PHOTOINTERPRETATION AND SMALL SCALE STEREOPLOTTING WITH DIGITALLY RECTIFIED PHOTOGRAPHS WITH GEOMETRICAL CONSTRAINTS 1

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1 PHOTOINTERPRETATION AND SMALL SALE STEREOPLOTTING WITH DIGITALL RETIFIED PHOTOGRAPHS WITH GEOMETRIAL ONSTRAINTS Gabriele FANGI, Gianluca GAGLIARDINI, Eva Savina MALINVERNI Universit of Ancona, via Brecce Bianche, 63 Ancona, Ital Phone: , KE WORDS: Architectural hotogrammetr, self-calibration, rectification, stereosco, vanishing oints ABSTRAT It is well know that it is ossible to use the vanishing oint geometr to assess the orientation arameters of the hotograhic image Here we roose a numerical or grahical rocedure to estimate such arameters, assuming that in the imaged object are resent lanar surfaces, straight-line edges, and right angles In addition, b means of the same estimated arameters, it is ossible to roject the same image onto a selected lane sa to rectif the image The advantages are that non-metric images, taken from archives or books also, rovided a good geometr and ualit, are suitable for the task From one side the role of the classical line hotogrammetr is taken more and more over b laser scanning, and on the other side, this simlified rocedure enables the researcher to use hotogrammetric techniues for stereosco and interretation, thematic maing, research The convergent nonstereoscoic images rectified with digital hotogrammetric techniues, are then made suitable for stereosco In fact the rectification corrects for tilt dislacement and not for relief dislacement, but it is just relief dislacement that enables stereosco Some eamles of stereolotting and hoto-interretation with digitall rectified hotograhs are shown INTRODUTION The ossibilit to use non-metric images is normall linked to the availabilit of the control information in the imaged object, usuall control oints to be inut in a bundle adjustment rocedure or DLT There is also the ossibilit to use a-riori knowledge of the geometr of the object, such as arallelism of lines and erendicularit of lanes (Williamston & Brill,, 987,3, 988, Ethrog, 8,984, Krauss, 5, 997, Van Heuvel, 7, 999) In this wa the stud and the safeguard of the monuments can be heled b the biggest eisting archive available to the researcher, the books We roose an aroach that has the advantage to be articularl simle and to be erformed also in a grahical wa b eole not articularl eert in comlicated comutations It uses the vanishing oints geometr We assume the geometr of the ideal inhole camera So far, the distortion is neglected With the same estimated arameters it is ossible to rectif the image and roduce a stereo-coule from convergent non-stereoscoic hotograhs Man comuters have alread main-board and grahical card suitable for stereosco (stereo-read) In addition, the digital workstations do not have a device such as dove-rism to rotate the otical field and to imrove stereosco; therefore a good stereocaabilit is more imortant than before THE VANISHING POINT GEOMETR In an image the arallel object lines converge in oints called Vanishing Points There are man methods for the detection of the Vanishing Points in the images A good review is given b (VHeuvel, 6, 998), together with a roosal for a new aroach, based on strong statistical base Here the detection of the vanishing oints will not be discussed Persective transformation wi th one vanishing oint The transformation matri, comosed b a ersective followed b a rojection onto Z lane, is written: [ ] T () l m n l m In the case that l m ( or we are not interested in the translation l, m ), an arbitrar oint P with homogeneous coordinates [,,,] is transformed or rojected, in [,,,] [,,,()] [,,, ] () When we have the image and we want the estimate the value of the arameter, we can use the vanishing oint in direction of ais that is transformed: The resent work has been financed b ofin, Italian Ministr for Scientific Research

[ ] [ ] [ ] [ ] / (3) / (4) Once the image co-ordinate of the vanishing oint is determined, in a reference sstem where, it is ossible to rectif the image with ens(), b means of the arameter In fact

images taken from books of architecture, where normall the lines, vertical in the realit, last vertical in the image Fig One Vanishing Point Image Figs, 3 - Florence SMiniato al monte The original

2 [ ] [ ] [ ] [ ] / (3) / (4) Once the image co-ordinate of the vanishing oint is determined, in a reference sstem where, it is ossible to rectif the image with ens(), b means of the arameter In fact the inverse transformation of () is obtained from ens () and isolating the and (5) This rocedure is useful when we want to rectif an image with one vanishing oint onl The case is ver freuent with the images taken from books of architecture, where normall the lines, vertical in the realit, last vertical in the image Fig One Vanishing Point Image Figs, 3 - Florence SMiniato al monte The original one VP image and the rectified one The ratio base/height deends on the translation m, that can not be determined Therefore the rectified image has two unknown different scale factor Persective transformation with two vanishing oints The transformation in this case is: [ ] T (6) An arbitrar oint P[,,,] is then transformed in [,,,] [,,,()] [,,, ] (7) The two vanishing oints of the and aes, are rojected:

