sale fator Thus Eq. (2.2) an be expressed as = Z Y X M s s x s (2.3) here 4 3 M is alled the perspetive transforation atrix and it an be also ritten as = M (2.4)

26 Thus, Eq. (2.2) beoes s. x s. s = X Y Z W W (2.5) Thus, the alibration proedure hih is used to estiate the intrinsi and extrinsi paraeters is obtained b estiating the perspetive transforation atrix. As the optial odels for both projetor and the aera are sae, the alibration proedure for a strutured light illuination sste is the alulation of perspetive atries of aera and projetor hih is given as M 3 4 = (2.6) p p p p p p p p p M 3 4 = (2.7) p p p p Fro Eq. (2.5) the aera oordinates ane be ritten as x X + Y + Z + W 2 W 3 4 = (2.8) 3 X W + 32 YW + 33 ZW + 34 X + Y + Z + 2 W 22 W = (2.9) 3 X W + 32 YW + 33 ZW + 34 This perspetive atrix has independent variables and it is oputed b to ost proinent tehniques. Singular Value Deoposition(SVD) tehnique 2. Least squares solution tehnique Singular Value Deoposition (SVD) tehnique: [5] B rearranging the Eq. (2.8) and Eq. (2.9) e an rite in a linear for as A 2 M 2 = 4

27 5 here M A 2 2 is given as = M M M M M M M M M M M M M M M M M M M M Z Y X Z Y X x Z x Y x X x Z Y X Z Y X Z Y X x Z x Y x X x Z Y X Z Y X Z Y X x Z x Y x X x Z Y X A (2.2) [ ] T = (2.2) B using SVD tehnique an be obtained ith the help of T M UDV A = 2 2 (2.22) Where U is a 2 2 M sized atrix and the oluns of this atrix are orthogonal vetors D is a positive diagonal eigen value atrix and V is a 2 2 sized atrix hose oluns are orthogonal. There exists onl one nontrivial solution that orresponds to the last olun of V and this is the solution to M 4 3. Siilar proedure is used to obtain p M 4 3. After the alibration is perfored, the reonstrution proedure is obtained using [ ] D C Z Y X P T = = (2.23) here = p p p p p p p p p x x x C = p p p x D In the above equations, onl the vertial diretion of the projetor is enoded.

28 Least squares solution ethod: The orld to aera oordinate transforations are given in the Eqns (2.8) and (2.9) Fro these equations e an observe that there are infinite nuber of solutions as there is an unknon oeffiient in ever ter so b aking 34 and p 34 equal to e an obtain a linear transfor at the orld origin. This assuption holds ell beause the perspetive transforation atries are defined to sale fator. [3]. Therefore, [ ] T = is obtained b solving the linear equation A = B here A is given as (2.24) A 2 i X i Yi Z i = xi X xi Y xi Z i i i T X i Yi A2 i = (2.25) Z i i X i i Yi i Z i and B is given as 2 i [ x i ] B i = [ i ] B = The vetor 2 (2.26) is obtained b pseudo inverse solution as T T ( A A) A B = (2.27) p Siilar proedure is used to obtain. After the alibration is perfored, the reonstrution proedure is obtained using 6

29 P T [ X Y Z ] = C D = (2.28) here C = 2 p p 3 x p 2 22 p p 32 x p 3 23 p p 33 x p D = p 34 x p 4 24 p 24 In the above equations, onl the vertial diretion of the projetor is enoded. 7

30 Chapter 3 Pattern Interleaving (PIL) Tehnique 3. Introdution Pattern Interleaving (PIL) is a novel tehnique used to obtain high densit single san iage hen the objet is in otion during the san tie. It uses the robust SLI sanning ethod, Phase Measuring Profiloetr (PMP) there b aking the traditional PMP insensitive to depth of z otion. When the objet is in otion during the san tie it is diffiult to get high densit single san iage beause of the oveent of the PMP sine ave patterns. In Figure 3. e sho the 3D reonstrution of a sooth surfae hen it is in stati state and in Figure 3.2 hen it is in otion during the san tie. Figure 3. Stati 3D reonstrution of a stati surfae 8

