TARGETLESS CAMERA CALIBRATION

Transcription

1 TARGETLESS CAMERA CALIBRATION L. Barazzetti a, L. Mussio b, F. Remondino, M. Saioni a a Politenio di Milano, Dept. of Building Engineering Siene and Tehnology, Milan, Italy {luigi.barazzetti, maro.saioni}@polimi.it, web: b Politenio di Milano, Dept. of Environmental, Hydrauli, Infrastrutures and Surveying Engineering, Milan, Italy luigi.mussio@polimi.it, web: 3D Optial Metrology Unit, Bruno Kessler Foundation (FBK), Trento, Italy remondino@fbk.eu, web: KEY WORDS: Automation, Auray, Calibration, Mathing, Orientation ABSTRACT: In photogrammetry a amera is onsidered alibrated if its interior orientation parameters are known. These enompass the prinipal distane, the prinipal point position and some Additional Parameters used to model possible systemati errors. The urrent state of the art for automated amera alibration relies on the use of oded targets to aurately determine the image orrespondenes. This paper presents a new methodology for the effiient and rigorous photogrammetri alibration of digital ameras whih does not require any longer the use of targets. A set of images depiting a sene with a good texture are suffiient for the extration of natural orresponding image points. These are automatially mathed with feature-based approahes and robust estimation tehniques. The suessive photogrammetri bundle adjustment retrieves the unknown amera parameters and their theoretial auraies. Examples, onsiderations and omparisons with real data and different ase studies are illustrated to show the potentialities of the proposed methodology. a) b) Figure. A target-based alibration proedure (a) and the targetless approah (b).. INTRODUCTION Aurate amera alibration and image orientation proedures are a neessary prerequisite for the extration of preise and reliable 3D metri information from images (Gruen and Huang, ). A amera is onsidered alibrated if its prinipal distane, prinipal point offset and lens distortion parameters are known. Camera alibration has always been an essential omponent of photogrammetri measurement. Self-alibration is nowadays an integral and routinely applied operation within photogrammetri image triangulation, espeially in highauray lose-range measurement. With the very rapid growth in adoption of off-the-shelf (or onsumer-grade) digital ameras for 3D measurement appliations, however, there are many situations where the geometry of the image network annot support the robust reovery of amera interior parameters via on-the-job alibration. For this reason, stand-alone and targetbased amera alibration has again emerged as an important issue in lose-range photogrammetry. In many appliations, espeially in Computer Vision (CV), only the foal length is generally reovered. In ase of preise photogrammetri measurements, the whole set of alibration parameters is instead employed. Various algorithms for amera alibration have been reported over the past years in the photogrammetry and CV literature (Remondino and Fraser, 6). The algorithms are usually based on perspetive or projetive amera models, with the most popular approah being the well-known self-alibrating bundle adjustment (Brown, 976; Fraser, 997; Gruen and Beyer, ). It was first introdued in lose-range photogrammetry in the early 97s by Brown (97). Analytial amera alibration was a major topi of researh interest in photogrammetry over the next deade and it reahed its full maturity in the mid 98s. In the early days of digital ameras, self-alibration beame again a hot researh topi and it reahed its maturity in the late 9s with the development of fully automated vision metrology systems mainly based on targets (e.g. Gani and Handley, 998). In the last deade, with the tremendous use of onsumergrade digital ameras for many measurement appliations, there was a renewed interest in stand-alone photogrammetri alibration approahes, espeially for fully automati on-the-job alibration proedures. Nowadays the state of the art basially relies on the use of oded targets whih are depited in images forming a blok with a suitable geometry for estimating all the alibration parameters (Cronk et al., 6). Target measurement and identifiation is performed in an automati way. A bundle 335