/ / (8) from where we get: / / (9) Determinate the image co-ordinates image and of the two vanishing oint, and arameters are solved The inverse transformation is obtained b develoing (7) and ordering

Figs 5, 6 - Assisi Basilica of S Francesco Original -two VP- image of the façade - The rectified image, modified to fit the rose window in a circle 3 PERSPETIVE TRANSFORMATION WITH THREE VANISHING

3 / / (8) from where we get: / / (9) Determinate the image co-ordinates image and of the two vanishing oint, and arameters are solved The inverse transformation is obtained b develoing (7) and ordering with resect to and ) ( ) ( () Fig 4 Two Vanishing oints image This rocedure is useful when we want to rectif an image with two vanishing oints onl, ug ens (7 and (), in a reference sstem where and Figs 5, 6 - Assisi Basilica of S Francesco Original -two VP- image of the façade - The rectified image, modified to fit the rose window in a circle 3 PERSPETIVE TRANSFORMATION WITH THREE VANISHING POINTS Let a reference sstem with horiontal and Z-aes, and vertical -ais be fied The oint of view M is laced along Z-ais at a distance Zc from the origin (fig ) The arallelogram ABDEFGH is then rotated, translated and finall rojected from M in a lane arallel to lane The resulting image is shown in fig ); it is ossible to detect three vanishing oints, according to the three orthogonal directions This is ver often the case of images in architecture Of course in a normal icture there are as man VP as man sets of arallel lines, but we restrict onl to the case of the rectangular solid in fig A general conform transformation in 3d sace can be erformed b the concatenation of the three rotations tilt k, aimuth ϕ, and swing ϑ about the aes of the sstem and three translations m, n, along three rincial directions, (Roger, Adams,, 98) [T ] [R Z ] [R ] [R ][T Z ] n m l ϑ ϑ ϑ ϑ ϕ ϕ ϕ ϕ κ κ κ κ () When in the image beond the solid ABDEFGH other arallelograms are resent also, whose main lanes are not arallel to those of the first one, we select the most suitable, that is the one with the longest ossible lines er VP detection In this case there are more than three VP Suose that k To let K be, first the three vanishing oints are found in the original image Then the whole image is rotated to let the of the two horiontal VP and VP3 be eual, so that k The line connecting VP and VP3 is the so-called

4 True Horiontal Line, THL Note that in the revious case,- two VP oint, VP and VP -, such k rotation cannot be determined and the directions of and ais are arbitrar This is the reason wh there are two different unknown scale factor in the two directions A ersective transformation [T] is given b the concatenation of the revious transformation [T ] followed b a ersective rojection [P r ] from the oint of view M ϕ [T] [T ][P r ] ϕ l ϕ ϑ ϑ ϕ ϑ m ϕ ϑ ϑ ϕϑ n / ϕ ϕ l ϕ ϑ ϑ ϕ ϑ m ϕϑ ϑ ϕϑ n () Fig 8 - The arallelogram after the transformation and rojection on Z lane For the determination of the values of ϑ, ϕ, Zc the three vanishing oints can be used We assume that the are the vanishing oints of the reference aes The ersective transformation of the three VP is then VP VF [ ] T VF VF VF3 VF 3 The image co-ordinates [ VP, VP,,] can be found, manuall or automaticall, b intersection of the straight lines, or b man other methods (6, Van Heuvel, 999) In this aer the image co-ordinates are reduced to the sstem with origin in the isocentre The following relationshis are then derived: We get from there: ϕ ϕ ϑ ϕ ϑ ϕ ϑ ϑ ϑ ϕ ϕ ϑ ϕ ϑ ϕ ϑ 3 3 cot gϕ ϑ tgϑ cot gϑ tgϕ ϑ tg ϑ 3 3 (3) (4) Z - (5)

