High-Accurate and Robust bust M Motion Estimation algorithm for mobile m robots Ghasem Mohammadi1, [email protected] 1 University of Kurdistan ABSTRACT Optical-flow is a well-known technique ue and there are important fields in which the applicatio cation of this visual modality commands high interest. Measurement of optica tical flow is a fundamental problem in the processing of image im sequences in mobile robots. In this paper, we presented a more accur ccurate and robust algorithm for motion estimation in real eal time t that can handle large movement of mobile robots. To enhance the accu accuracy, we use Harris corner detector in 4 levels of Gauss aussian pyramids of frames to select good corners as a features to track them m fr from one frame to the next using proposed algorithm which hich is called PLKCT. We put more emphasis on robust corners by using specia ecial weightening function. The proposed method is moree accurate acc and robust than the previously published algorithms for motion est estimation problem. We demonstrated the effectiveness ss of o our algorithm through experimental results. Error analysis on a syntheti thetic image sequence is given to show its effectiveness. Keywords: Mobile robots, machine vision, ego go m motion estimation, pyramid Lucas and Kanade, Harriss corner cor detection.

1.

INTRODUCTION Leonard and Durrant-Whyte [1] summariz arized the general problem of mobile robot navigation by three th questions: "Where am I?" "Where am I going?" and "How should I get tthere?" The first question correspond to localization that is the process of updating the pose of a robot in an environment, based ed on sensor readings. Localization is one of the main problem blems that to date there is no truly elegant solution for it. Whiteout accurate loc localization, mobile robots unable to navigate the environm onment properly and face lots of problem so it is a critical underlying factor tor ffor successful mobile robot navigation in a large enviro vironment, irrespective of the higher-level goals or applications. All of the localization methods can be categorized as follow (table 1). Relative localization ion techniques are based on determining incrementally the position and orien rientation of a robot from an initial point. To provide this his information in it uses various onboard sensors, such as encoders, gyroscopes, es, aaccelerometers, etc. [2] The absolute localization techniques dete determine the position of the robot with respect to a globa lobal reference frame [2], for example, using beacons or landmarks. The mos most popular technique is GPS which is based on satellite ellite signals to determine the absolute position. Position Measureme nts Cat

Method Name

Description

Pros

Uses encoders to measure wheel heel rotation • totally self-contained and/or steering orientation Odometry

Relative Inertial Navigation

Optical Flow

Absolute

Active Beacons (like GPS)

Uses gyroscopes and so sometimes • Self-contained accelerometers to measure re rate of rotation and accel acceleration. Measurements are integrated ed oonce (or twice) to yield position extracting a dense velocity field ield from an • Self-contained image sequence assuming that hat intensity • low equipment cost is conserved during displacemen ment • Computes the absolute positio sition of the • Simple deployment robot from measuring the dire direction of incidence of three or more ore actively transmitted beacons.

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Cons • position error grows without with bound if don’t use independent nt reference r • non-systematic errors • systematic errors which ich relates to unequal wheel diameters, d uncertainty about the effective distance between wheels heels centers, limited encoder resolution ution, etc. • Unsuitable for accurate te positioning p over an extended period od of o time • High equipment cost • non-systematic errors • systematic errors • Intensity should be conser nserved • Aperture Problem • The transmitters mustt be located at known sites in the environ ironment. • three or more landmarks arks must be "in view" • Small accuracy of data ively large • sampling time is relatively • signal can be lost in close losed spaces

International Journal of Scientific Research arch and Innovative Technology ISSN: 2313-3759 Vol. Vo 3 No. 1; January 2016

Artificial Landmark Recognition

Natural Landmark Recognition

Model Matching

Distinctive artificial landm ndmarks are • Can be designed for optimal placed at known location tions in the detectability environment. • The position errors are bounded • Additional information can be derived from measuring the geometric properties of the landmark The landmarks are distinctive tive features in • There is no need the environment. preparation of environment

• Three or more landma dmarks must be "in view" • Computationally intens tensive • Not very accurate. • Real-time position fixing fixi may not always be possible • Landmarks may nott can be defined as a set of features,, e.g., e.g. a shape or an area. for • The environment must ust be b known in the advance. • The reliability of this is method m is not as high as with artificial landmarks.

