Active Vision Robot Head. Jorge Batista, Jorge Dias, Helder Araujo, A. T. Almeida

Transcription

1 The ISR Multi-Degrees-of-Freedom Ative Vision Robot Head Jorge Batista, Jorge Dias, Helder Araujo, A. T. Almeida Institute of Systems and Robotis (ISR), and Eletrial Engineering Department, University of Coimbra, 3000 Coimbra - PORTUGAL; phone: /34884 ; fax: ; batista@merurio.u.pt Abstrat - Experiments in ative vision require having the ability to manipulate the visual parameters. The entral issue in develloping a Multi-Degrees-of-Freedom (MDOF) Ative Vision Robot Head is the design strategy of the system. Bringing all the issues of suh a system and their solutions together and build a head-eye system with reasonable performane vs. ost is an engineering problem. This paper presents the main aspets of the ISR MDOF ative vision system, design, performane, ontrol and the arhiteture of the all system, inluding mehanial and optial degrees of freedom. To be able to eetively use multi degree of freedom (MDOF) amera systems we need to know how variations in the amera's ontrol parameters are going to ause hanges in the produed images. For this we need to have good mathematial models desribing the relationships between the ontrol parameters and the parameters of the resulting images, i.e., we need to alibrate the system. The alibration of the system inludes two parts: the amera alibration problem, i.e., the alibration of the intrinsi and extrinsi parameters of the amera, and the so-alled kinemati alibration to alibrate relationships (rotation and translation) between dierent systems. In this paper only the amera alibration problem is addressed. A method for omputing the amera parameters by traking features in the image when the amera undergoes pure rotation is used. Keywords - Ative Vision, Robot Heads, Systems Arhitetures, Ative Calibration 1. Introdution Experiments in ative vision requires the ability to manipulate the visual parameters. This ability and assoiated issues form the subjet of this paper. The entral issue in developing a Multi-Degrees-of- Freedom (MDOF) Ative Vision Robot Head is the design strategy of the system. This problem in our work was formulated as : "how should a head-eye system be designed, what are the design riteria, how and in aordane with what strategy should the head be designed and ontrolled, what kind of degrees of freedom must be inluded?". The design of a MDOF head-eye system for ative vision is dependent on what we put into this notion. First of all, an ative vision system is not just an optomehanial devie feeding a omputer and arrying out the ommands from the omputer. The degree of integration is ruial for suh a system, and of ourse the issue of real-time proessing and ontrol. These fators determine the behaviour one an obtain. The more elaborately the visual system reats to the surrounding environment, the more evolved the primary tasks will be. The nature of the visual proess we want to integrate will be related to the arhiteture hosen. One important aspet in the designing stage of these roboti systems is the performane they should aomplish. The analisys of some harateristis of the human ative visual system an be usefull for determining performane requirements for veloity and aeleration of a mehanial devie that intend to simulate the human visual system behaviour. Muh work has been done in develloping vision systems to study how these and other features of the visual system are used to failitate pereption (see [7] for an overview). One of the earliest ative vision systems was built by Krotkov et al. [23] at the University of Pennsylvania and the system inluded two ameras with omputer ontrolled motorized lenses, pan and tilt rotation of both ameras, two translational degrees of freedom and oupled symmetri vergene. Many other researhers have assembled ommerial motion-ontrol omponents suh as rotational and translational stages, providing small systems with good repeatability, high-speed motions, but with some restritions in terms of the degrees of freedom available [21;26]. In the late of the eighties, Poggio et al. [22] develloped at the MIT a vision system where two ameras with motorized lenses are rigidly attahed to a mobile platform, and the amera movement is ahieved indiretly by pivoting a front surfae mirror mounted in front of eah amera. At the University of Rohester and Harvard University, binoular ative vision systems have also been develloped. The Rohester ative vision