Active Monocular Fixation using the Log-polar Sensor

Transcription

1 Active Monocula Fixation using the Log-pola Senso Albet Yeung Depatment of Compute Science and Softwae Engineeing, Univesity of Melboune, Victoia, 3010, AUSTRALIA Nick Banes Autonomous Systems and Sensing Technologies Pogamme, National ICT Austalia Ltd. Locked Bag 8001, Canbea, ACT, 2601, AUSTRALIA Abstact This pape pesents a fast cone fixation algoithm fo log-pola cameas. The algoithm uses the log-hough tansfom to fixate on the dominant cone in the image by aligning the optical axis with the cone. The algoithm has been implemented in a eal-time closed-loop contol system, which exhibits stable behaviou as the tacking eo minimises towads the image cente. This system demonstates an impotant benefit of utilising the logpola senso with log-hough line detection that thee is an automatic bias to cones close to fovea. This emoves the need fo seaching explicitly though all detected cone positions in ode to locate the one closest to an abitay point. In addition, since the log-pola senso has a lage field of view fo a given numbe of pixels compaed to Catesian space-invaiant cameas, it emoves the need to use a tacking window to incease pefomance, while still suppoting high esolution at the fovea. 1. Intoduction Fixation is a specialisation of visual tacking and is the task of keeping the gaze diection on the same taget point ove time [Ahns and Neumann, 1998]. It is pat of the active vision paadigm, whee the obseve, manipulates visual paametes to obtain exta infomation about the envionment. This ability to fixate simplifies many highelevel vision poblems, such as docking [Banes and Sandini 2000]. Tacking itself is a fundamental opeation in obotic vision to facilitate contol [Jeon, et al., 2001]. It also facilitates image undestanding by ecoveing motion [Shi and Tomasi 1994] and though ecognition of object [Wang, et al., 1995] and shape [Deguchi and Yonaiyama, 2000]. Many solutions exist fo space invaiant cameas. Howeve, these usually utilise a subsampling window to cut down on pixel count [Lee, et al., 1999] and thus educe image pocessing time, (e.g., [Reid and Muay, 1996], [Shi and Tomasi 1994] and [Wang, et al., 1995]). A log-pola camea educes logaithmically in esolution towads peiphey, thus natually educes pixel count. A few binocula tacking systems have been implemented using this mapping to eplace the subsampling window technique [Oshio, et al., 1996] and [Petes and Bishay, 1996]. The focus is on binocula fixation athe than fixation pe se. Template-based algoithms have been devised fo the log-pola domain. Benadino and Santos-Victo [Benadino and Santos- Victo, 1999] fomulated a template-based binocula fixation algoithm using the visual sevoing famewok. Ahns and Neumann [Ahns and Neumann, 1998] poposed a view-based fixation contol algoithm using monocula vision, which involves compaison against a efeence view to obtain a similaity measue. These template-based algoithms ae geneal in natue, but this geneality comes at a computational cost. In the case whee a cone is visible, such as manufactued objects, cone-based methods should be exploited fo the speed inceases that ae possible though specialised algoithms. Cone-based fixation also can be used to establish a pecise coespondence between a fixated taget and a coesponding object model, and thus facilitate knowledge-based inteaction. Howeve, Catesian-based cone tacking methods ae not diectly applicable to log-pola domain, thus a new appoach is needed to combine the advantages of log-pola fixation with gains fom specialised cone tacking algoithm. In this eseach, we focus on cones as the fixation taget because they ae commonly encounteed in indoo obot navigation, such as stuctual cones in coidos and manufactued objects. A widely used definition of a cone fo detection elates to cuvatue o intensity discontinuity of edges. Thee is a class of well-established detectos that uses a local measuement of coneness, geneally based on cuvatue o gadient. These detectos diffe in the way they classify and find highly pobable cone points. Fo an evaluation of classical cone detectos: Beaudet, Deschle and Nagel, and Kitchen and Rosenfeld, see [Deiche and Giaudon, 1990]. Some moe ecent cone detectos take advantage of development in othe fields of eseach, such as neual netwoks, cuvatue scale space and the wavelet tansfom. Fo example, [Basak and Page 1