31 Figure 3.2 3D reonstrution of a sooth surfae in otion The ain objetive of the PIL tehnique is to orret the oveent of the sine aves that ours during the san tie and thereb reduing the otion banding. Thus, aking traditional PMP insensitive to z otion and thereb preventing otion banding b orreting for the otion. 3.2 Desription of Pattern Interleaving (PIL) Tehnique In PIL tehnique, traditional PMP patterns are projeted in beteen the triangular ave patterns (PIL patterns) of onstant frequen. The pattern sequene is shon in Figure 3.3 9

32 t = t t = t t = t 2 t = t 3 t = t 4 T P T P T 2 Figure 3.3 Pattern sequene here T n is the PIL pattern and n varies fro to N here N + is the total nuber of PIL patterns and P n is the PMP pattern and n varies fro to N and = p= p n t p is the san tie here t > p+ t p. The otion orretion is aoplished ith the help of to triangular ave patterns (PIL patterns) projeted before and after the sine ave pattern. The pitorial representation of the PIL tehnique is shon in Figure 3.4 PMP patterns Triangular snake patterns Differene Iage offset (in pixels) offset(in pixels) 2 N- N Figure 3.4 Pitorial representation of PIL tehnique 2

33 With the help of to triangular ave patterns the oveent of the target objet fro one tie frae to another tie frae is traked. The proess of reating a differene iage as shon in the Figure 3.4 is the differene of the to respetive triangular ave peaks. The peaks are enoded as + and non-peaks as so the differene results in the values of {,, } +.The lines in the differene iage are the snakes here the bold lines in the differene iage indiates the positive peak loations and the dotted lines indiates the negative peak loations, the distane beteen these to (hih is easured in pixels) gives the oveent of the target objet fro one PIL pattern to the next PIL pattern. This traked oveent or the offset beteen the to PIL patterns helps to orret the PMP pattern in beteen these to PIL patterns. That is, the oveent in the sine ave pattern is orreted b shifting the sine aves ith half aount of the alulated offset (sine PMP pattern is half a beteen the PIL patterns) plus the auulated su of the offsets of the previous PIL patterns. For exaple, for orreting P PMP pattern the offset beteen T and T snakes is alulated and the sine aves of the P pattern are shifted b half aount of the offset of T andt. For orreting P 4 PMP pattern the offset hih is used to orret the sine aves is half of the offset of T4 and T 5 PIL patterns and su of the offsets of the previous PIL patterns, that is, T and T ; T and T 2 ; T 2 and T 3. 2

34 3.3 PIL Algorith Let P n ( x, ) be the n th PMP pattern hih is in otion here x =,,..( N ) and =,,2 ( M ) and n is the frae nuber ranges fro to N here N + represents the total nuber of the PIL fraes. Let ( x ) is also in otion. Step: Filtering the PIL patterns The PIL iages are filtered to reove the noise. Let ( x ) T n, be the n th PIL pattern hih C n, be the PIL iage hih is filtered b using a oving average filter suh that C x, = T x, * h x (3.) ( ) ( ) ( ) n n, x ret τ and * represents onvolution Step 2: Finding the peak to side lobe ratio here h( x, ) = ret τ x Let ( x ) PSR n, be the peak to side lobe ratio for the filtered PIL iages and it is alulated as PSR n ( x ) Cn ( x, ) { C ( x, τ ), C ( x, +τ )}, = (3.2) ax here τ is the side lobe spaing Step3: Snake detetion and enoding n Snakes detetion is perfored b looking at the loations here snakes represent the axiu n PSR n is axiu as PSRn loations. B perforing snake detetion, e an ake snakes visible and thus ake it easier to alulate the offset that ourred due to the otion in the PIL pattern iages. Let ( x ) ainl arried out in to steps. Snake Loations 2. Snake Peaking S n, be the snake iage. The snake asking is x 22