system [24] was mounted on a six-degrees-of-freedom robot arm and it has independent vergene axes and oupled tilt movement for both ameras. No motorized lenses has been used. The Harvard system [25] was mounted on a mobile platform and the head itself performes pan, tilt and anti-symmetri vergene motions to ontrol the orientation of the ameras, and fous and aperture ontrol for aomodation of the optial system. The Yorik head developed at the Oxford University [28] as well the Trilops develloped at the NIST [27] are based on the same mehanial struture, inluding pan, tilt and independent vergene, being the Yorik equipped with independent amera tilt movement, and the Trilops equipped with a third low resolution amera loated at the nek rotation enter. Both of these systems presents remarkable performanes in terms of speed and auray. The KTH head developed at the Royal Institute of Tehnology in Sweden [10] was one of the rst systems ompletely motivated by biologial reasons, and it inludes 13 degrees of freedom, with two mehanial degrees of freedom for eah of the two eyes, pan and tilt for the nek, baseline ontrol, and three optial degrees of freedom for eah of the eyes. One interesting feature of this system is the optial enter adjustment degree of freedom that allow the translation of the eye (amera and lens) in order to ompensate the drift

2 of the optial enter when fous and zoom movements are performed. This degree of freedom keeps the optial enter near the vergene rotation enter, despite hanges in optial parameters. The ISR MDOF ative vision robot head is probably the head that urrently has more degrees of freedom. In addition to the ommon degrees of freedom for amera heads (pan, tilt and independent vergene for eah of the eyes), this head inludes the swing movement of the head nek, baseline ontrol, ylotorsion of the lenses and the ability of adjusting the optial enter of the lenses. The mehanial struture of this head is quite similar to the KTH head struture, and just like the KTH head, biologial reasons played the main role in the design strategy. In spite of all the performanes and degrees of freedom of the ative vision system, to be able to eetively use these systems we need to know how variations in the amera's ontrol parameters are going to ause hanges in the produed images. For this we need to have good mathematial models desribing the relationships between the ontrol parameters and the parameters of the resulting images, i.e., we need to alibrate the system. Reently, a lot of emphasis has been plaed on algorithms that do not require any amera alibration and on amera alibration tehniques that allows the amera to alibrate itself as it moves in an unstrutured world. \Eyes in humans and other animals do not need any artiial assistane for alibration". The answer to the above observation ames with the fat that eye movements simplify the alibration problem. Methods for omputing the amera parameters by traking features in the image, without using speial patterns for alibration, have been developed by Faugeras [19], Hartley [16], Dron [11], MLauhlan [14], Brady [5], Stein [6] and Basu [2]. We based our approah on the use of feature orrespondenes from a set of images where the amera has undergone pure rotation. The loser the features are loated to the amera the more important it is that the amera does not undergo any translation during the rotation. A method to ensure that the axis of rotation passes lose to the enter of projetion (front nodal point in a thik lens model) is presented. An important aspet for the MDOF optial systems alibration is the fat that the parameters are hanging from time to time, whih requires a real-time alibration of the parameters or a pre-alibration of these parameters to build up a look-up-table. To be able to adjust the intrinsi parameters in real-time, we modelize the underlying behaviour of the amera for a large group of dierent setups, hanging the intrinsi parameters on these setups. We use bivariate ubi polynomials to model the relationships between the amera's ontrol parameters and the parameters of the resulting images, suh has image magniation, fous distane, optial enter adjustment, et.. The alibration involves performing a least square t of the model to olleted data to determine the oeients of best t for the bivariate polynomials. For the extrinsi parameters (pose estimation of the amera), and sine the movements of the head-eye system are ontrolled, we know how muh it has