2 Mahata, 2000] apply a neual netwok to popagate neighbouhood infomation about a coneness measue. Cuvatue scale space and the wavelet tansfom enable multi-scale appoaches to impove localisation, such as [Mokhtaian and Soumela, 1998] and [Pedesini, et al., 2000] espectively. Othe innovations in cone detection include the use of suface cuvatue measuement to intepolate sub-pixel diffeentiation [Wang and Bady, 1994] and methods based on a mophological closing opeato [Laganiee, 1998] and iteated Gabo filteing [Quddus and Fahmy, 1998]. Theoetically, since chaacteistics of a cone, such as cuvatue discontinuity, ae geneally peseved in logpola tansfomation, they can be adapted to wok in logpola space as well. This would wok fo most cases of cones at abitay points in the image. Howeve, the cone is lost in the singulaity at the cente of the image. Given that the aim of cone fixation is fo the cone to be in the image cente, this endes cone detection unusable in a significant subset of cases. A diffeent appoach to cone detection is thus equied to facilitate fixation in the log-pola domain. In this pape, the appoach emphasises stuctual suppot of cones by defining a cone as the intesection of two staight lines. The basic equiement of fixation is to fixate moving objects. If the objects ae moving away fom the obot, the pojection of the edges will change in scale, thus stable fixation equies edges with significant spatial extent. Cones that ae only a few pixels can quickly disappea. This definition of a cone gives ise to a simple and fast detection algoithm using the Hough tansfom. (a) (b) (c) Figue 1. Log-pola camea image of a cone at an abitay position. (a) Catesian emapped image, (b) logpola image, (c) edge map of the log-pola image. (a) (b) (c) Figue 2. Log-pola camea image of a cone at the cente. (a) Catesian emapped image, (b) log-pola image, (c) edge map of the log-pola image. A novel algoithm to detect, tack and fixate cones in log-pola space is pesented in this pape. A space-vaiant camea can captue the same field of view as a conventional camea at lowe pixel count, eliminating the need fo windowing. A log-pola camea achieves this by having the maximum spatial esolution at cente (fovea) and logaithmically educing towads the peiphey. Although this does not suppot tacking at high esolution acoss the senso, it suppots high-esolution fixation. The contibutions of this pape ae two-fold: a highly effective algoithm fo monocula fixation; and a demonstation of the advantages of using the log-pola camea fo fixation. Specifically, inceased field-of-view while maintaining foveal esolution and a natual bias towads cones close to cente. This natual bias aligns with the goal of fixation, which is to keep the cone at image cente yielding stable behaviou. A closed-loop contol system based on the poposed fixation algoithm has been implemented and expeimentally veified to be stable and sufficient fo eal-time pefomance. 2. Backgound 2.1. The log-pola mapping The log-pola senso imitates the mapping fom the etina to visual cotex of pimates [Schwatz, 1977]. In the etinal plane (Figue 3a), a point can be epesented by Catesian coodinates (x, y) o pola coodinates (, θ), which ae elated by: x = cosθ, y = sinθ (1) The mapping between a pola plane (, θ) (etinal plane) and a Catesian plane (ξ, η) (log-pola cotical plane, Figue 3b), can be witten: ξ = log, (2) a 0 η = qθ, (3) whee 0 is the adius of the inne-most cicle and 1/q is the minimum angula esolution of the log-pola layout. A CMOS implementation has been ealised [Questa and Sandini, 1996] and is used in this eseach. O y P θ i x (a) (b) Figue 3. An annulus in the image plane (a) maps to a vetical stip in the log-pola plane (b) Achitectue Figue 4 illustates system achitectue adopted. The contol hadwae consists of Giotto log-pola camea as input and a pan-tilt moto contol boad as output unning a popotional, integal and deivative (PID) contolle. η i Fovea η ξ i P ξ Page 2