2 adjustment allows then the estimation of all the unknown parameters and their theoretial auraies. On the other hand, amera alibration ontinues to be a more ative area of researh within the CV ommunity, with a perhaps unfortunate harateristi of muh of the work being that it pays too little heed to previous findings from photogrammetry. Part of this might well be explained in terms of a lak of emphasis on (and interest in) auray aspets and a basi premise that nothing whatever needs to be known about the amera whih is to be alibrated within a linear projetive rather than Eulidean sene reonstrution.. CAMERA CALIBRATION IN PHOTOGRAMMETRY AND COMPUTER VISION In photogrammetry amera alibration is meant as the reovery of the interior amera parameters. Camera alibration plays a fundamental role in both photogrammetry and CV but there is an important distintion between the approahes used in both disiplines. Even the well-known term self-alibration has different meanings. Lens distortion generates a misalignment between the perspetive entre, the image point and the objet point. It is quite simple to understand that the ollinearity priniple, whih is the basis for image orientation, is no longer respeted ( departure from ollinearity ). Modelling lens distortion allows to strongly redue this effet. A alibrated amera is a powerful measuring tool, with a preision superior to :5, as reported in different vision metrology appliations (Maas and Niederöst, 997; Albert et al., ; Amiri Parian et al., 6; Barazzetti and Saioni, 9; Barazzetti and Saioni, ). The importane of amera alibration is onfirmed by the vast number of papers in the tehnial literature: auray aspets, low-ost and professional ameras, stability and behaviour of the parameters, variations in the different olour hannels as well as algorithmi issues were reported in Fraser and Shortis (995), D Apuzzo and Maas (999), Läbe and Förstner (4), Fraser and Al-Ajlouni (6), Peipe and Teklenburg (6) and Remondino and Fraser (6). During a photogrammetri amera alibration proedure, the systemati errors in digital CCD/CMOS sensor are universally ompensated with an 8-terms physial mathematial model originally formulated by Brown (97). This omprises terms for the prinipal distane () and prinipal point offset (x, y ) orretion, three oeffiients for the radial distortion (k, k, k 3 ), and two oeffiients for the deentring distortion (p, p ). The model an be extended by two further parameters to aount for affinity and shear within the image plane, but suh terms are rarely if ever signifiant in modern digital ameras, espeially for heritage and arhitetural appliations. The orretions terms are generally alled Additional Parameters (APs). The three APs used to model the radial distortion δr are generally expressed with an odd-ordered polynomial series: δ r = k + () r + kr k3r where r is the radial distane of the generi image point (x, y) from the prinipal point (x, y ): ( x x ) + ( y ) r = () y The omponents along x and y of δr may be estimated as follows: δr δr x = ( x x ), δy = ( y y ) (3) r r δ The oeffiients k i are a funtion of the used prinipal distane and are usually highly orrelated, with most of the error signal generally being aounted for by the ubi term k r 3. The k and k 3 terms are typially inluded for photogrammetri (low distortion) and wide-angle lenses and in higher-auray vision metrology appliations. Reent researh has demonstrated the feasibility of empirially modelling radial distortion throughout the magnifiation range of a zoom lens as a funtion of the foal length written to the image EXIF header (Fraser and Al- Ajlouni, 6). A misalignment of the lens elements along the optial axis instead generates deentring distortion. The orretions terms for the measured image oordinates are given by: t [ r + ( x x ) ] + p( x x )( y y ) r + ( y y ) + p x x y y δ x (4) δt y = p = p [ ] ( )( ) The deentering distortion parameters p and p are invariably strongly projetively oupled with x and y. Deentering distortion is usually an order of magnitude or more less than the radial distortion and it also varies with fous, but to a muh less extent. Considering all the APs, the image oordinates orretion terms an be formulated as: x x x = x + + δx + δtx y y y = y + + δx + δt y The simultaneous estimation of APs and amera parameters is generally referred to as self-alibrating bundle adjustment. The bundle adjustment with APs needs a favourable network geometry to be orretly solved i.e. onvergent and rotated images of a preferably 3D