been moved relatively to some initial position. With this proedure, the alibration of the extrinsi parameters must only be done at the initial position, and real-time alibration of the extrinsi pa- Eye Pan/Tilt Nek Pan Nek Tilt Range of Motion up?60 down Peak Aeleration =s 2 Peak Veloity 600 =s Interoular distane 64:0mm Foveal-Peripheral resolution ratio 10 : 1 Table 1. Human ative visual system harateristis rameters an be performed. This paper is divided in two major parts: rst we are going to desribe all the aspets of the ISR MDOF ative vision system, namely the design stategy, performane, ontrol and system arhiteture, and in the seond part we will desribe the optial alibration of this system taking advantage of the ontroled movements that an be done with this system. 2. The ISR-Coimbra MDOF Ative Vision Head Ative vision systems are often modeled on attributes of the human visual system sine this is the most well-studied visual system. The human oulomotor is one of the best known funtions of our brain. Two attributes of the human vision system, oular motion and foveal-peripheral vision, are essential to human visual pereption. Oular motion allows movements of the eyes to diret the view point of the visual system. Foveal-peripheral vision enables humans to pereive small regions in ne detail in ombination with a wide eld of view at oorse detail. Taking advantages of the oular visual system, the human head also has the apability of hanging gaze and xate on features of the environment. Our main purpose for building these vision robot head was not just having an ative vision system with the basi degrees of freedom (vergene, pan and tilt) to perform traking or to be used on mobile platforms, but also to have a devie where we an study and simulate some of the human visual behaviours. One important aspet in the designing stage of these roboti systems is the performane they should aomplish. The analisys of some harateristis of the human ative visual system an be usefull for determining performane requirements for veloity and aeleration of a mehanial devie that intend to simulate the human visual system behaviour. Some harateristis of the human visual system are sumarized in table 1, being the information presented in the table obtained from Carpenter [15], Yarbus [1], Geiger and Yuille [3], Webb Assoiates [20] and Wurth and Goldberg [18]. 2.1 Mehanial Struture The ISR MDOF ative vision robot head has the following mehanial degrees of freedom and some harateristis of the mehanial degrees of freedom are summarized in table 2: Eyes-mehanial Eah eye has three degrees of freedom (a total of six): elevation (tilt) azimuth (pan) ylotorsion (being developed)

3 Fig. 1. ISR MDOF Ative Vision Head Preision Range Veloity Nek Pan 0:0036 [?110 :: ] 360 =s Nek Swing 0:0036 [?27:5 :: + 27:5 ] 360 =s Nek Tilt 0:0036 [?32 :: + 32 ] 360 =s Eye Pan 0:0036 [?45 :: + 45 ] 360 =s Eye Tilt 0:0031 [?20 :: + 20 ] 330 =s Cylotorsion 1 0:0031 [?25 :: + 25 ] 330 =s OCA 2 8nm [0::80]mm 1mm=s Baseline 20nm [137::287]mm 5mm=s Table 2. Mehanial struture harateristis of the ISR MDOF ative vision system an aditional degree of freedom is inluded to keep the optial enter at the rosspoint of the azimuth and elevation axes of the lens. Nek-mehanial The nek has three degrees of freedom: tilt pan swing or lateral tilt movement Baseline The ability of mehanialy hange the distane between the two eyes. The ISR MDOF ative vision robot head is probably the head that urrently has more degrees of freedom. In addition to the ommon degrees of freedom for amera heads (pan, tilt and independent vergene for eah of the eyes), this head inludes the swing movement of the head nek, independent tilt movement for both eyes, and the ability of adjusting the optial enter of the lenses. The latter is to ensure pure rotation when verging the ameras and ompensate for the translation movement of the optial enter when hanging the foal length of the lens. Cylotorsion of the eyes is at the moment being developed. This design of the head inspired by biologial motivation has diret onsequenes on the kinematis of the head. No oinident axes have been possible for all the three nek degrees of freedom. Only the pan and swing axes interset. The tilt axis does not interset any of these two axes and it was put 8 m ahead and 14 m above of the pan and swing axes. With this partiular design the eyes will have a translational omponent added to the pan and swing rotation movement. Due to this