35 Snake Loations: For a pixel to be enoded as a peak the PSR at that pixel ust be greater than the predeterined threshold and the intensit or the peak value at that pixel ust be greater than a predeterined iniu value. The resulting regions enoded ith 255 ontain the snake enter positions. To deterine the ost likel snake enters, e appl Snake Peaking proess. Snake Peaking: After reating lo region (zero values) and a high region (255 values) e need to run the snake proess in to states. Searh for the start of high region (state ) 2. Searh for the end of high region (state ) First, searh for the start of high region (searh for value 255) if a value of 255 is found then enode that loation as peak and as a start loation and then go to state. In state, searh for value and assign the loation as an end loation. Searh for axiu PSR beteen the start and end loations, if a axiu PSR is obtained enode that loation as peak and assign a value of 255 at that loation and go to state. 23

36 A flohart explaining the proess of snake detetion is shon in Figure 3.5 Creating a Snake Mask S n ( x, ) Initializing the ask: x, = S n ( ) 255 If C ( x, ) < Peak in S ( x, ) = n If PSR ( x, ) < PSR in S ( x, ) = n n n Snake Proess Loop through x values State : searh for high region Searh for the value 255 peak =, Peak = Cn ( x, ) If S n ( x, ) = 255, start =, PSR = PSRn x, Go to state ( ) Loop through values State : searh for lo region Searh for the value If S n ( x, ) = for start end S n ( x, ) = S n ( x, peak ) = 255 Go to state Else end = If PSR( x, ) > PSRn ( x, ) PSR = PSRn ( x, ) Peak = Cn ( x, ) = peak Figure 3.5 Flohart of snake detetion 24

37 Step 4: Finding the offset Let the differene iage beteen the to snake iages be D ( x, ) S ( x, ) S ( x ) = (3.3) n n n, if the differene beteen the to snake iages is zero, then there is no oveent that is, if D n ( x, ) = there is no oveent otherise if ( x, ) > oveent. Let { } p D n there is x, here p =,, 2. P be the positive peak loations in the differene iage, that is, D ( x, ) > n p. As e are onsidering the oveent in diretion, the x value an be ignored and P is the total nuber of positive peak loations in the differene iage. Siilarl let { } q peak loations in the differene iage, that is, (, ) < x, here q =,, 2. Q be the negative D x n q. Q is the total nuber of the negative peak loations in the differene iage. The offset, due to otion, is alulated as the agnitude of the differene beteen the positive peak and its assoiated negative peak Let d dn be the offset hih is alulated as n (3.4) p q Step 5: Copensating the PIL patterns: The PIL iages an be opensated ith the help of the offsets obtained in Eq.(3.4) depending on the oveent of the objet ith referene to aera Let us onsider and be the loations of the adjaent snakes in ( x ) S n, here =,, 2 M. M is the total nuber of snakes in the iage. Fro Eq.(3.4) e kno that ourred due to otion at in S n ( x, ) iage ith respet to S n ( x, ) Siilarl e kno that d is the offset due to otion at in ( x ) respet to S n ( x, ). These an be expressed as d ( x) dn ( x, ) ( x) d ( x ) d is the offset iage. S n, iage ith = (3.5) d (3.6) = n, 25