Information acquired from m tthe robot's • Map-based positioning often • costly installation onboard sensors is compared ared to a map includes improving global or world model of the environ vironment. The maps based on the new maps used include two ma major types: sensory observations in a Geometric maps that represent esent the world dynamic environment and in a global coordinate te ssystem,and integrating local maps into topological maps representt the world as the global map to cover a network of nodes and arcs. previously unexplored areas.

Table1 - classification of localization methods Among all of the methods, Optical Flow (OF1) command high interest because of its capabil abilities. Motion is an intrinsic property of the world and an integral part of ou our visual experience. It is a rich source of information n that tha supports a wide variety of visual tasks. The 2D velocities for all visiblee sur surface points are often referred to the 2D motion field. The OF computation consists in extracting a dense velocity field from an imag image sequence assuming that intensity is conserved during ring displacement [3]. For OF algorithms, brightness constancy constraintt is the basic assumption, which assumes that camera or object ob motion is the cause of image brightness changes between frames. OF can be used for applications such as 3-D reconstruction, tion, time interpolation of image sequences, video compression and segmentation ation from motion, tracking, robot navigation and time-to-col collision estimation. Most of the OF algorithms alreadyy ha have been widely described in the literature [3] [4] [5]. Some of the authors have addressed a comparative study of the accuracy racy of different approaches with synthetic sequences [6]. Their evaluation using real sequences is difficult to address because thee re real optical flow of such sequences is unknown. We have ve focused f on a gradient model based on Lucas & Kanade’s approach [6],, [9] Lucas & Kanade tracker, also known as the Kanade-L Lucas-Tomasi (KLT) tracker. Invented in the early 80s, this method hass be been widely used to estimate pixel motion between two wo consecutive c frames. Several authors have emphasized the satisfactory tradeo adeoff between accuracy and efficiency in this model, which ich is an important factor when deciding which model is most suitable to use aas a real-time processing system. For a comparativee study stu [6], the L&K algorithm provides very accurate results, added to which, ich, other authors specifically evaluating the efficiency vs. s. accuracy a tradeoff of different optical-flow approaches [10] also regard the he L& L&K model as being quite efficient. Finally, McCane ett al. [11] also give L&K a good score and conclude that the computational pow power required by this approach is affordable. This hass prompted pr later researchers to focus on the L&K algorithm [12], [13]. One of the main challenges in L&K alg algorithm is aperture problem. For overcome this problem blem, finding proper features in sequences of frame is very important and dire directly affect the efficiency and accuracy of the algorithm. thm. To this end we must track features instead of single points. To performin rming tracking of image features, the image features must ust be b discrete, and not form a continuum like texture, or edge pixels. We use se th the extraction and tracking of feature-points that here it is corners. Corner is one of the most important feat feature of the image. The accuracy and quality of the corner rner detection directly affect the results of image processing, and can determine mine the outline features and important information of the image. i Corner detection can not only keep the useful image information but also can reduce data redundancy and improve the detection dete efficiency [14]. There are many methods to make corner detection. n. T The most common method for corner detection is Harris rris corner detector. The Harris algorithm provides very accurate results [15] 5] [1 [16]. For enhance the accuracy of proposed ed aalgorithm and overcome the small motion constraint off mobile mo robots, the optical flow computation is implemented in pyramidal fash fashion, from coarse to fine resolution. Consequently, the algorithm can handle large pixel flows, while keeping a relatively smalll win window of integration, and therefore achieve high local accuracy accu [13]. The remainder of the paper is organize anized as follows. In Section 2, we introduce the proposed osed algorithm for improve the accuracy and speed of L&K. In Section 3 the he m mathematics of proposed algorithm are discussed. In Section Sect 4 we evaluate proposed algorithm. Finally, Conclusions and future work works are discussed.

1

OF acronym for Optical flow

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International Journal of Scientific Research rch aand Innovative Technology ISSN: 2313-3759 Vol. 3 No. 1; January 2016 2. Optical-Flow Model OF is defined as an apparent motion of bbrightness patterns in sequential images. Let I(x, y, t)) be the image brightness that changes in time to provide an image sequence. e. Tw Two main assumptions can be made: 1. Brightness I(x, y, t) smoothly depends nds on coordinates x, y in greater part of the image. 2. Brightness of every point of a moving ing or static object does not change in time. Let corners have movement. After time dt the displacement of object is (dx, dy). Using Taylor series seri for brightness I(x, y, t) gives the following: 2.