objet should be aquired, with well distributed points throughout the image format (Figure a). If the network is geometrially weak, high orrelations between the unknown parameters may lead to instabilities in the leastsquares estimation. The inappropriate use of the APs an also weaken the bundle adjustment solution, leading to overparameterization, in partiular in the ase of minimally onstrained adjustments (Fraser, 98). The ollinearity model and the related bundle adjustment problem must be linearized to obtain a system of linear observation equations. The linearized model an be solved with the Gauss-Markov model of least squares (Mikhail et al., ) and its solution is rigorous in a funtional and stohasti sense. Good initial values of the unknown parameters are needed for the linearization proess based on the Taylor series expansion. External onstraints (e.g. GNSS/INS data, GCPs) an also be effiiently inorporated into the general model. The final system is made up of observation equations (those written as funtions of both observations and parameters) and onstraint equations (those written in terms of the parameters). The seond group of equations is usually formulated as pseudo-observation equations, where the unknown parameters are linked to their measured values. All the variables in the adjustment beome weighted observations. By properly tuning eah weight it is possible to give more or less emphasis to the observed values of eah unknown parameter. (5) 336

3 If the observations are image oordinates, the reonstrution is affeted by an overall ambiguity (i.e. a 3D similarity transformation). This datum problem (or rank defiieny) an be solved by introduing ground ontrol points (GCPs) and/or GNSS/INS information. The seond solution is almost the standard in aerial photogrammetry, while these data are not generally available in lose-range surveys. The rank defiieny of the Least Squares problem an also be removed with an inner onstraint. This does not involve external observations and leads to the so-alled free-net solution (Granshaw, 98; Dermanis, 994). The theoretial auray obtainable with a free-net adjustment, oupled with preise image points and good alibration parameters is superior to :,. In some ases, a theoretial auray of about one part in a million was reahed (Fraser, 99). (a) objet distanes. What is sought is the maximum possible imaging sale variation throughout the image format. orthogonal roll angles must be present to break the projetive oupling between IO and EO parameters. Although it might be possible to ahieve this deoupling without 9 o image rotations, through provision of a strongly 3D objet point array, it is always reommended to have rolled images in the self-alibration network; the auray of a network inreases with inreasing onvergene angles for the imagery. Inreasing the angles of onvergene also impliitly means inreasing the base-todepth (B/D) ratio. In CV, the orientation proedures are (often) unalibrated. This allows one to deal with simple, quik, and flexible aquisition proedures. The mapping between objet (X) and image (x) points with the general projetive amera model may be written as (Hartley and Zissermann, 4): f px x = PX = f py, [ R, t] X = K[ R t]x (6) The matrix K is the alibration matrix, here written for CCD or CMOS sensors with square pixels and a skew parameter equal to. This relationship inludes the foal length f and the prinipal point offset, so that the model is equivalent to that with interior orientation parameters (although the foal length is not the prinipal distane, exept for lenses foused at infinity). To ompensate for the image distortion, a distortion fator L(r) is generally onsidered, that depends on the radius only (Hartley and Zissermann, 4): (b) x y orr orr = x + L( r)( x x ) = y + L( r)( y y ) (7) Figure. An appropriate image network whih allows the orret estimation of all alibration parameters (a). An image network inappropriate for amera alibration and more effiient for sene reonstrution and 3D modeling appliations (b). Some good and pratial rules for amera alibration an be summarized as follows: self-alibration is only reliable when the image network geometry is favourable, i.e. the amera station onfiguration omprises highly onvergent images, orthogonal roll angles and a large number of well distributed objet points. A ompensation for departures from