38 The offsets beteen the adjaent snakes an be estiated b the interpolation of the offsets that ourred at the snakes. That is, the offsets beteen and an be estiated b interpolating ith the help of d and d. The offset values beteen the peaks is interpolated suh that n ( x, ) = a b for ( x) ( x) d + (3.7) The values of a and b are obtained ith the help of to equations shon belo d n ( x ( x) ) = a + b d n ( x ( x) ) = a + b As e kno dn ( x, ( x) ), ( x), dn ( x, ( x) ) and ( x) alulated easil, (3.8), (3.9) d ( x, ) d ( x, ), a and b values an be n n a = (3.) b n ( x ) a The otion orretion of the snake iage is S = d, (3.) ( x + d ( x, ) ) = S ( x ) for ( x) ( x) n, n n, (3.2) With the help of Eq(3.7) the PMP iages are otion opensated. As the PMP iages ontributes onl half of that of PIL iages the offset is taken as ( x ) d n ( x, ) instead of 2 d n, and e require the previous offsets to auratel align all the PMP patterns The opensation of the PMP patterns is as follos ( x, ) k n dn Pn x, + + = dk n, 2 k = ( x, ) = P ( x ) for ( x) ( x) (3.3) 26

39 3.4 Experients and results 3.4. Estiating offset beteen the to suessive PIL patterns As explained in the setion 3.3, in order to trak the oveent of the target objet during the san tie e need to find the differene beteen the to suessive snake asked PIL patterns. The to suessive PIL snake asked patterns are shon in Figure 3.6 and Figure 3.7 Figure 3.6 Snake asked T PIL pattern Figure 3.7 Snake asked T PIL pattern 27

40 The differene beteen the to snaked asked PIL patterns (Figure 3.6 and Figure 3.7) is shon in Figure 3.8 Figure 3.8 Differene iage of the snake asked TPIL pattern and T PIL pattern A ropped out setion of Figure 3.8 is shon in Figure 3.9 Negative peak Figure 3.9 Cropped setion of the differene iage Positive peak The hite line in the differene iage indiates the positive peak loations and the blak lines in the differene iage indiate the negative peak loations. The differene beteen 28

41 these to gives the offset or the oveent of the objet at that loation fro one PIL frae to the next PIL frae. A ross setional plot of the intensit of the iddle olun of the differene iage is shon in Figure 3. for better visualization of the positive and negative loations Figure 3. Middle olun intensit of the differene iage If the objet is oving toards the aera the differene beteen the negative peak and the orresponding positive peak ill give the oveent or the offset hih is the ase as shon in the figure above siilarl if the target objet is oving aa fro the aera the differene beteen the positive peak and the orresponding negative peak ill give the offset. That is, fro Eq(3.4) e have n ( p, q ) > (, ) < d When the objet is oving aa fro the aera d n p q When the obj et is oving toards the aera Hoever, the agnitude of the distane beteen the negative peak and positive peak (or positive peak and negative peak) ill give the offset. 29

42 A ross setional plot of the offsets (the oveent of the T PIL pattern ith respet to T PIL pattern) for the iddle olun loations is shon in Figure 3. Figure 3. d for the pixel loations of the iddle olun at snake loations Fro the Figure 3. e an deterine the offset at the pixel loations (snake loations) for the iddle olun of T PIL pattern ith respet to the T PIL pattern. Siilarl one an find out the offset at the other oluns snake loations for T PIL pattern. 3

43 3.4.2 Interpolating the offset to orret the PMP pattern The offset hih is alulated above is used onl to orret the snake loations, so in order to orret the tpial PMP pattern e need to kno the offset beteen the snakes. Figure 3.2 Need for interpolating the offset beteen the snake regions To alulate the offset beteen the snake regions, as explained in setion 3.3, e use linear interpolation to find out the offsets beteen the snake regions ith the help of knon offsets at the snake loations hih is explained in the setion

44 A ross setional plot of the interpolated offsets for a iddle olun is shon in Figure 3.3 Figure 3.3 Figure shoing the offset at the snake loations and the interpolated offset beteen the snake regions Fro the Figure 3.3 e an observe that the blue lines indiate the offsets hih are alulated in the setion 3.4. and the green line indiates the interpolated offsets beteen the snake loations b using the help of the offsets at the snake loations. 32

