Simultaneous image orientation in GRASS

Transcription

1 Simultaneous image orientation in GRASS Alessandro BERGAMINI, Alfonso VITTI, Paolo ATELLI Dipartimento di Ingegneria Civile e Ambientale, Università degli Studi di Trento, via Mesiano 77, 38 Trento, tel , fa , paolo.zatelli@ing.unitn.it Abstrat The urrent proedure for the reation of othophotos in GRASS allows the orientation and the retifiation of a single image at a time. This approah an be troublesome when the final produt is a mosai of orthophotos, sine the orientations of the single images are independent and thus usuall non oherent. Therefore inonsistenies an be present between parts of the mosai oming from different images, in partiular in the overlapping areas of the orthophotos. A new proedure has been set up to partiall solve this problem b the simultaneous orientation of all the images to be retified and pathed into the mosai. The proedure uses a new program that performs bundle blok adjustment and is full ompatible with GRASS orthoretifiation proedure. Tests show a signifiant better performane of the new proedure with respet to the traditional one.. Introdution Orthophotos are images of objets in an orthogonal projetion rather than a entral projetion, as usual images are. Unlike ommon images, orthophotos are ompatible with artograph and the an be superimposed to it. Orthophotos are used when speed or/and ost are ritial parameters for artograph prodution, as it happens in the ase of alamit or in the poor regions of the world. The retifiation of aerial images is a routine proedure for artographers and it is usuall performed digitall, with the possibilit of writing epliit equations for the transformation. Nowadas, the most ommon environment for the elaboration of artographi data is a Geographi Information Sstem, therefore the more advaned GIS are able to perform image retifiation, usuall with some restritions as to the ompleit of the terrain surfae and to the attitude of the amera beause this allows the adoption of a simplified formulation, thus simpler and faster programs. Most of the available sstems for image retifiation an operate on one image at a time, however in pratial appliations more of one image is needed to over the investigated area: it is therefore required the union of different orthophotos. This proedure is not tpiall simple as it is for ommon artograph, sine the images to be joined differ from a geometri and a radiometri point of view. The aim of this work is to solve in part the problem of geometri differenes between adjaent orthophotos for the reation of mosais from geometriall oherent images.. Orthophotos Normal images are entral projetions of a 3D objet into a D plane (Fig. ). These tpes of projetions result in images where the sale hanges from point to point: this behavior is inompatible with artograph, where the sale is onstant on the whole map.

2 The proess of transforming a entral projetion into an orthogonal projetion is alled retifiation. It is usuall performed analtiall using the ollinearit equations r ξ r r η r 3 3 ( P) r( P) r3( P) ( P) r3( P) r33( P) ( P) r( P) r3( P) ( ) r ( ) r ( ) P 3 P 33 P ξ η () whih epress the ollinearit of the point in the objet spae, the amera prinipal point and the point on the image, relating the image oordinates ξ and η to the foal length of the amera, the rotation matri omponents r ij, the oordinates of the amera prinipal point (,, ), the oordinates of the point in the objet spae ( P, P, P ), and the internal orientation parameters ξ and η. Figure Central projetion of the 3D spae into a D plane. Collinearit equations an be used for different tasks in photogrammetr, depending on whih parameters are known and whih are unknown. In the ase of image retifiation the foal length of the amera, the rotation matri omponents r ij, the oordinates of the amera prinipal point (,, ), and the internal orientation parameters ξ and η are known, and for the enter of eah piel of the orthophoto of oordinates ( P, P, P ) in the objet spae the orresponding image point is loated on the image b its oordinates ξ and η. The olor (or gra tone) of the point on the image is assigned to the piel on the orthophoto. In general the oordinates ξ and η do not orrespond to a piel enter on the original image, therefore programs usuall operate an interpolation to selet the proper olor; the most ommon interpolation methods are the bilinear or the nearest neighbors interpolation, whih provide good results with low omputational osts. An eample of image retifiation is given in figures to 4, showing the original image (fig. ) the orresponding orthophoto (fig. 3) and its 3D view (fig. 4).

3 Figure Aerial image of the town of Trento (ourtes of Provinia Autonoma di Trento). Figure 3 Orthophoto from the image of fig.. Figure 4 3D view of the orthophoto of fig. 3. 3

4 3. Orthophoto mosaiing For pratial uses most of the times a single image is not suffiient sine the interesting area is larger or beause it falls on the boundar of the image: it is therefore neessar to join more orthophotos into a mosai. Orthophoto joining an lead to inonsistent mosais due to the lak of oheren from the geometri and radiometri points of views between different images. Geometri inonsisten (fig. 5) is mostl due to the approimations operated b retifiation algorithms to approimations in the determination of the orientation parameters and b the fat that the orientation parameters of different images are evaluated using different ground ontrol points, whose oordinates an have ver different preisions. Figure 5 Geometri inonsisten between two adjaent orthophotos. Radiometri inonsisten (fig. 6) is aused b non uniform film sensibilit, different attitudes during the image taking and different environmental onditions. Figure 6 Radiometri inonsisten between two adjaent orthophotos. Radiometri inonsisten an be redued b modifing the olor histogram of the images to make them math so that the transition between one image to another is unnotieable. The redution of geometri inonsisten an be obtained b implementing an algorithm that uses the ollinearit equations without approimations, but this leads to high omputational osts, while the orientation inonsisten an be redued b the simultaneous evaluation of the orientation parameters of all the images used in the mosai. This paper presents the implementation of a proedure for the simultaneous evaluation of the orientation parameters of images using the bundle blok adjustment approah. The proedure is integrated in the usual image orthoretifiation proedure of the GRASS GIS. 4. Bundle blok adjustment In the bundle blok adjustment approah the sstem of equations () is solved in one step for all the images and all the point involved. Usuall more ground ontrol points oordinates than those needed to solve a sstem of equations like () are provided and a least square estimation is arried out. Equations () are not linear and must be linearized. Moreover, approimate values for the unknown parameters must be provided. 4