mehanial design a muh more 1 Being developed 2 OCA : Optial Center Adjustment demanding kinematis alibration and ontrol of the head are required. The eyes of this head are equipped with fully independent movements and azimuth, elevation and ylotorsion are available. The inlusion of independent nek and eyes elevation movements was motivated by the fat that a smoothpursuit of light loads is aomplished with muh more auray and saadi movements of the eye an be performed muh faster than nek saadi movements. We inluded the optial enter adjustment due to the fat that this head is equiped with motorized zoom lenses. Pure rotation vergene movements are possible using this degree of freedom. We don't think that the adjustment of the optial degree of freedom is ruial for ative vision robot head, but the kinemati of the eye beomes a lot easier, in speial for motorized zoom lenses. Pure rotation is also important to implement distane-independent saade algorithms, and is essential for algorithms that assume that the relationship between motion spae and motion in joint spae may be learned without knowledge of the target distane. This ould be extremely important for example to perform ative alibration of the optial degrees of freedom, as it will be show later. The optial enter adjustment only takes plae along the optial axis of the lens, sine the larger variation of the enter of projetion ours along this axis as a result of fous and zoom hanges. A small variation on the loation of the enter of projetion also ours on the other two axes, but we onsidered that variation negligible ompared with the variation that ours along the optial axes. The eye mehanial struture of this head and its optial enter adjustments onstraints limits the type of lenses that an be used. The mehanial struture develloped for the ylotorsion movement of the eye limits also the type of amera that an be used. Only small ameras an be used, not only beause of its weight but also due to its size. The dynami performane, auray, and other requirements are ahieved with harmoni drive DC motors. In order to simulate the performanes of the human visual system there is a requirement for large aeleration, low frition, high repeatability and minimal transmission errors. These are some of the primary harateristis of systems that use motors and feedbak devies mounted diretly to the axes of motion. With the harmoni drive gearboxes, transmition ompliane and baklash, whih an ause inauray and osilations, are almost eliminated. Unfortunately, in order to inlude all the degrees of freedom desribed, it was impossible to redue the loads on the axes only to inertial loads. This imposes the use of higher torque DC motors. All the motors are equipped with optial enoders that provide good resolution but requires initialization proedures eah time the system is powered up. 2.2 Optial Struture In real world environment the range of onditions that a amera may need to image under, be it foused distane, spaial detail, lighting onditions or radiometri sensitivity, an often exeed the apabilities of a amera with a xed parameters lens. To adapt the imaging onditions the amera system requires lenses whose intrinsi parameters an be hanged in a preise and fast ontrolable manner. Motorized lenses oer greater apability and exibility than xed-parameter lenses, however, most ative vision systems have been limited to ameras with xed lenses beause of the diulty of modeling ameras with motorized lenses, their weight and the preision they oer. Nowadays, mo-

4 Green Channel Video Signal Red Channel Video Signal Optial Degrees of Fredom Mehanial Degrees of Freedom MASTER Imaging Tehnology DCX-AT100 SLAVE Image Proessing DCX-AT100 DCX-AT100 Fig. 2. ISR MDOF Eye with the ISR MDOF Motorized Zoom lens Command Exeute Command Exeute Preision Range Veloity Zoom Range=90000 [12; 5::75]mm 1:2 range=s Aperture Range=50000 [1; 2::16] 2:2 range=s Fous Range=90000 [1::1]m 1:2 range=s Command Interpreter Command Exhange Manager PENTIUM-90Mhz UDP/IP Command Interpreter Command Exhange Manager 486DXII Table 3. Optial struture harateristis of the ISR MDOF ative vision system Fig. 3. The ISR MDOF system Arhiteture torized zoom lenses beames more and more important in ative vision systems, e.g., for depth reonstrution, magni- ation, fousing, et.. Zoom an be used to aquire images at dierent magniation, e.g., simulate foveation and onentrate the view on a partiularly feature, fous an be used to automatially refous on objets