I ( x + dx , y + dyy , t + dt ) =I(x, y, t) +

∂I ∂I ∂I dy + dt + H.O.T. H.O. dx + ∂x ∂t ∂y

(1)

Where “H.O.T.” are higher order terms. s. A According to Assumption 2:

I ( x + dx , y + dy , t + dt ) =I(x,, y, t)

(2)

∂I ∂I ∂I dy + dt + H.O.T .O.T = 0 dx + ∂x ∂y ∂t Dividing the equation by dtgives an equati uation:

−

∂I dx ∂I dy ∂I + = ∂x dt ∂y dt ∂t

(3)

Equation (3) usually called OF constrai straint, where dx/dt and dy/dt are components of OF field in x and y coordinates respectively. This is an equation in two unknown owns and cannot be solved as such. This is known as thee aperture ap problem of the OF algorithms. To find the OF another set of equatio uations is needed, given by some additional constraint. To o solve so this problem L&K [8] introduce additional conditions for estimatingg th the actual flow. In the next section the proposed version ion of L&K algorithm will be introduced. 2.3- Feature Selection The term “corner” is used to refer to poin point features that represent two-dimensional intensity change. chan Corners impose more constraint on motion parameters than edges,, and often more abundant that straight edges as well, makin aking them ideal features for track in an indoor and outdoor environment.. For feature extracting, we use Harris corner detector that at it i has been widely used for corner detection and its effectiveness alreadyy ha has been proved [21]. The Harris algorithm is based on an a assumption that corners are associated with maxima of the local autoc utocorrelation function. It is less sensitive to noise in n the th image than most other algorithms, because the computations are based sed entirely on first derivatives. Its high reliability in findin ing “L” junctions and good temporal stability make it an attractive corner er de detector for tracking. Not only do we need corner classifi ssification regions, but also a measure of corner and edge quality or response. nse. The size of the response will be used to select isolated d corner co pixels and to thin the edge pixels. Harris help us to have a robust and nd aaccurate feature matching. Smoothing is very important to the algori lgorithm performance. Smoothing mask parameters weree determined det by three factors: mask shape, mask size, and mask kernel compone ponents. In software, large smoothing masks (e.g., 19 × 19 9 or larger) are often used. In hardware, smaller masks must be used because se oof resource limitations (e.g., 7 × 7 or smaller). As for mask mas shape, a square mask is usually used for the sake of simplicity and effic efficiency. Spatial and temporal smoothing can use differe fferent size masks to improve performance. Temporal smoothing is significant icantly more complicated than spatial smoothing because se it i involves multiple image frames.. Parameters of all the smoothing masks sks aare in a shape of Gaussian function. To increase efficienc ciency, a 2D Gaussian mask is decomposed into two 1D Gaussian masks which hich are cascaded and convolved along x and y directions ons separately [22]. Different settings of these masks are simulated by software ware at bit-level accuracy and evaluated to obtain an optima timal combination in practice. We set the size of the smoothing mask to 9 × 9. To determine whether a pixel is a corner ner or not, at first, gradients along x-direction and y-directi rection (first-order derivative) should be calculated. The window size can be cho chosen as any odd number larger than 3 arbitrarily. Howev wever, in this implementation, a size of 9 × 9 is selected without losing gene generality. Then as already said matrix G is obtained, eve very element of which is a

I (i , j )

I (i , j )

summation of certain values in a window. After fter getting x and y we apply a Gaussian ian filter to smooth them and result in a more reliable matrix G. For a pixel, l, a ccornerness value C is defined as

C ( G ) = det ( G ) + k × trace 2 ( G )

(5)

Where

det( et(G ) = ∑ I x2 ∑ I y2 − (∑ (I x I y ) 119

2

(6)

International Journal of Scientific Research arch and Innovative Technology ISSN: 2313-3759 Vol. Vo 3 No. 1; January 2016

trace (G ) = ∑ I x2 + ∑ I y2

(7)