5 5 An original proedure for the determination of the approimate values of the orientation parameters has been implemented. This proedure is based on the similarit of the triangles in fig. 7. Figure 7 Triangles used for the determination of the approimate orientation parameters. For eah point ouple it is possible to write the following relations H H H H setting These lead to ( ) ( )

6 These equations are used to evaluate the oordinates of the amera prinipal point (,, ), while the attitude angles are all set to zero sine this is reasonable for most of the images. This equations sstem shows two singularities for aligned points and for points lose to the origin of the image referene sstem. Infat, for aligned points the terms - and/or - vanish therefore and/or tend to infinite. For points lose to the origin of the image referene sstem the term vanishes, therefore tends to infinite. Using the law of the propagation of the errors it is possible to estimate how the alignment of the points affets the approimation of the oordinates: for eample if - - m then σ - m, i.e. σ - m, while if - - m then σ 4 8 m, i.e. σ 4 m. For points lose to the image referene sstem s origin, if - m then σ m, i.e. σ m, while if - m then σ 4 m, i.e. σ m. 5. Implementation The bundle blok adjustment proedure has been implemented in a program that is ompatible with GRASS, in the sense that its output is the same of the i.points GRASS module and it an be used as input for the i.orthophoto module. The program reads from an auiliar file (FOTO_PNTS.dat) the maimum number of images and points used. Image oordinates are read from a file (C_OMOLOG.dat) that arries a reord for eah point, indiating the number of the point, the indees of the images the point is visible on and its oordinates on eah image. Ground oordinates are read from (INPUT.dat) along with the foal length of the amera and the orientation parameters. To eah parameter in this file a flag is assoiated, indiating if the parameter is onstrained, i.e. its values is known and not to be evaluated: it is possible in this wa to pass to the program known (onstrained) or approimate (not onstrained) values. 6. Tests Tests have been arried out to hek if the simultaneous image orientation gives more oherent orthophotos and in whih situation the gain is more relevant. As referene situations against whih the results are mathed, two approahes to image orientation are used: in the first ase eah image is oriented as to reate a single orthophoto without taking into aount the sequent pathing, following the standard guidelines for the hoie of the ground ontrol points, i.e. seleting points in the peripheral areas of the image. The seond approah uses the same ground ontrol points (tie points) for different images in the overlapping areas (fig. 8): this should give a better onsisten of the orthophoto to be pathed. Figure 8 Tie points for overlapping images. The tests have been arried out for aerial images of a part the Adige valle around the it of Trento. Sine the ritial fator for image retifiation is slope and its variation, a map of the slope has been reated using the r.slope.aspet GRASS module. 6

7 Figure 9 Slope map [degrees] for the Adige valle near Trento, vetor roads and settlements have been superimposed. Four points showing different situations with respet to slope have been seleted as test points (figures -): the first one is loated on a ver slanting slope, the seond one on a variation of the slope angle, the third one on the bottom of the valle with no slope, the fourth and last one on a mild slanting area on the east side of the Adige valle. Figure Test points on the seam line between two orthophotos. 7

8 Figure Test points on 3D view. Figure Test points on the slope map. For eah test point the distane of two orresponding points (suh as road or building sides) in two different orthophotos on the seam line has been measured for the tree approahes to the evaluation of the orientation parameters. The results are shown in table, where with the red olor the worst results are highlighted, while the green olor indiates the best results. Mean shift [m] Traditional approah Tie points approah Simultaneous orientation Test Area (ver slanting slope) Test Area (variation of slope angle) Test Area 3 (plane plane).3.3. Test Area 4 (mild slope) Table Distane between orresponding points on the seam line between two orthophotos. 8

9 The resolution of the orthophotos is of one meter, therefore shifts of this order of magnitude reah the intrinsi preision limit of the measurement on the images. In the first three test areas the simultaneous orientation of the images provides the best results, while for the fourth test area the naïve approah apparentl performs best: this is probabl due to the approimations of the retifiation algorithm, whih are somehow ompensated b the inonsisten of the orientation parameters. The use of tie points an lead to good results onl when the overlapping area is relevant. 7. Conlusions The new proedure, that uses a bundle blok adjustment approah for the simultaneous orientation of the images to be pathed after their retifiation, allows a signifiant advane with regard to the ontinuit between adjaent orthophots. While the tests of the previous paragraph have been arried out with two images, the proedure is read for the use with an arbitrar number of images, with the limit set b the hardware apabilit. 8. Bibliograph Kraus K., 994, Fotogrammetria, vol. Teoria ed appliazioni on il ontributo di Peter Waldhaussl, traduzione ed ampliamenti di Sergio Dequal, Libreria Universitaria Leprotto e Bella Torino. Kraus K., 997, Photogrammetr, vol. Advaned Method and Appliations with ontributions b J. Jansa and H. Kager, Ümmler/Bonn. GRASS 5 programmer s manual, 9