ollinearity might well be ahieved in a bundle adjustment with APs for a weak network, but the preise and reliable reovery of representative alibration values is less likely to be obtained; a planar objet point array ould be employed for amera alibration if the images are aquired with orthogonal roll angles, a high degree of onvergene and, desirably, varying where (x orr, y orr ) are the orreted (or undistorted) oordinates, and (x, y ) is the entre of radial distortion. For the solution of Eq. 6 (based on the orreted image oordinates), a bundle adjustment generally based on the Levenberg-Marquard algorithm is employed. Given a set of n image points and m 3D points, the reprojetion error (i.e., the distane between the bak projeted 3D point and the orresponding measured image point) is minimized (Triggs et al., ): n m min w i= j= ij x P (K, X ) (8) ij i i where x ij is the measured image point, K i are the amera parameters, P i is the projetion matrix, X j is a 3D point. The oeffiient w ij is set to if amera i observes point j, and otherwise. In CV appliations all amera parameters (interior and exterior) are usually reovered simultaneously and diretly from the same set of images employed to reonstrut the sene. This solution is aeptable if the main goal is not an aurate metri reonstrution. On the other hand, in photogrammetri appliations, although the estimation of the amera parameters is still arried out within a bundle adjustment, the network geometry used for objet reonstrution is generally not suffiient to estimate the interior parameters at the same time (Figure ). Therefore, it is strongly suggested to separate the j 337

4 reovery of the interior and exterior orientation parameters by means of two separate proedures with adequate networks. 3. TARGETLESS CAMERA CALIBRATION Sine many years ommerial photogrammetri pakages use oded targets for the automated alibration and orientation phase (Gani and Handley, 998; Cronk et al., 6). Coded targets an be automatially reognized, measured and labelled to solve for the identifiation of the image orrespondenes and the suessive amera parameters within few minutes. Figure 3. Examples of oded targets. Commerial software (e.g., iwitness and PhotoModeler) typially works with small oded targets (Figure 3) that an be distributed in order to form a 3D alibration polygon. The main advantage of this proedure is related to the possibility to have a portable solution. This is useful in many photogrammetri surveys and to assure a orret and automated identifiation of the image orrespondenes. This paper presents a new methodology to effiiently alibrate a digital amera using the ATiPE system, widely desribed in Barazzetti et al. (a) and Barazzetti (). ATiPE an automatially and aurately identify homologues points from a set of onvergent images without any oded target or marker. A set of natural features of an existing objet are used to determine the image orrespondenes. These image points are automatially mathed with the implemented feature-based mathing (FBM) approahes. The objet should have a good texture in order to provide a suffiient number of tie points well distributed in the images. The operator has to aquire a set of images (-5) with a good spatial distribution around an objet (inluding 9 o amera roll variations). Arhitetural objets (e.g. arades, building faades, olonnades and similar) should be avoided beause of their repetitive textures and symmetries. Big roks, bas-reliefs, deorations, ornaments or even a pile of rubble are appropriate (Figure 4). Figure 4. Examples of good alibration objets. ATiPE uses SIFT (Lowe, 4) and SURF (Bay et al., 8) as feature detetors and desriptors. A kd-tree searh (Arya et al., 998) speeds up the omparison between the desriptors of the adopted FBM algorithms. The experimental tests demonstrated that points are rarely mathed with onvergene angles superior to 3-4. A normal exhaustive quadrati omparison of the feature desriptors is a more robust approah in ase of very onvergent images. This is the most important drawbak of the method, whih leads to a long elaboration time. The global proessing time is often unpreditable. It ranges from few minutes up to some hours for large datasets with very onvergent images. 4. EXAMPLES AND PERFORMANCE ANALYSES 4. Pratial tests Figure 5a shows a alibration testfield reated with some oded targets. 