The parameter k is a (usually small) scal scalar, and different choice of k may result in favoring gradi radient variation in one or more than one direction, or maybe both [23]. A thres threshold is to be set, and if C passes it, the pixel is identifie tified as a corner. Nevertheless, simple thresholding operations sometimess do not yield satisfactory result, which lead to a detec etection of too many corners. Improvement can be achieved by finding local cal m minima in the regions, where response of the detectorr is high. Simple thresholding is used here. Here we select 0.4 and 0.6 for k. keep the subset of those pixels so that the minimum distance nce between b any pair of pixels is larger than a given threshold distance (e.g.. 10 or 5 pixels). After that process, the remaining pixels ls are ar typically "good to track". They are the selected feature points that are fed to the PLKCT. 2.2- Pyramidal Lucas-Kanade corner tracker acker (PLKCT) To improve the feasibility and accuracy racy of method we add some modification to the Pyramidal al Lucas-Kanade L algorithm [9] [17]. We use smoothing masks to improve accu ccuracy, speed and resistance to noise. Another slight modif odification provides estimations when the aperture problem appears in the dir direction of the maximum gradient. We have added a small sma constant, α to the matrix diagonal as suggested in [18], which allows ws uus to estimate the normal velocity field in situationss where wh 2-D velocity cannot be extracted due to the lack of contrast informatio ation. The two key components to any feature tracker aree accuracy ac and robustness. The accuracy component relates to the local sub-pi pixel accuracy attached to tracking. Intuitively, a small ll integration in window would be preferable in order not to "smooth out" the he ddetails contained in the images (i.e. small values of wx and wy). That is especially required at occluding areas in the images es w where two corners potentially move with very different rent velocities. The robustness component relates to sensitivity of trackingg wi with respect to changes of lighting, size of image motion otion. In particular, in order to handle large motions, it is intuitively preferable able to pick a large integration window. Indeed, it is preferab ferable to have dx ≤ wx and dy ≤ wy where [dx,dy] is image movement. There re is therefore a natural tradeoff between local accuracy and robustness when choosing the integration window size. In provide to provi rovide a solution to that problem. Using windows wasn’t enough to gett a ggood comparison between process speed and large moves oves detection. A way to fix it is the use of pyramids. We propose a pyramidal idal implementation of the classical Lucas-Kanade algorit orithm that use Harris Corner Detectoralgorithm for feature selection so we call it as Pyramidal Lucas-Kanade corner tracker trac (PLKCT).An iterative implementation of the Lucas-Kanade OF compu mputation provides sufficient local tracking accuracy. The base of the pyramid, level 0, is the he ooriginal image. Each subsequent level in the pyramid is obtained ob by low-pass filtering and subsampling the previous level. Typically lly eeach level is subsampled by a factor of two. Motion estima timation is then performed from coarse to fine levels with motion vectors refine efined at each level. Hierarchical methods have been used ed for fo block matching [19] and phase correlation. [20]. Hierarchical methods ods aare particularly useful for gradient based algorithms as they t allow for the estimation of large displacements. By definition, the upda updates that are generated should be small to keep the Taylor Tay Series expansion valid. When the image is subsampled the displacemen ment in the image is also reduced. Because at the lowest levels leve the displacement is small, the estimated vectors are passed to the higher her llevels as an initial estimate of the displacement. The higher high levels can then fine-tune the displacement vector for accurate motion est estimation (Figure 1).

Figure 1 - PLKCT implementation

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International Journal of Scientific Research rch aand Innovative Technology ISSN: 2313-3759 Vol. 3 No. 1; January 2016 In this section PLKCT will be briefly sum summarized based on the description of [9] with modificatio cations. Let I and J be two 2D gray scaled images. The two quantities I(X) = II(x; y) and J(X) = J(x; y) are then the grayscale value lue of the two images are the location X = [x y] T, where x and y are the two pixel coordinates of a corner X. The image I will be referenced refe as the first image, and the image J as the second image. T

u u Consider an image corner u = x y on the first image I. The goal of feature tracking is to find ind the th location v = u + d = T

T

u x + d x , u y + d y d d on the second image J su such as I (u) and J (v) are "similar". The vector d = x y is the image velocity at X, also known as the OF at X. It is essential tial tto define the notion of similarity in a 2D neighborhood ood sense. Let ωx and ωy two integers determine the half size of the so called ed in integration window above X. We define the image velocity city d as being the vector that minimizes the function ε defined as follows:

ε (d ) = ε (d x , d y ) =

u y +w y

u x +w x

∑

∑

(A ( x , y ) − B (x + d x , y + d y )) 2

x =u x −w x y =u x −w x

(4)

ade OF computation provides sufficient local tracking accur ccuracy. Corners that found in An iterative implementation of the Lucas-Kanade all levels have the powerful respond to C(G) and so we add weight WC to improve the accuracy to give ve them th more impact on result. Let is now summarize PLKCT in a form of a pseu pseudo-code.

{I }

and {J L }

L

1- Build pyramid representations of I and J:

L = 0,..., L m

L = 0,..., L m

Goal: Let U be a set of corners rs on iimage I. Find its corresponding location V on image age J. 2- Perform Harris Corner Detector on all pyrami yramids 3- For every c that ∈ in all pyramids WC=1; 4-

For every c found in level Lm WC = WC + number of found correspo rrespond coordinate on other pyramids End for weight

g Lm = g x Lm , g y Lm = [ 0, 0] 5- Initialization of pyramidal guess: T

T

6- For L = L down to 0 with step of -1 m

For c = 1 to MaxP (for all cornerss obta obtained by Harris) L

Location of corner c that

on image

T

L

: uc = [p p ] = uc/2 x

y

(Px and Py is coordinate of corner rner c obtained by Harris)

Use I (x; y) and I (x; y) calculate lculated for Harris algorithm x

y

G=

Spatial gradient matrix:

p y +w y

p x +w x

∑

∑

x = p x −w x y = p y −w y

I x2 (x , y ) I x ( x , y ) I y (x , y ) I ( x , y ) I ( x , y ) I y2 (x , y ) y x k

T

Initialization of iterative Lucas ucas-Kanade method: v c = [0 0] For k = 1 to K with step of 1 (o (or until ||ηk || < accuracy threshold) Image difference:

δ I k (x , y ) = I L (x , y ) − J L (x + g xl +v xK −1 , y + g yl +v yK −1 ) p x +w x

bk =

∑

p y +w y

∑

x = p x −w x y = p y −w y

Image mismatch vector vector: k

η = G −1b k OF (Lucas-Kanade): c k

v =v c Guess for next iteration ration: c

k −1

+ ηc

End of for-loop on k Final OF at level L for corner er c:

d

L c

=v c

k

121

k

δ I k (x , y )I x (x , y ) δ I (x , y )I (x , y ) y k

International Journal of Scientific Research arch and Innovative Technology ISSN: 2313-3759 Vol. Vo 3 No. 1; January 2016 End for-loop on c

d

L

Final OF at level L:

k MaxP = ∑Wc vc c =1

Guess for next level L - 1: End of for-loop on L 0

( ∑W ) c

g L −1 = [ g xL −1 + g yL −1 ]T = 2[ g L + d L ]

0

7- Final OF vector: d = g + d 8- Location of point on J: v = u + d End while all points processed Solution: The corresponding point is at location ation v on image J

3. Performance analysis of proposed algorith orithm The performance of proposed algorithm discuss scussed in this paper were evaluated using synthetic sequence ences. The algorithm have been programmed and tested under the same condi onditions of image noise with the aim of giving an exhausti austive comparison of methods. Hence, in following sections we compares the three methods. The "Urban" and "Yosemite" datasett have hav been used that originally created in Middlebury university and compare are tthe results with [8] [9] that have been implemented and nd reported r in [24]. The size of images were 315×252. We use OpenCV librarie raries to implement proposed algorithm in Visual Studio using usin VC++. The partial use of a library permits us to validate the programmed med methods and compare the obtained results with otherr methods. me Robustness of the methods in the presence of im image noise has been validated too. In reporting the performance perf of the OF methods applied to the synthetic sequences, for which ch 22-d motion fields are known, we concentrate on Average rage angle error. The results of experiments are presented as follow. 3.1 Time Execution time of methods, running on a Pentiu entium IV core I3 Computer at 2.13 GHz is shown in table le 1. While L&K methods obtain a time less than 0:1 s; our method obtain a mov movement estimation greater than 0:1 s. this greater timee is for increasing accuracy and robustness. Av Averageexecution time Urban Yosemite PLKCT 1100 ms 1050 ms LK 720 ms 730 ms Pyramid LK 850 ms 950 ms

Table 1: Result of speed analysis on sequences 3.2 Accuracy The Accuracy of the methods evaluated by Aver Average angle error and standard deviation that reported d in [24]. Results are presented in Table 2.