3 The tacke softwae module connects these two pieces of hadwae and implements the poposed cone fixation algoithm. The softwae achitectue of the tacke is shown in Figue 5. Giotto Camea Log-Pola Senso Paallel pot Log-Pola Image Log-Hough Tacke RS232 pot Moto position command Pan-Tilt Contolle analogy. In this section, we pesent a full deivation of the log-hough voting equation fo eal digital images. Fistly, we follow the convention defined in Figue 6 to avoid confusion of nomenclatue. We use (, θ) to epesent the pola coodinates. Hence, the standad Hough line paameteisation [Duda and Hat, 1972] can be witten as: ρ = x cosω + ysinω, (6) Figue 4. Physical camea movement Contol stuctue of the cone tacke. Now, we use ω to define the line equation in pola coodinates instead of φ: ρ =, 0 < θ ω < π, (7) cos ( θ ω ) Figue 5. Camea Input (paallel pot) Log-Pola Image Edge detection Edge map 3. Theoy Log-Hough Voting Vote map Peaks Finding Line Paametes of peaks Contol (intesection) Calculation Moto/position command To contol boad (RS232 pot) The log-hough tacke softwae schematics. The Hough tansfom [Hough, 1959] finds staightlines fom edge pixels in a Catesian image. Howeve the log-pola senso tansfoms staight-lines, thus modelling based on staight lines is inadequate. In this eseach, a Catesian line model is tansfomed to log-pola space to ovecome this limitation The log-hough tansfom Weiman s deivation [Weiman, 1990] of the log- Hough tansfom begins with the following staight-line equation in pola coodinates: ρ =, 0 < θ φ < π, (4) sin ( θ φ ) whee φ is the slope of the line (Figue 6). He then applies log-pola tansfom of (2) and (3) to (7): ξ = log ρ log sin a a ( ( η φ )) To utilise the tansfom on eal cameas, the Hough voting equation needs to account fo the singulaity of the logaithm of zeo and the finite discete epesentation of digital imagey. Howeve, Weiman did not pesent such a deivation and only povided a poof of concept by (5) Figue 6. y (x, y) θ ρ ω φ x Catesian pola coodinate system. whee ω is the angle, fom x-axis, of the pependicula line passing though the oigin. The Hough voting pocess incements an accumulato of all possible line paametes fo a given candidate pixel. The voting equation effectively is the invese of the line equation (7): ρ ω = η ± acos. (8) This is a pola voting equation, allowing iteation though ρ to obtain all solutions fo a given candidate pixel (, ω). It is also possible, but less elegant in implementation, to make ρ the subject in (8) and iteate though ω instead: ( ω η), ρ = ( η ω ) ρ = cos cos. (9) Howeve, we must map into a finite log-pola space. ξ max and ξ min ae simply the bounds of the ξ dimension of log-pola space. min is 0 the adius of the inne-most cicle of sensing element and max is the adius of the maximum cicle of sensing elements. Thus, we have: = a ξ ξ ξ max min ( log log ) a max a min. (10) This can be substituted into (8) to obtain the log-hough voting equation Intesection of two lines The output of the log-hough tansfom is a list of ecognised lines defined by two paametes ρ i and ω i : Page 3