5 ϑ a tan (6) ϕ a tan (7) ϑ 3 ϑ ϕ a tan (8) ϑ (9) 3 For the comutation of ϑ, ϕ, Z the VP image co-ordinates have been utilised; the arameters are invariant with resect to l, m, n The Zc arameter can be regarded as the rincial distance The isocentre, ie the intersection on the three altitudes of the triangle formed b the three VP, is then the rincial oint, sa the origin of the aes In fact the object vertical lines are not vertical an more in the rojection lane, ce the ass through the vertical VP The onl object vertical line that remains vertical after the rojection is the -ais, erendicular to the THL horiontal line VP-VP3 For smmetr the same holds for the other two altitudes in the triangle of the three vanishing oints Then the intersection of the three altitudes, the isocentre, is the intersection of the otical ais with the rojection lane, that is, in the erfect inhole camera model, the rincial oint Note that we used onl image co-ordinates and that the onl control information from the object is the erendicularit of the three main object lains and the horiontalit and verticalit of lines The isocentre and the rincial distance Zc must be invariant with resect to the arbitrar selected solid ABDEFGH If we selected another solid, the vanishing oints VP and VP would change, but THL, Z and isocentre, would remain the same The angles ϑ, ϕ would be different Note that a grahical-numerical solution is also ossible: - imort the image in a AD - draw the intersecting lines to find the vanishing oints, VP, VP, VP3, - rotate the image to level the horiontal line VP VP3, - draw the altitudes of the VP triangle, - find the isocentre O, and reduce to it the image co-ordinates of the VP, - comute ϑ, ϕ, Z b (5), (6), (7), (8), (9) A ver common case is when the rojection lane is arallel to the vertical line In this case the rotation angle ϑ, the vertical VP goes to infinit, the isocentre lies in the HL (horiontal line VP - VP3), the euations (4) reduce to one onl with the remaining two unknowns Zc and ϕ The rocedure then fails This is ver often the case for images of buildings taken from books, ce the have been roduced with still life cameras that kee the negative lan vertical and shift the lens So onl ens (4) and (5) can be used, relative to one VP case Finall for rectified images onl one VP is finite, the remaining two are at infinit The VP triangle reduces to one oint onl that coincides with the isocentre and the finite VP 3 The rectification with three VP image Once ϑ, ϕ, Zc, are comuted, it is not ossible to al the inverse transformation because in the rojection on the lane there is a loss of information Nevertheless the lane inverse transformation is ossible, assuming as known one of the three object coordinates, or, that is the same, the euation of the new rojection lane The rojection onto a co-ordinate lane is then a rectification In fig, the rectified sides of the arallelogram, the rectangles ABD, or BEF, or DFG Having set: a ϕ ; a ϕϑ ; a 3 (ϕϑ)/zc, a 4 ; a 5 ϑ; () a 6 - (ϑ)/zc; a 7 ϕ; a 8 - ϕ ϑ ; a 9 -( ϕ ϑ)/zc the rojection of an arbitrar oint from the 3D sace onto Z lane is: a a [ ] [ U V W T] [( a a a ); ( a a a ); ; ( a a a ); ] a7 a a a8 a3 a a9 The normalisation is U/T ; V/T, that is to divide the first two co-ordinates b the third one: a a4 a7 a3 a6 a9 a a5 a8 a3 a6 a9 Note that ens () are nothing but the homograhic transformations We reorder and isolate and as unknowns: ( a a3 ) ( a4 a6 ) ( a7 a9 ) (3) ( a a3) ( a5 a6 ) ( a8 a9) hoog for an arbitrar value, and are then derived The same holds when an euation of a lane is added Note that the inverse transformation here is intended as rectification onl, ie the rojection into a lane Zconst When Z varies, so does the () ()

scale The final scale of the rectified image is then unknown In fig 8 the three rectified rectangles have a side in common two b two, letting onl a common scale factor to be established 4 MUNIIPALIT

6 scale The final scale of the rectified image is then unknown In fig 8 the three rectified rectangles have a side in common two b two, letting onl a common scale factor to be established 4 MUNIIPALIT HALL - PALAZZO DEL POPOLO ANONA We show, as test, the surve of the Municialit Hall in Ancona, Ital (fig3) First, we made a traditional hotogrammetric surve We used a calibrated camera Fuji GSW69 II, (late format 69 cm ) and a calibrated digital camera Fuji Finei 49 (resolution 84 iel) (Fangi, 9, 999) We determine 3 control oints included the camera station oints with centimetre accurac Then we al the VP rocedure to estimate the interior orientation arameters In table the comarison between the interior orientation arameters from the calibrations and the ones from the VP rocedure are shown Table - alibration Vs Vanishing Points rocedure ( iel ) alibrati VP Differences on Procedure Fuji GSW % No dist corr % % Fuji GSW % Dist corr % % 3 Rectified image % % 4 Fuji Finei49 No distcorr 5 Fuji Finei49 No distcorr 6 Fuji Finei49 Dist corr % % % % % % % % % % In figs and the rectified images for the main facade and the lateral façade are shown These are derived from the same image Although the lateral facade doesn't aear ver attractive, the transformation is geometricall corrected In the rectified images the rincial oint coincides with the onl finite vanishing oint: the self-calibration rincial oint has coordinates -; 359 while the transformed VP has co-ordinates -4; 378, and the difference is iel in and 9 in From the rectified image the new rincial distance cannot be derived from ens (5) or (9), ce the image coordinates for VP are null The differences of the orientation arameters range from 5,% to 64% The same test has been erformed without lens distortion correction and after the correction The distortion curve was obviousl evaluated in advance (Fangi,, 999) No significant imrovement seems to derive from the correction of the lens distortion 8% 6% 4% % % -% -4% -6% Fig 9 - alibration Vs Vanishing Points rocedure Differences in ercentage for the orientation arameters O Fig Municialit Hall in Ancona The original image ad the grahical solution