45 3.4.3 Result of PIL tehnique The 3D reonstrution of a sooth surfae b using PIL tehnique is shon in Figure 3.4 (a) and the filtered 3D reonstruted iage is shon in Figure 3.4 (b). (a) (b) Figure 3.4 (a) 3D reonstrution of a sooth surfae using PIL tehnique (b) filtered 3D reonstruted sooth surfae using PIL A ross setional side vie of the 3D reonstrution of stati sooth surfae, sooth surfae in otion and sooth surfae in otion orreted b PIL tehnique are shon in Figure 3.5 for better visualization of the results. 33

46 (a) (b) () Figure 3.5 (a)side vie of stati 3D reonstrution of sooth surfae (b) side vie of the 3D reonstruted sooth surfae in otion () side vie of the 3D reonstruted sooth surfae using PIL tehnique Fro the Figure 3.5 (b), e an learl see that due to otion on the sooth surfae during san tie the 3D reonstrution of sooth surfae ontains ripples unlike stati sooth surfae as shon in Figure 3.5 (a). Fro the Figure 3.5 (), e an see that b appling the PIL tehnique the ripples are signifiantl redued and the 3D reonstrution of sooth surfae using PIL tehnique looks approxiatel siilar to the stati 3D reonstrution. 34

47 3.5 Band Ripple Measureent 3.5. Calulation of Band Energ for an ideal ripple To objetivel evaluate the perforane of PIL, e need a otion banding easure. We introdue a band energ easure here band energ is defined as the ratio of the peak to peak distane of ripples to the avelength of the ripples. b h e = (3.4) λ Where b e is the average band energ, λ is the avelength of the ripples and h is the peak to peak distane of ripples. The alulation of band energ for an ideal ripple (sine ave) is shon in the Figure 3.6 A = λ B b h a C Figure 3.6 Ideal ripple Fro the Figure 3.6, e an observe that the points A, B and C for a triangle here A and B are the axiu peaks of a ripple and C is the valle point of a ripple and a, b and are the orresponding distanes or the length of sides of a triangle. Therefore, the avelength of a ripple is nothing but the distane beteen the points A and B, hih is. 35

48 To alulate the peak to peak distane of a ripple, initiall e use Heron s forula to alulate the area of the triangle and after that e an get the peak to peak distane of the ripple fro the area alulated. The area of a triangle is alulated fro Heron s forula as follos ( s a) ( s b( s ) ) Area = s here sei-perieter The peak to peak distane of the ripple is alulated as h = 2 Area λ sine λ is the base of the triangle. s = a + b + 2 As the peak points and the valle points are expressed in orld oordinates, the band energ easure is independent of the orientation Calulation of Band Energ ithout PIL orretion Band energ for a sooth surfae target ithout PIL orretion is alulated ith the help of GL3D Vie softare as shon in Figure 3.7 Figure 3.7 Measuring Band Energ of a sooth surfae ithout PIL orretion 36

49 Fro the Figure 3.7, the green and red points denote the axiu peak points and blue point is valle point. The horizontal orientation of ripples is shon in Figure 3.8 Figure 3.8 Measuring avelength of ripples of a sooth surfae ithout PIL orretion Fro Figure 3.8, e an learl see that these three points for a triangle and the length of the sides an be easil easured ith the help of easureent panel. The avelength of the ripple is nothing but the distane beteen the red point and the green point as shon in the Figure 3.8. As e kno the length of the sides of the triangle e an easil easure the peak to peak distane of the ripple as explained in the setion 3.5. The avelength hih is easured in orld oordinates is obtained as and the approxiate peak to peak distane alulated is Therefore, average band energ is be =.9265 / = The average band energ ithout PIL orretion is Calulation of Band Energ after PIL orretion The proedure for alulating the band energ after PIL orretion is sae as alulating the band energ ithout PIL orretion. The 3D reonstrution of a sooth surfae after PIL orretion is shon in Figure

50 Figure 3.9 Measuring Band Energ of a sooth surfae after PIL orretion The horizontal orientation of the ripples after PIL orretion is shon in Figure 3.2 Figure 3.2 Measuring avelength of the ripples of a sooth surfae after PIL orretion 38