4 ρ cos 1 2 =, =. (11) ( θ ω ) cos( θ ω ) 1 The cone fo any line pai lies at thei intesection. Fo non-paallel lines (ω 1 ω 2 ), an intesection can be obtained in pola coodinates fom the standad equations: ρ 2ρ ρ cos( ω ω ) ( ω ω ) 2 2 ρ + ρ 1 2 =, (12) sin 1 2 ( ω ) ρ sin( ω ) ρ ρ cos( ω ω ) ρ sin 1 = 2 θ cos. (13) 2 2 ρ + ρ 1 2 Howeve, Equation (13) only gives the magnitude of θ, to obtain the sign of θ equies substitution into the line Equations (11) to check fo consistency and obtain Contol The intesection solution fom the pevious section povides the taget cone position. The algoithm convets this point to elative pan-tilt coodinate and dispatches a positional command to the moto contol sub-system. As a whole, the poposed fixation algoithm foms a closedloop visual feedback contol stuctue. (a) Catesian image domain (b) Log-pola image domain Figue 7. Illustation of foveal voting bias. Note that the high-esolution fovea is patially shown Foveal voting bias The high-esolution fovea natually gives ise to a highe pixel count when a cone is close to the cente (Figue 7). This inheent bias fits well with the log-hough tansfom pocess. Without futhe intoducing atificial bias, the line detection pocess is going to find the line with moe votes fist. Effectively, the votes fom the log- Hough tansfom seve as a confidence measue. In the majoity of cases, the two most dominant lines coespond to the cone closest to the cente. Thus, to find the cente-most cone with edge suppot, we only need to conside a few edges with the lagest Hough vote count. 2 The automatic bias fo cones close to fovea is one impotant benefit of the log-pola senso with log-hough line detection. This emoves the need fo explicit seach though all detected cones to locate the one closest to an abitay point. Futhe, since the log-pola senso has a lage field of view fo a given numbe of pixels compaed to Catesian space-invaiant cameas, it thus emoves the need to use a tacking window to incease pefomance. 4. Implementation Contol calculation: The intesections of all pais of lines fo the n lines with the highest vote count ae solved using the method descibed above. If multiple intesections exist, the algoithm simply picks the one with the smallest adial component () as the estimated fixation point. This does not guaantee coect cone will always be found, but in most cases is Figue 8. Complete assembled sufficient to implement cone fixation system mounted on Pionee 1 obot. stable fixation. Results and analysis in section 5.2 futhe exploe these stability issues in multi-cone envionment. Hough quantisation: The Hough space dimension of 60 (ρ) 100 (ω) has been found expeimentally to be a good compomise between computation expense in voting and quantisation eo. Lage Hough space tanslates to a bigge vote map, but this will esult in fine esolution. This Hough space dimension tanslates to a minimum esolvable line oientation (ω) of 3.6. The minimum adial esolution vaies fom 0.12 pixels nea cente to 11.1 pixels (of a compaable space invaiant senso) at peiphey due to the logaithmic effect. Hough peak finding and non-maximum suppession: Locating one global peak is tivially implemented using linea seach. Howeve, since image space is discete, quantisation eos cause the pixels neighbouing a peak to also have high numbe of votes. Figue 9 shows these false peaks ovewhelming othe lowe but significant local peaks. To ovecome this poblem, non-maximum suppession is applied aound the cuent global peak. We clea a numbe of ows (θ) in both diections. Fo most common situations, we cleaed fou ows o ±14.4. This assumes all individual lines in an image diffe in oientation by at least 14.4, which is made to impove tacking pefomance fo a single dominant cone. Altenatively, we could have limited the ange of suppession along ρ also, but widely sepaated paallel lines will not have a cone. Page 4

5 Figue 10 shows the aveage eo at each of the fou positions, aveaged acoss all tials. These esults futhe suppot the stability and veified the oientation invaiance of this fixation algoithm. (a) (b) (c) (d) Figue 9. False peaks aound a tue peak in Hough space causes detection of eoneous lines aound edges. (a) Catesian emapped image, (b) log-pola image, (c) edge map image and (d) Hough vote map. 5. Results and analysis Extensive expeiments have been conducted to evaluate the pefomance of the fixation algoithm. We conducted a seies of tial with simple clean cones, such as Figue 1, to evaluate the quantitative accuacy of cone localisation. We also tested diffeent cone angles and moe complex scenaios of multiple and