PLKCT LK Pyramid LK

Urban Yosemite Average angle ngle error standard deviation Average angle error standard rd deviation de 10.3 19.05° 5.42 2.85° 32.2 22.8° 8.67 3.90° 21.2

6.41 29.9° Tab Table 2: Result of Accuracy analysis on sequences

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9.01°

International Journal of Scientific Research rch aand Innovative Technology ISSN: 2313-3759 Vol. 3 No. 1; January 2016 3.3 Robustness To evaluate the robustness of proposed algorithm ithm we use different magnitude of movement on handmade ade sequences. The results are presented in Table 3. Result have differences with previous table, it is for using simple sequences.

Method/Movement 1 Pixel 2 Pixel 4 Pixel 8 Pixel PLKCT 0.15° 0.43° 1.17° 1.1 3.3° LK 1.37° 3.18° 8.61° 8.6 14.2° Pyramid LK 0.18° 0.51° 1.24° 1.2 3.65° Table 1 - robustness evaluation ation of o PLKCT

Figure 2 -Handmade images for diffeerent movement comparison

3.4 Harris To check the impact of using corner algorithm m oon accuracy, we perform proposed algorithm of syntheti thetic sequences without using Harris corner detector then we compare it with ith th the state that we use it. The results are presented in Table able 4 show that using Harris algorithm help PLKCT to be more accurate. Ave Averageexecution time Urban Yosemite PLKCT 10.3 5.42 PL PLKCT Without Harris 21.2 6.41

Table 2 - Impact of Harris algorithm on accuracy of PLKCT 3.5 Weightening function To check the impact of using Weightening funct unction on performance, first we perform proposed algorith orithm of synthetic sequences using Weightening function then we compare it w with the state that we don't use it. The results are presented nted in Table 4. Ave Averageexecution time Urban Yosemite PLKCT 10.3 5.42 PLKCT KCT Without weightening func. 17.6 8.68

Table 4: Result of using Weightening function

4. CONCLUSION AND FUTURE WORK We have described an optical-flow algorithm tha that have been used for motion estimation in mobile robo obots and efficiently can deal with large movement of robots and have a bette better accuracy. We use special filter and corner detection tion algorithm to improve the accuracy and performance of the estimated flo flow. In order to improve the performance of our metho ethod further we considered spatiotemporal variants that are well-known from robust statistics and pyramid levels strategies that allow allo for correct handling of large image displacements. Experiments have ve sh shown that using Harris corner detector to find good d features, fea help PLKCT to be reliable and local estimates can easily be fou found. The expected design performance in terms of better bet movement estimation, robustness and speed was carefully evaluated.. Re Results of simulation prove the efficiency, robustness and d accuracy ac of our method. Despite of all efforts, we have certainly not reach eached the end of the road yet. Therefore, we are currently ly investigating in special kind of implementations of our technique and we are stud studying parallelization possibilities on hardware to reach ch more m performance. 5. References [1] J. J. Leonard and H. F. Durrant-Whyte,(1991 991)"Simultaneous map building and localization for an autonomous auto mobile robot", In Proc. IEEE Int. Workshop on Intelligent Robots ots aand Systems, pp. 1442-144.. [2] R. Gonzalez, F. Rodriguez, J.L. Guzman, n, M M. Berenguel,(2009) "Comparative Study of Localizatio zation Techniques for Mobile Robots based on Indirect Kalman Filter", IFR Int International Symposium on Robotics, Barcelona, Spain,, pp. pp 253 – 258. [3] Siegwart, R., Nourbakhsh, I., and Scaramuz amuzza, D.,(2011)“Introduction to Autonomous Mobile Robots, Ro Second Edition”. A Bradford Book, MIT Press, February. [4] Scaramuzza, D., Fraundorfer, F.,(2011) Visu Visual Odometry: Part I - The First 30 Years and Fundame amentals, IEEE Robotics and Automation Magazine, Volume 18, issue 4. [5] Fraundorfer, F., Scaramuzza, D.,(2012) Visua isual Odometry: Part II - Matching, Robustness, and Applic plications, IEEE Robotics and Automation Magazine, Volume 19, issue 2. [6]J.L. Barron, D.J. Fleet & S. S. Beauchemin,((1994) "Performance of Optical flow techniques", Internati rnational Journal of Computer Vision, 12(1):43–77. [7] E. De Castro & C. Morandi,(1987) "Registr gistration of Translated and Rotated Images Using Finite te Fourier F Transforms", IEEE Transactions on pattern analysis and machine int intelligence.