51 B appling the sae proedure hih is used to find band energ for a sooth surfae ithout PIL orretion e get the avelength of ripples after PIL orretion in orld oordinates is and the approxiate peak to peak distane is.87 Average band energ b e =.87 /6.359 =.368. Therefore, band attenuation hih is defined as the ratio of the band energ using PIL tehnique to the band energ ithout using PIL tehnique is b a =.368/.2735 =.5 39

52 Chapter 4 Lateral Corretion Approah Pattern Interleaving (PIL) Tehnique is used to orret the z otion of the objet that ours during the san tie. In this hapter, an approah to orret the lateral oveent of the objet during the san tie is presented. In this approah, an objet ith distintive features and a unifor blak bakground is onsidered as shon in the Figure 4. Figure 4. Setup arrangeent for lateral orretion 4. Steps to orret the lateral oveent Step : Edge enhaneent of the PMP patterns: To suessive PMP patterns are onsidered to trak the lateral or left to right otion. These to aptured iages are edge enhaned b using sobel edge enhaneent tehnique so that the distintive features ore visible. 4

53 The first aptured PMP pattern hih is used as a referene to orret the aptured seond aptured PMP pattern is shon in the Figure 4.2 (7, 58) Figure 4.2 First aptured PMP pattern A arker point is used to sho the oveent fro one frae to another frae. The seond aptured PMP pattern hih needs to be opensated in the otion in the lateral diretion is shon in the Figure 4.3 (955,58) Figure 4.3 Seond aptured PMP pattern 4

54 We an learl see that there is a oveent in the lateral diretion on the seond aptured PMP pattern. That is, the oveent fro {, } = { 7,58} { x, } = { 955,58} shon in the Figure 4.4 x to. The sobel edge enhaned iage of the first aptured PMP pattern is Figure 4.4 Sobel edge enhaneent iage of the first aptured PMP pattern The sobel edge enhaneent of the seond aptured PMP pattern is shon in the Figure 4.5 Figure 4.5 Sobel edge enhaned iage of the seond aptured PMP pattern 42

55 Step 2: Noralized ross orrelation of the edge enhaned iages The to edge enhaned iages obtained in the step are ross orrelated and noralized to find out the offset or the oveent of the PMP pattern fro one frae to another frae. 3D ross orrelated plot is shon in Figure 4.6 Figure 4.6 3D plot of ross orrelation beteen the to sobel edge enhaned iages Peak loation of the plot helps to figure out the offset that needs to be opensated. In general, the offset in x diretion ould be the differene beteen the peak x loation and the nuber of ros in the iage. 43

56 Step 3: Copensating the PMP patterns The PMP pattern that needs to be orreted is oved laterall ith the help of the offset obtained in the step 2. The PMP pattern hih is laterall orreted is shon in the Figure 4.7 (7, 58) Figure 4.7 Correted seond aptured PMP pattern Fro the Figure 4.7 and Figure 4.2 e ould see that the seond aptured PMP pattern is otion opensated in the lateral diretion. Thus, using this approah e are able to orret the lateral oveent in all the PMP patterns. 44

57 Chapter 5 Experients and Results In this setion, different experiental results onduted on different objets b onsidering to tpes of z otion are presented. The to tpes of z otion are. unifor z otion 2. non-unifor z otion In a unifor z otion, the objet oves in the z diretion in equal inreents and in onl one diretion during the san tie either toards the SLI sste or aa fro the SLI sste. In a non-unifor z otion, the objet oves in the z diretion in both as during the san tie that is it oves bak and forth (toards the SLI sste and aa fro the SLI sste) during the san tie. The oparison of 3D reonstruted results ith and ithout using the PIL algorith is presented. 5. 3D reonstrution of objets in unifor z otion We present the oparison of the 3D reonstrution of the objets hen the are in stati, unifor z otion during the san tie and otion orreted using PIL tehnique The z otion toards the aera and z otion aa fro the aera are onsidered. The side vies of the 3D reonstruted iages are presented for better visualization of the ripples that ourred due to the otion of the objet during the san tie and the side vies of the 3D reonstruted iages using PIL are also presented to sho the orretion. A sooth surfae hih is subjeted to unifor z otion toards the aera is onsidered and the oparison of the 3D reonstrution of the sooth surfae hen it is in stati, z otion toards the aera and otion orreted using PIL tehnique is shon in the Figure 5. 45