6 images are aquired using a Nikon D7 (4,56,83 pixels) equipped with a 35 mm Nikkor lens (foused at ). The amera alibration solution was omputed within Australis, whih an automatially deteted all the oded targets and ompute the alibration parameters (Table ) aording to the 8-term mathematial model desribed in Setion. The same images were then proessed with ATiPE in order to extrat a set of natural points randomly distributed in the sene (Figure 5b). The suessive estimation of the bundle solution (within Australis) provided all alibration parameters with the amera poses and 3D points (Figure 5 and 5d). The orresponding alibration parameters and their preisions are equal and shown in Table. The projet with targets omprehends 55 3D points (5 irles targets). The estimated theoretial auraies along the x, y and z axis were :83,, :4,9 and :64,5, respetively. The proessing with ATiPE provided for,53 3D natural points (at least 4 images for eah point;,356 points were mathed in 6 or more images). The estimated theoretial auraies along the x, y and z axis were :,, :6,5; :9,4, respetively. This disparity is motivated by the use of different mathing strategies leading to different auray in the image measurements. The measurement of the entre of the targets is performed more preisely than natural points extrated using FBM methods. Indeed, as also stated by Fraser (996), the auray of the omputed objet oordinates depends on the image measurement preision, image sale and geometry as well as the number of exposure. Targets Value Std.dev RMSE (µm).89 (mm) ±.5 x (mm) ±.4 y (mm) -.7 ±.4 k e-5 ±6.5e-7 k e-8 ±3.964e-9 k e- ±5.4357e- p e-6 ±.74e-6 p e-6 ±9.99e-7 ATiPE Value Std.dev RMSE (µm).97 (mm) ±.3 x (mm) -.73 ±. y (mm) -.76 ±. k e -5 ±3.647e -7 k e -8 ±.338e -9 k e - ±3.45e - p e -6 ±6.64e -7 p -5.57e -6 ±6.68e -7 Table. Camera interior parameters estimated with the target-based approah and using ATiPE (targetless) method for a Nikon D7 mounting a 35 mm lens. 338

5 a) b) ) d) Figure 5. The alibration polygon with iwitness/australis targets (a). Tie points extrated by ATiPE using the natural texture of the sene (b). The bundle adjustment results ahieved in Australis using oded target image oordinates () and natural features image oordinates (d). The reovered amera parameters of both approahes are reported in Table. Figure 6 shows another example of the experiments. The amera employed is a Nikon D with a mm Nikkor lens. A set of 3 images was aquired, inluding oded targets to perform an automated amera alibration. The self-alibrating bundle adjustment with and without oded targets ahieved very similar results for the interior parameters (Table ). Targets ATiPE Value Std.dev Value Std.dev RMSE (µm) (mm) x y k.873e -4.65e e -4.5e -6 k e e e e -8 k e -.45e e e - p 7.849e -6.3e e e -6 p -.684e -5.47e e e -6 Table. Results for a Nikon D equipped with a mm Nikkor lens, with and without targets. 4. Auray analysis with independent hek points Figure 6. The sene used for the automated amera alibration with and without oded targets (top). The amera network of the targetless solution with the reovered amera poses and sparse point loud (bottom). The onsistene and auray of the first targetless alibration experiement were verified using a speial testfield omposed of irular targets whih are used as Ground Control Points (GCPs). Their 3D oordinates were measured with a theodolite Leia TS3, using three stations and a triple intersetion to obtain high auray results. The standard deviation of the measured oordinates was ±. mm in x (depth) and ±. mm in y and z. A photogrammetri blok of 6 images was also aquired. All target entres were measured via LSM to obtain sub-pixel preisions. The photogrammetri bundle adjustment was arried out with the two sets of alibration parameters. Both photogrammetri projets were run in free-net and then transformed into the Ground Referene System (GRS) using 5 GCPs. The remaining 6 points were used as independent hek points (ChkP) to evaluate the quality of the estimation proedure. The following quantities were omputed for eah ChkP: 339