shot cones to ensue stable fixation. Lastly, the eal-time fixation pefomance was veified. All tials wee conducted with the Giotto camea and custom pan tilt platfom mounted on a Pionee obot as shown in Figue 8. Cuent non-optimised pefomance with an Intel Pentium III 600MHz is aound 20 fames pe second, which is adequate fo eal-time fixation. Video of the system demonstating its closed-loop pefomance is available with this submission Quantitative Veification In ode to evaluate the pecise eo in estimation, we disabled the contol system. The fist tial examined stability with espect to distance fom the cente of the image. A simple clean cone of 90 degees, such as in Figue 1, was moved to the left of the image acoss 39 tials. Figue 11 plots the position estimation eo against adial distance. The eo shown is the visual angula distance between a hand selected cone point and the point selected by the system. Visual angle fom camea calibation gives a cleae esult than the pixel count, which is non-linea. This educing estimation eo tend appeas to be appoximately logaithmic, which coesponds to camea sampling esolution. Results fo moving ight wee compaable. Thus, fo the majoity of cases, an accuate estimate of cone position is obtained when a single clean cone is pesent. To veify pefomance with diffeent cone shapes and diffeent diections of motion away fom the image cente, we used 14 diffeent cone sizes anging fom 15 to 340 degees. Each cone was moved to fou standad positions between the fovea and 15 degees fom the cente of the image, at fou 90 degee intevals cicling the cente, with some tials the points wee on the x and y axis, while othes wee not. The diection that the lines of the cone extended fom the cone was also vaied Cone angula dimension limit Within the above tial, we tested nine diffeent cone angles ove the ange of 15 to 165. Fo this ange of cone sizes we found that the eo estimates wee at an acceptable level fo fixation. Outside these anges between 0 to 15 and 165 to 180, cones wee not stably tacked, see Figue 12. This coesponds to the minimum line oientation eo incued by non-maximal suppession. Note that the ange fom 180 to 360 is symmetic to this and shows simila pefomance. Unde low illumination, thee was also instability close to minimum cone angle. We attibute this to bluing aound the densely packed sensing element in the fovea. Absolute eo (degee view angle) Aveage eo vesus adial distance Radial distance (degee view angle) x y Log. (x) Log. (y) Figue 10. Aveage estimation eos vesus adial distance fom the cente point. Absolute eo (degee view angle) Estimation eo vesus adial distance (Move left seies) Radial distance (degee view angle) x y Log. (x) Log. (y) Figue 11. Estimation eos vesus adial distance in move left seies (moe data points). Note that fou outlies, thee of appoximately 10 and one at 14.5 degees ae not shown in the plot fo fomatting claity, but ae included in the tendline calculation. Page 5

6 5.2. Special cases: multiple and shot cones Many cases of fixating a cone in multiple cone scenes wee evaluated. In the majoity of cases whee a significant cone exists in the image fame (Figue 13, 16), the fixation algoithm coectly detects the two majo suppoting lines and thus obtains the coect intesection and fixation point. Howeve, in some ambiguous situations such as Figue 15, the intesection closest to the cente of two significant edges is not actually a cone. This will not be a stable solution and will geneally disappea given motion of the platfom towads the nonexistent cone. (a) (b) (c) Figue 15. Images of a multi-cone scene degeneate cases: (a) and (b) will disappea as soon as the camea moves, howeve fo (c) the incoect fixation may be stable. Figue 12. At the accuacy limit of log-hough tansfom, the 190 -cone taget causes platfom to oscillate aound the cente. Images shown in ows, with time pogessing fom left to ight, log-pola images and emapped images with matched edges supeimposed. Nevetheless, thee exist degeneate cases, such as