58 (a) (b) () Figure 5. (a) side vie of the 3D reonstruted sooth surfae in stati, (b) side vie of the 3D reonstruted sooth surfae in otion and () side vie of the 3D reonstruted sooth surfae using PIL tehnique. Fro the Figure 5. e ould learl see that there is no variation in the z diretion hen the objet is in a stati position and there is a variation in the z diretion hen the objet is subjeted to z otion during the san tie and e also see the opensation of the z otion b using PIL tehnique. The ripples hih appeared in Figure 5. (b) are signifiantl redued b using PIL tehnique as shon in Figure 5. (). Siilarl, a fae annequin, Alie is subjeted to unifor otion in z diretion during the san tie. 46

59 The 3D reonstrution of the Alie in stati is shon in the Figure 5.2. Figure 5.2 3D reonstrution of a fae odel The side vies of the stati, otion and otion orreted (using PIL) 3D reonstruted iages are presented to opare the results are shon in the Figure 5.3. (a) (b) () Figure 5.3 (a) ropped side vie of the stati 3D reonstruted fae odel (b) ropped side vie of the 3D reonstruted fae odel in otion () ropped side vie of the 3D reonstruted fae odel using PIL tehnique. 47

60 Instead of oving toards the aera, a sooth surfae is subjeted to z otion aa fro the aera during the san tie. The oparison of the side vies of the 3D reonstruted sooth surfae hen it is in stati, z otion aa fro the aera and the otion orreted using PIL are shon in the Figure 5.4 (a) (b) () Figure 5.4 (a) side vie of the stati 3D reonstruted sooth surfae (b) side vie of the 3D reonstruted sooth surfae in z otion aa fro the aera () side vie of the 3D reonstruted sooth surfae using PIL tehnique D reonstrution of objets in non-unifor z otion We present the 3D reonstrutions of the objets hih are subjeted to non-unifor z otion. Cropped side vies of the 3D reonstrution of the objets are presented to sho the ripples that ourred due to non-unifor z otion during the san tie and also ropped side vies of 3D reonstrution of the objets using PIL orretion are presented to sho the orretion of the ripples. 48

61 In this setion, a sooth surfae hih is oved bak and forth is onsidered and also a ard board hung ith strings suh that it exhibits free osillation during the san tie is also onsidered. A sooth surfae hih is oved bak and forth in the z diretion during the san tie is onsidered and the oparison of the ropped side vies of the 3D reonstrution of the sooth surfae in stati, in non unifor z otion and the otion orreted using PIL tehnique is shon in the Figure 5.5 (a) (b) () Figure 5.5 (a) ropped side vie stati 3D reonstrution of a sooth surfae (b) ropped side vie of the 3D reonstrution of the sooth surfae hih is subjeted to non-unifor otion and () ropped side vie of the 3D reonstrution of the sooth surfae using PIL tehnique. 49

62 Instead of anuall oving the objet during the san tie, the objet that is held ith strings is alloed to freel osillate during the san tie as shon in the Figure 5.6 Figure 5.6 objet held ith strings to freel osillate during the san tie Thus, the objet is held suh a a that it exhibits osillating otion in z diretion. The 3D reonstrution of the objet hen the objet is in stati, hen the objet is in non-unifor z otion is onsidered and the 3D reonstrution of the objet b using PIL tehnique is obtained. 5