at dierent distane and ompute relative depth maps, and the aperture an be used to automatially adjust the iris aording to the hanges in lighting onditions. Most of the existing heads uses standard motorized lenses with poteniometers as feedbak information. These lenses has the disadvantage of moving too slow for real-time aommodation purposes (5-6 seonds to full range movement), and the auray for position ontrol is not very good due to the type of information they provide as feedbak. New motorized lenses have been developed to enable this head to aommodate the optial system in almost real time, with very good preision (see g. 2). These lenses have ontrollable zoom, fous and iris and they use small harmoni drive DC motors with enoder feedbak information. For these lenses we used zoom lenses from Computar that we motorized (see g. 2). By using DC harmoni drives we are able to span the full range of zoom (12.5 mm to 75 mm) and fous ( 1 m to innity) in 0.8 se and the full range of the iris in 0.45 se.. Also the full range of fous and zoom are disretized into positions whereas the full range of iris is disretized into positions (see tab. 3). This motorized zoom lens weight almost 1kg and its dimensions are 8.0m x 10.5m x 10.0m [W x H x D]. With this kind of design we hope not only to fully haraterize the operation of this kind of lenses (in terms of the trajetory of the optial enter) and alibrate them, but also to try them in appliations where this type of speed is ruial. With suh suh performanes, the lens is able to make ontinuous, small optial adjustments required by many algorithms in near real time with exellent preision. Qualitative improvements in lens performenes inrease the advantage aorded by ative vision tehniques that rely on ontrolled variations of intrinsi parameters. 2.3 System Arhiteture The ISR MDOF ative vision robot head is onneted to a pair of PC's being one dediated to the ontrol of the mehanial degrees of freedom and the other dediated to the ontrol of the optial degrees of freedom and image aquisition (see g. 3). This later PC is a Pentium (90Mhz) running as a Master being the other PC the Slave unit. These ontrol units are onneted between eahother through an Ethernet link. A speial protool for ommands exhange as been developed using the UDP/IP protool. A modular multi-axis motion ontroller from Preision Miro Control (DCX-AT100) was used to ontrol all degrees of freedom of the head. This modular system onsists of a motherboard where up to six daughterboards or modules an be onneted, and it is based on a 32-bit RISC CPU with oating point math proessor. On-board Multitasking exeutes up to 10 independent programs or bakground tasks simultaneously without interrupting motion ontrol. The DCX-AT100 motherboard performs two key funtions. First it provides both a physial struture to onnet the modules mehanially and eletrially. Seond, it ontains omputer logi whih is used for ontrolling and ommuniating with the individual modules. Another feature is that multiple DCX's an be built into a single system when the appliation requires more than six modules, just like the ISR MDOF robot head. The omputer logi in the DCX system is programmed to interpret and exeute ommands sent to it by the user. The ability to ombine sequenes of ommands (maro ommands) provides the user with a powerful tool for implementing various ontrols requirements. Three ontrol boards from Preision Miro Control are used to ontrol the 18 degrees of freedom of the robot head. The DC servo ontroller module (DCX-MC200) that was pluged in on the motherboard ontains a trapezoidal veloity prole generator and a digital PID ompensation l-

5 (1 to 6 axes of ontrol on a single board) Motion Program(s) PC BUS DCX AT -100 Controller Board Interfaes RS 232 IEEE DX II - Motion Conpensation Amplifier Drive Brush-Type PWM Servo Amplifier existene of a amera oordinate system loated at the lens optial enter and the Z axis viewing along the optial axis of the lens. A 3D point P (x ; y ; z ) in the amera oordinate system will move after rotation to a point P(x 0 0 ; y; 0 z) 0 through the matriial relationship " r11 r12 r13 # P 0 = R P = r21 r22 r23 P : (1) r31 r32 r33 Using the perspetive projetion pin-hole geometry the 3D amera point P 0 projets to the undistorted image point p 0 u(x 0 u; y 0 u) where Digital I/O Analog I/O Limits Swithes Home Detetor Joystik/Trakball Display Keypad Enoder Harmoni Drive DC Motor LOAD x 0 u = f x0 z 0 y 0 u = f y0 z 0 