Figue 15, whee the cente-most intesection does not identify the coect cone to fixate. These degeneate cases can cause instability by saccading to the fictitious cone point. Subsequent oscillations may occu if this degeneate condition is polonged. Howeve, with the camea being an active obseve, such polonged eoneous states ae aely encounteed. Figue 15(c) shows a case whee incoect fixation may be polonged. This case could be coected by additional pocessing to check fo edge pixels close to the intesection. (a) (b) (c) (d) Figue 13. Images of multi-cone scene a dominant cone exists and is ecognised coectly. (a) (b) (c) Figue 14. Images of multi-cone scene multiintesection cases: (a), (b) ae deteminate cases due to poximity to the cente of one cone, wheeas fo (c) eithe cone may be selected. Figue 16. Catesian emapped images of shot cones tial, demonstating the coect ecognition of cente-most cones. Fo shot cones, the algoithm maps all pixels of the edges that make up a cone, thus cones with adequate spatial extent ae fixated stably (Figue 16) Indoo scene In addition to these contolled cases, we also veified the system pefoming in a closed-loop in two indoo scenes. The system fixated on a cone of a doo window and cone of a oom unde obot motion. Fo both these scenes the fixation was un ove a peiod of seveal minutes and despite occasional poo estimates, it exhibited stable fixation (unning at aound 20 fps). Figue 17 shows images taken at andom intevals duing this tial, displaying the estimated lines and cones. It can be seen that fo the fist sequence (Figue 17(a)), one fifth of the images show that the cone was not accuately detected. Howeve, this did not pevent stable fixation. Figue 17(b) shows a difficult case fo cone fixation whee one of the edges is wide, due to selfshadowing in low illumination conditions. Again, fixation was stable, even though a quate of the cases veified wee in eo. Fo both these tials the incoectly detected cones ae due to dominance of nea paallel lines. This could be impoved by tuning the algoithm, such as boadening non-maximal suppession. Howeve, the absence of such tuning demonstates obustness of the algoithm. Page 6

7 (a) Figue 17. (b) Catesian emapped images of indoo scene tial, demonstating the pefomance of line and cone ecognition. 6. Conclusion This pape pesented a new log-pola cone fixation algoithm. In the couse of developing the fixation algoithm, we fully deived the finite Hough tansfom voting equation in log-pola domain. A full hadwae and softwae closed-loop system was developed to implement the algoithm. Expeimental veification has shown that the system is stable and has demonstated eal-time pefomance. This confims the advantages of the logpola senso fo fixation. The two majo advantages ae: lage field of view fo a given pixel count; and, a natual bias towads cones closest to the cente. The fist benefit esults in tacking pefomance gains without the use of sub-window sampling techniques, while the second benefit eliminates the need to explicitly find all cones in an image in ode to locate the cente-most one. Thus, the log-pola senso is highly suitable fo fixation tasks whee the focus of attention is at the high-esolution image cente. Page 7

8 7. Acknowledgement The authos would like to thank Pofesso Giulio Sandini fo the use of the log-pola camea. 8. Bibliogaphy [Ahns and Neumann, 1998] Ahns I, Neumann H. Real-time monocula fixation contol using the log-pola tansfomation and a confidence-based similaity measue. In Poc. 14th Intl. Conf. on Patten Recognition., IEEE Comput. Soc. Pess. vol.1, 1998, pp vol.1. Los Alamitos, CA, USA. [Banes and Sandini 2000] Banes N, Sandini G. Diection Contol fo an Active Docking Behaviou Based on the Rotational Component of Log-Pola Optic Flow. In Poc. Sixth Euopean Confeence on Compute Vision, Pat II, June/July Spinge 2000, pp Dublin, Ieland. [Basak and Mahata, 2000] Basak J, Mahata D. A Connectionist Model fo Cone Detection in Binay and Gay Images. In IEEE Tansactions on Neual