6 x = x GRS - x Photo, y = y GRS - y Photo, z = z GRS - z Photo (9) The differenes in both onfigurations are shown in Table 3. It an be noted that the behaviour is quite similar and the standard deviations of the differenes along x, y and z are equivalent. a) b) ) GRS Targets x y z Mean (mm) Std.dev (mm) Max (mm) Min (mm) GRS ATiPE x y z Mean (mm) Std.dev (mm) Max (mm).8.6. Min (mm) Table 3. Comparison between ChkP oordinates measured with a theodolite (GRS) and photogrammetri measurements with and without targets (ATiPE). The behaviour and the residuals are similar for both photogrammetri approahes. Differenes (mm) Differenes (mm) Differenes (mm) GRS - Targets GRS - ATiPE Targets - ATiPE delta x delta y delta z delta x delta y delta z delta x delta y delta z Figure 7. Graphial behaviour of the differenes of the ChkP oordinates in the solution obtained using oded targets (a) and natural features extrated with ATiPE (b). The differenes between the target and targetless approah are shown in (). It is also interesting that the differenes are superior to mm for some points. This is probably due to a residual movement of the targets during the data aquisition phase. Indeed, both referene data and images were aquired at different epohs. All targets are made of paper and probably there was a small deformation of this deformable material. This is also demonstrated by the oherene of both photogrammetri projets (Figure 7). The oordinates of both photogrammetri projets were then ompared. They onfirm the onsistene between these alibration datasets. A graphial visualization of the differenes between the ATiPE proedure (targetless) and the estimation based on targets is shown in Figure Analysis of ovariane and orrelation matries The use of a free-net bundle adjustment for the estimation of the alibration parameters leads to a modifiation of the general form of the least squares problem. In some ases, if the network geometry is not suffiiently robust to inorporate all alibration parameters (basi interior plus the APs), the adjustment an provide highly orrelated values. Therefore, a statistial evaluation of the obtained APs is always reommended (Gruen, 98; Jaobsen, 98; Gruen, 985). This an be arried out by using the estimated ovariane matries and not only with the independent analysis of the standard deviations of eah single unknown (Cox and Hinkley, 976; Kendall, 99; Sahs, 984). In the following, the dataset with targets is used as referene, as it an be assumed as the urrent state of the art for traditional photogrammetri alibrations. In partiular, C T is the 8 8 ovariane matrix of all alibration parameters estimated using targets. The ovariane matrix with the targetless proedure is named C A (A = ATiPE). The aim is to demonstrate that C T and C A are similar, in order to onfirm the onsistene of both alibrations. There exist several riteria for omparing ovariane matries, e.g. different distanes d(c T, C A ) whih depend on the hoie of the model employed. However, it is quite ompliated to understand when d is small, espeially if the estimated values have different measurement units. A possible solution ould be to use the eigenvalues λ i of the ovariane matries, in order to obtain new diagonal matries that an be ompared (Jolliffe, ). Aording to this proedure, the diretions of the prinipal axes of the onfidene ellipsoids are given by the eigenvetors. To hek the equality of the ovariane matries, the Hotelling s test ould also be used: ( C) m / log m / n σ xj j= det χ = () where m is the number of data and n the number of alibration parameters (8 in this ase). For both matries the ratio of the values given by Eq. was estimated, obtaining a large disparity between C T and C A beause of the different number of observations used during the estimation of the photogrammetri bundle solutions. To understand better the results ahieved with both alibration proedures it is possible to use the orrelation matrix R. It is well-known that some alibration parameters are highly orrelated, e.g. the oeffiient k i modelling radial distortion. In addition, there is a projetive oupling between p and p with x and y, respetively. The experimental results provided two orrelation matries (R T, R A ) very similar, where the orrelations between the listed parameter onfigurations are quite strong (>.8), although the targetless proedure seems slightly better (Table 4). 34