r11x + r12y + r13z = f (2) r31x + r32y + r33z r21x + r22y + r23z = f : (3) r31x + r32y + r33z Multiplying equations 2 and 3 by f=z and substituting x u = f(x =z ) and y u = f(y =z ) results Fig. 4. Motion Control System x 0 r11xu + r12yu + r13f u = f r31x u + r32y u + r33f (4) ter. Eah module is a self-ontained intelligent ontroller. Several ontrol signals are available, inluding limit swiths, home detetor and drive fault (see g. 4). A low-level motor ontrol interfae is provided by the motherboard, being the ommand exhange between the user and the board realized through a ASCII ommand management. The image aquisition is done by an Imaging Tehnology True Color PC board, being eah of the monohrome Cohu 4990 video ameras onneted to the red and green hannel of the RGB input of the board. All the image proessing is at the moment taking plae at the Pentium Master PC. The ommand exhange protool developed to onnet the Master and Slave units uses three levels of protool. At the lowest level the ommand exhange manager is responsible for sending and reeiving pakets of data through the UDP/IP protool. The ommand interpreter establishes the onnetion between the lowest and the highest level of the protool, analising the pakets of data and deiding to whih mahine should the ommand be sent. This level is only ative at the Master unit. At the higest level is the ommand exeute that is responsible to send the ommands to the board ontroller. 3. Optial Calibration : Mathematial Bakground 3.1 The Rotation Method - Theory The main purpose of this pure rotation alibration proedure is to nd amera parameters whih will enable one to best predit the eets of amera rotation in some optimal manner. Given any pair of images where the amera has undergone pure rotation over some axis, if the intrinsi amera parameters and the angle and axis of rotation are known one an ompute where some feature points from one image will appear in the seond image after rotation. This is the main observation that allows us to use pure rotation to obtain some of the intrinsi amera parameters. Let us assume that the amera is rotated in a rigid world environment around some axis (see g. 5). Also assume the yu 0 r21xu + r22yu + r23f = f r31x u + r32y u + r33f : (5) Observing these last two equations, we an onlude that the position of the point in the image after pure rotation depends only on the intrinsi amera parameters, the rotation matrix and the loation of the point in the image before the rotation. The 3D point oordinates are not required in the ase of pure rotation. As we will see in the nest point, this is not the ase when we have rotation with translation. 3.2 The Importane of Pure Rotation If the axis of rotation does not pass exatly through the optial enter of the lens (enter of projetion) then there will be some translation in addition to the rotation around the enter of projetion. Considering the existene of a translation vetor T = t x t y t z T the amera oordinate of the point P after rotation is obtained using P 0 = R P + T and the loation of an image point after rotation and translation will be tx x 0 r11xu + r12yu + r13f + f z u = f (6) r31x u + r32y u + r33f + f z tz ty yu 0 r21xu + r22yu + r23f + f z = f : (7) r31x u + r32y u + r33f + f z tz Pure Rotation over X P Z Z X Y Y X Pure Rotation over Y Fig. 5. Pure Rotation around some axis

6 As we an see from the equation 6 and equation 7 the loation of the point in the image after rotation is no longer independent of the depth of the 3D amera point and it also depends on the translation vetor. However, if we use feature points that are loated far from the amera (z onsiderably large), then the eet of the translation beomes negligible (z ft x, z ft y, z ft z). 3.3 How to Obtain Pure Rotation As we hange the fous or the zoom position of the lens, the optial enter of the lens (enter of projetion) will move along its optial axis. To ompensate this displaement the MDOF Ative Vision Head build at the ISR-Coimbra has the ability to move the lens along its optial axis with an auray of 0:015m. The test whether there is little or no translation is very simple and it involves the use of parallax. The motion of parallax is based on the fat that two 3D points P 1 and P 2 and the enter of projetion all lie on a straight line, even if we perform pure rotation of the amera along its enter of projetion. If we don't have pure rotation, and some translation ours during the rotation, then the three points will no longer