Fig The rectified main facade Fig The rectified lateral facade ONLUSIONS The resent aroach has some advantages First of all, it is simle, and a numerical-grahical solution is ossible, allowing not

non-stereoscoic images The longer the lines of the three main directions, the better the determination of the VP On the other side not high accurac can be eected Some assumtions on the objects are

7 Fig The rectified main facade Fig The rectified lateral facade ONLUSIONS The resent aroach has some advantages First of all, it is simle, and a numerical-grahical solution is ossible, allowing not ver eert eole to calibrate non-metric images No measurement on the object is needed Then last but not least, with the same arameters, it is ossible to rectif the images, enabling the stereosco from non-stereoscoic images The longer the lines of the three main directions, the better the determination of the VP On the other side not high accurac can be eected Some assumtions on the objects are needed, such as erendicularit of the main lanes, and the resence of the horiontal and vertical lines, that often are not comletel fulfilled, mainl for ancient buildings Another ossible shortcoming is the necessit of the resence in the image of three grous of lines, intersecting in three vanishing oints, which is again not ver often the case In fact, unfortunatel in the books of architecture almost an icture is made with still life cameras were the negative lane is ket vertical; the vertical vanishing oint goes to infinit, making the rocedure fail Anhow the described rocedure ermits to rectif the images, allowing stereosco from convergent non-stereoscoic imager While we are asking whether or not laser scanning will take the lace of the traditional line hotogrammetr, the simle and efficient tool of stereosco and hoto-interretation will last REFERENES DFRogers, J A Adams, - Mathematical Elements for omuter Grahics, Mc Graw Hill, 99 JR Williamson, M H Brill - Three-Dimensional Reconstruction from Two-Point Persective Imager - Photogrammetric Engineering and Remote Seng Vol 53, n3, (987), JR Williamson, M H Brill - Three-Dimensional Reconstruction from Three-Point Persective Imager - Photogrammetric Engineering and Remote Seng Vol 53, n, (987), M Straforini, oelho, M amani - A fast and recise method to etract vanishing oints - 56 / SPIE Vol 395 lose- Range Photogrammetr Meets Machine Vision (99) 5 KKrauss - Photogrammetr - Vol - Advanced Methods and Alications, Ummler, Bonn (997) 6 FVan den Heuvel - Vanishing oint detection for architectural hotogrammetr - ISPRS Archives, Vol II, art (999) 7 FVan den Heuvel - Estimation of interior orientation arameters from constraints on line measurement in a gle image ISPRS Archives, vol II art 5W, Thessaloniki, Greece Jul (999) 8 UEthrog Non- metric camera calibration and hoto orientation ug arallel and erendicular lines of the hotograhed objects, Photogrammetria, 39 (984), 3-

8 9 Fangi, G, Nardinocchi, (999) The Grid Method, A Simle Procedure For The Determination Of The Lens Radial Distortion ISPRS Archives VI WG III Mariano unietti Memorial Meeting Parma Februar 5-9 vol II art 6W7 5-9, g 9-35 Fangi G (999) - ontrol Directions for the alibration of Terrestrial Non-Metric ameras ISPRS - ommission VI, WGIII, ISPRS Archives vol II art 6W7 - ommission VI, WGIII, Bandung, g 4-7

Image Formation. 2. Camera Geometry. Focal Length, Field Of View. Pinhole Camera Model. Computer Vision. Zoltan Kato

Image Formation. 2. Camera Geometry. Focal Length, Field Of View. Pinhole Camera Model. Computer Vision. Zoltan Kato Image Formation 2. amera Geometr omuter Vision oltan Kato htt://www.in.u-seged.hu/~kato seged.hu/~kato/ 3D Scene Surace Light (Energ) Source inhole Lens Imaging lane World Otics Sensor Signal amera: Sec