Netwoks, vol.11, no.5, Sept. 2000, pp USA. [Benadino and Santos-Victo, 1999] Benadino A, Santos- Victo J. Binocula tacking: integating peception and contol. In IEEE Tansactions on Robotics & Automation, vol.15, no.6, Dec. 1999, pp Publishe: IEEE, USA. [Deguchi and Yonaiyama, 2000] Deguchi K, Yonaiyama K. Real-Time 3D Shape Recognition of High Speed Moving Object by Fixation Point Tacking with Active Camea. In Poc IEEE/RSJ Intl. Conf. on Intelligent Robots and Systems, vol.1, 2000, pp Piscataway, NJ, USA. [Deiche and Giaudon, 1990] Deiche R, Giaudon G. Accuate Cone Detection: An Analytical Study. In Poc. 3d Intl. Conf. on Compute Vision, IEEE Comput. Soc. Pess. 1990, pp Los Alamitos, CA, USA. [Duda and Hat, 1972] Duda RO, Hat PE. Use of the Hough Tansfomation To Detect Lines and Cuves In Pictues. In Communications of the ACM, vol. 15, Issue 1, Jan 1972, pp ACM Pess. [Hough, 1959] Hough PVC. Machine Analysis of Bubble Chambe Pictues. In Intenational Confeence on High Enegy Acceleatos and Instumentation, CERN [Jeon, et al., 2001] Jeon YB, Kam BO, Pak SS, Kim SB. Seam tacking and welding speed contol of mobile obot fo lattice type welding. In Poc IEEE Intl. Symposium on Industial Electonics, vol.2, 2001, pp Piscataway, NJ, USA. [Laganiee, 1998] Laganiee R. Mophological Cone Detection. In 6th Intl. Conf. on Compute Vision, Naosa Publishing House. 1998, pp New Delhi, India. [Lee, et al., 1999] Lee SW, You BJ, Hage GD. Model-Based 3D Object Tacking using Pojective Invaiance. In Poc IEEE Intl. Conf. on Robotics and Automation, vol.2, 1999, pp Piscataway, NJ, USA. [Mokhtaian and Soumela, 1998] Mokhtaian F, Suomela R. Robust Image Cone Detection Though Cuvatue Scale Space. In IEEE Tansactions on Patten Analysis & Machine Intelligence, IEEE Comput. Soc. Pess. vol.20, no.12, Dec. 1998, pp USA. [Oshio, et al., 1996] Oshio N, Mau N, Nishikawa A, Miyazaki F. Binocula Tacking using Log Pola Mapping. In Poc. of the 1996 IEEE/RSJ Intl. Conf. on Intelligent Robots and Systems, vol.2, 1996, pp New Yok, NY, USA. [Pedesini, et al., 2000] Pedesini F, Pozzoli E, Sati A, Tubao S. Multi-esolution cone detection. In Poc Intl. Conf. on Image Pocessing, vol.3, 2000, pp Piscataway, NJ, USA. [Petes and Bishay, 1996] Petes RA II, Bishay M. Centeing Peipheal Featues in an Indoo Envionment Using a Binocula Log-Pola 4 DOF Camea Head. In Elsevie. Robotics & Autonomous Systems, vol.18, no.1-2, July 1996, pp Nethelands. [Quddus and Fahmy, 1998] Quddus A, Fahmy MM. Cone detection using Gabo-type filteing. In Poc. of the 1998 IEEE Intl. Symposium on Cicuits and Systems, vol.4, 1998, pp New Yok, NY, USA. [Questa and Sandini, 1996] Questa P. Sandini G. Time to contact computation with a space-vaiant etina-like C-mos senso. In Poc. of the 1996 IEEE/RSJ Intl. Conf. on Intelligent Robots and Systems, IEEE. Pat vol.3, 1996, pp vol.3. New Yok, NY, USA. [Reid and Muay, 1996] Reid ID, Muay DW. Active tacking of foveated featue clustes using affine stuctue. In Intenational Jounal of Compute Vision, vol.18, no.1, Apil 1996, pp Kluwe Academic Publishes, Nethelands. [Schwatz, 1977] Schwatz EL. Spatial mapping in the pimate sensoy pojection: Analytic stuctue and elevance to peception. In Biological Cybenetics, vol.25, no.4, 1977, pp West Gemany. [Shi and Tomasi 1994] Shi J, Tomasi C. Good featues to tack. In Poc IEEE Compute Society Conf. on Compute Vision and Patten Recognition, IEEE Comput. Soc. Pess. 1994, pp Los Alamitos, CA, USA. [Wang and Bady, 1994] Wang H, Bady M. A Pactical Solution to Cone Detection. In Poc. ICIP-94 Intl. Conf. on Image Pocessing, IEEE Comput. Soc. Pess. vol.1, 1994, pp Los Alamitos, CA, USA. [Wang, et al., 1995] Wang H, Goh WL, Chua CS, Sim CT. Realtime object tacking. In Poc. of the st Intl. Conf. on Industial Electonics, Contol, and Instumentation, vol.2, 1995, pp New Yok, NY, USA. [Weiman, 1990] Weiman CFR. Pola Exponential Senso Aays Unify Iconic and Hough Space Repesentation. In Poc. SPIE - the Intl. Society fo Optical Engineeing, vol.1192, pt.2, 1990, pp USA. Page 8