be on a straight line and the two points P 1 and P 2 will projet at two dierent image points 1. Assume that the rotation is around the vertial axis (Y axis of the amera oordinate system). We plaed on the wall a pattern with blak vertial lines on a white bakground, printed on a laser printer. To reate the parallax eet we plaed between the amera and the pattern a transparent aryli sheet with just one vertial blak line. The thikness of this line is less than the thikness of the lines of the pattern in order to reate the illusion that this single line is a extension of one of the lines of the pattern. This adjustment has been done by hand, and an edge detetor was used to onrm the straightness of the resulting line. If after the rotation the straightness is not the same, this means that we don't have pure rotation and the position of the enter of projetion must be adjusted by displaing the lens amera body along the optial enter adjustment (OCA) degree of freedom. 3.4 The Rotation Method - Implementation and Experimental Details Sine after rotation we have a pair of images, we have hosen to minimize the sum of squared distanes between the feature points in the image obtained after rotation and those omputed from the initial image and using the pure rotation model desribed in setion III, summed over all the feature points of eah pair of images. To be more preise, the intrinsi parameters an be obtained using N pairs of images taken with the amera rotated at various angles. The relative angles of rotation are measured preisely. The ISR-Coimbra MDOF ative vision system has a rotation degree of freedom for eah amera (vergene) with a preision of 0:0036. Corresponding features in eah pair of images are found and their pixels oordinates are extrated. There is no speial reason to detet the same number M of features in eah images, but this is what we did in pratie. 1 This observation is not valid for the ase of a translation along the projetive line dened by the three points. Sine the translation is due to rotation about some point, the diretion of translation ontinuously hange and therefore only momentarily is aligned with the projetive line. We dene the ost funtion: NX MX E = k=1 n=1 where x k f n 2? xk f nrot 1; yf k? n 2 yk f nrot 1;2 (8) (x k f nroti;j ; yf k nroti;j ) are the oordinates of (x k f ni ; y k f ni ) after rotation from image i to image j in eah pair. Combining the ost funtion with equations 4 and 5 and dening the image points on the frame-buer plane the ost funtion E an now be dened by NX MX E = k=1 n=1 where h? k 2? x? fn2 x0k f? n 2 x + k 2 i y? fn 2 y0k f? n 2 y x 0k f n 2 = kxfx r11(x k f n 1? x) + r12(yk f n 1? y)k?1 + r13f xk x r31(x k f n 1? x) + r32(yk f n 1? y)k?1 + r33f xk x f = r21(x k n 2 kyfy f? x)k + r22(yk n 1 f n? y) + r23fyky 1 r31(x k f? x)k + r32(yk n 1 f n? y) + r33fyky 1 y 0k The task is now to nd the intrinsi parameters of the amera (f xk x; f yk y; k; x; y) by a straightforward nonlinear searh, assuming some initial values to the parameters. A detailed desription of the approah used to obtain the initial values for the intrinsi parameters an be found on [4]. 4. Conlusions Some harateristis of the ISR MDOF Ative Vision Systems and some mathematial bakground of its optial system alibration have presented in this paper. This ative vision system was designed to be a Lab instrument with redundany on the degrees of freedom and high performanes in terms of speeds, aeleration and resolution. Its performanes should approah those of a human head. Biologial reasons played a role in the design options of this system. The ability of the ative vision systems to perform aurate movements have been used to perform the ative alibration using just features of the environment has the amera undergoes an aurate and ontrollable movement. In the ase of the approah used and desribed on the paper a pure rotation of the amera was onsidered and a proedure to ensure pure rotation around the enter of projetion was presented. Aknowledgement This work has been partially supported by Junta Naional de Investiga~ao Cienta e Tenologia (JNICT) projet VARMA. Referenes [1] A. Yarbus, \Eye Movements and Vision", Plenum Press, New-York, [2] A. Basu, \Ative Calibration: Alternative Strategy and Analysis", in Pro. IEEE Conf. on Computer Vision and Pattern Reognition, pp , [3] D. Geiger, A. Yuille, \Stereo and Eye Movements" inbiologial Cybernetis, vol. 62, pp , 1989.

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