7 R T x p y p K K K 3 P P C x p.3 y p K K K P P R A x p y p K K K 3 P P x p. y p K...5 K K P P Table 4. The orrelation matries estimated with targets (top) and ATiPE (bottom). For the remaining parameters, the orrelations are instead orretly redued. A onsideration deserve to be mentioned: in the ase of unorrelated parameters the relationship det(r) = must be verified. Therefore, a simple general riterion to assess the quality of these ovariane matries an be the simple omparison of the determinants: det(r T ) =.3 6 < det(r A ) = 7. 5 This values are quite similar, beause the matries look quite similar. Therefore test the equality of the orrelation strutures, a multi-dimensional statistial analysis should be employed. Lawley s proedure (963) requires the estimation of the following statisti: n n n + 5 χ = m r ij () 6 i= j= i+ where m is the number of data and n the number of alibration parameters (8 in this ase). The appliation of this riterion shows that C A and C T are not equal (the ratio between the χ values is superior to 4), but this is mainly due to the different number of observations between the proedures (e.g. 55 3D points with the target-based method, 7,593 with ATiPE). The estimation of the ratio log(det(r( A ))/log(det(r T )) 3 onfirms the previous results. In summary, the statistial interpretation of the results is quite diffiult beause of the different numbers of input data. The omparison between different sets of alibration parameters using total station measurements is probably a better fator to hek the final quality of the targetless alibration parameters. 5. CONCLUSION This paper has presented a new proedure for amera alibration based on the natural texture of an objet whih has to be properly seleted. The method an also be assumed as the initial step for a omplete 3D reonstrution pipeline of some ategories of objets. It is worth noting that different phases of the reonstrution problem an be now arried out in a fully automated way. The proposed methodology for amera alibration is not based on targets, but it is apable of providing the unknown amera parameters values with the same theoretial auray of the more familiar target-based proedure. It has also been proved that the larger number of tie points extrated for omputing selfalibration gives rise to slightly smaller orrelations among the parameters. But further statistial analyses should be performed. The key-point leading to a suessful alibration is (i) the seletion of a proper objet featuring a good shape and textures and (ii) the aquisition of a set of images whih results in a suitable image blok geometry. For industrial and highly-preise photogrammetri projets, the target-based amera alibration proedure will probably remain the standard solution while for many other 3D modeling appliations, the presented method an be the ideal solution to speed up the entire photogrammetri pipeline, avoid targets and allow on-the-job self-alibration in a preise and reliable way. REFERENCES Albert, J., Maas, H.G., Shade, A. and Shwarz, W.,. Pilot studies on photogrammetri bridge deformation measurement. Proeedings of the nd IAG Symposium on Geodesy for Geotehnial and Strutural Engineering: Amiri Parian, J., Gruen, A. and Cozzani, A., 6. Highly aurate photogrammetri measurements of the Plank Telesope refletors. 3rd Aerospae Testing Seminar (ATS), Manhattan Beah, California, USA, - Otober. Arya, S., Mount, D.M., Netenyahu, N.S., Silverman, R. and Wu, A.Y., 998. An optimal algorithm for approximate nearest neighbor searhing fixed dimensions. Journal of the ACM, 45(6): Barazzetti, L. and Saioni, M., 9. Crak measurement: development, testing and appliation of an image-based algorithm. ISPRS Journal of Photogrammetry and Remote Sensing, 64: Barazzetti, L. and Saioni, M.,. Development and implementation of image-based algorithms for measurement of deformations in material testing. Sensors: Barazzetti, L., Remondino, F. and Saioni, M., a. Extration of aurate tie points for automated pose estimation of lose-range bloks. Int. Arhives of Photogrammetry, Remote Sensing and Spatial Information Sienes, Vol. 38(3A), 6 pages. Barazzetti, L., Remondino, F. and Saioni, M., b. Orientation and 3D modelling from markerless terrestrial images: ombining auray with automation. Photogrammetri Reord, 5(3), pp Barazzetti, L.,. Automati Tie Point Extration from Markerless Image Bloks in Close-range Photogrammetry. PhD Thesis, Politenio di Milano, Milan, 55 pages. Bay, H., Ess, A., Tuytelaars, T. and van Gool, L., 8. Speeded-up robust features (SURF). Computer Vision and Image Understanding, (3):

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