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International Journal of Scientific Research arch and Innovative Technology ISSN: 2313-3759 Vol. Vo 3 No. 1; January 2016 [8] B. D. Lucas, T. Kanade,(1984) "An iterativ rative image registration technique with an application to stereo st vision”, Proc. DARPA Image understanding Workshop, pp. 121-130. [9] Bouguet JY,(2013) Pyramidal implementatio tation of the lucas kanade feature tracker description of the algorithm, a 2000. Cité en. [10] H. C. Liu, T. S. Hong, M. Herman, T.. Ca Camus, & R. Chellappa,(1998) "Accuracy vs efficiencyy trade-offs tra in OF algorithms", Comput. Vis. Image Understanding, vol. 72,, no. Issue 3, pp. 271–286. [11] B. McCane, K. Novins, D. Crannitch, & B. Galvin,(2001)"On benchmarking OF”, Comput. Vis.. Image Im Understanding, vol. 84, pp. 126–143. [12] Shantaiya, Sanjivani, Kesari Verma, and Kamal Mehta, (2015) "Multiple Object Tracking using sing Kalman Filter and Optical Flow." European Journal of Advances in Engin ngineering and Technology 2.2 , 34-39. [13] S. H. Lim & A. E. Gamal,(2001) "OF esti estimation using high frame rate sequences", in Proc. Int. nt. Conf. C Image Process., vol. 2, pp. 925–928. [14] Cai LH, Liao YH, Guo DH.(2008) "Study udy on Image Stitching Methods and Its Key Technologies es [J], [J computer technology and developmemt", pp.1-4, 20. [15] F. Mohanna and F. Mokhtarian.(2001) ""Performance Evaluation of Corner Detection Algorithms hms under Similarity and Affine Transforms". BMVC. 2004)"Evaluation of image corner detectors for hardware are implementation." Electrical [16] Wang, Wenxin, and Robert D. Dony. (200 and Computer Engineering, Canadian Conferen ference on. Vol. 3. IEEE. [17] J. Y. Bouguet,(2002) "Pyramidal implemen ementation of the lucas kanade feature tracker": Description tion of the algorithm. Jean-Yves Bouguet. [18] K. Sims.(1991) "Artificial Evolution forr Co Computer Graphics". Computer Graphics, 25(4):319-328.. [19]. M. Bierling,(1988) "Displacement estimat imation by hierarchical block-matching", in Proceedingss of Visual V Communications and Image Processing, SPIE vol. 1001, pp. 942-951 951.. [20]. Y. M. Erkam, M. I. Sezan, and A. T. E Erdem,(1991) "A hierarchical phase-correlation method thod for motion estimation", in Proceedings Conference on Information Science ience and Systems, pp. 419-424.. [21] P. Tissainayagam, D. Suter,(2004) Assess ssessing the Performance of Corner Detectors for Point Feature Fea Tracking Applications. Elsevier Image and Vision Computing, Vol.22, 22, IIssue. 8, pp.663-679. [22] Lu, Tongwei, Ying Ren, Wenting L., and nd A Anyuan C.(2015) "Dense Optical Flow Estimation with h 3D Structure Tensor Models." In Robot Intelligence Technology and Applicatio ications 3, pp. 685-691. Springer International Publishing. [23] Yi Ma, Stefano Soatto, Jana K.& S. Shanka ankar S.,(2003) "An Invitation to 3-D Vision', springer-Verlag erlag, ch.4. [24] http://vision.middlebury.edu/flow/eval/

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