Underwater Stereo Mapping with Refraction Correction

James Servos∗, Michael Smart∗, and Steven L. Waslander†

University of Waterloo, Waterloo, ON, Canada, N2L 3G1

Abstract— This work presents the a method for underwa-ter stereo mapping and localization for detailed inspectiontasks. The method generates dense, geometrically accuratereconstructions of underwater environments by compensatingfor the negative effects caused by image distortions due torefraction. A refractive model of the camera and enclosureis calculated offline using calibration images and producesnon-linear epipolar curves for use in stereo matching. Anefficient block matching algorithm traverses the precalculatedepipolar curves to find pixel correspondences and depths arecalculated using pixel ray-casting. Finally the depth maps areused to perform dense simultaneous localization and mappingto generate a 3D model of the environment. The localizationand mapping algorithm incorporates refraction corrected ray-casting to improve map quality. The method is shown to greatlyimprove overall depth map quality and to generate high quality3-D reconstructions.

I. INTRODUCTION

Underwater simultaneous localization and mapping(SLAM) has a wide breadth of applications and has beena field of great interest to many roboticists for severalyears. Operating underwater presents many new challengeswhen compared to standard approaches and can have vastlydifferent requirements. These challenges can include unpre-dictable motion due to surf and currents, particulate matterand sediment floating in the water, as well as a very diverseand often unstructured environment. In particular this workfocuses on detailed inspection tasks which are very difficultto perform underwater as there are many significant sourcesof error which are not present in the equivalent terrestrialapplications.

Many researchers have developed submersible vehicleswhich are capable of SLAM operations in various forms.These vehicles have been used to perform a wide range oftasks including, coral reef inspection and monitoring [1] [2],inspection of archaeological sites [3], geological surveying[4], and profiling of norther icebergs [5]. Researchers suchas Zhou and Bachmayer[5] and Clark et al. [3] have success-fully used sonar sensors for the mapping of underwater struc-tures such. Sonar sensors however are limited in that they canonly map macro-features due to there limited resolution andsample density. Camera based methods are commonly usedto get more detailed reconstructions but present additionalchallenges which include poor lighting conditions, washedout colors, and distortion due to refraction. One of thesimpler methods of generating maps from camera images is

* M.A.Sc. Candidate, Mechanical and Mechatronics Engineering, Uni-versity of Waterloo; adas@uwaterloo.ca,jdservos@uwaterloo.ca

† Assistant Professor, Mechanical and Mechatronics Engineering, Uni-versity of Waterloo; stevenw@uwaterloo.ca

image mosaicing, which has been demonstrated by Bagheriet al. [6] for species counting. The mosaicking method canproduce detailed two dimensional maps of the sea floor butis not capable of reconstructing 3-D features. Mosaickinghowever has been combined with sonar sensing to generate3-D top down topological maps in [7] and [8]. Recentdevelopments in full 3-D visual SLAM have also been imple-mented underwater in order to create better reconstructions.These techniques use stereo cameras to generate depth mapswhich can be used to create detailed reconstructions of theenvironments. Warren et al. [1] were able to generate highquality maps of a coral reef by using visual odometry forpose estimation and overlaying consecutive stereo frames tocreate a 3-D mesh. Alternatively, in [9] and [2], a featurebased approach is used to to track features over time andand align successive frames.

One of the major problems which is found in underwaterstereo mapping applications is caused by the refractiveinterface between the air in the enclosure and the exteriorwater. Refraction can cause major distortions to the indi-vidual camera images as well as to the calculated depthsproduced from the stereo correspondences. These errors canaccumulate over time while mapping and result in largergeometric errors. These types of errors where observed by[2] who used an additional inertial measurement unit (IMU)to compensate for the undesirable curvature created in themap. However, several researchers have presented methodsto directly account for refraction in the images. Mechanicalmethods such as using calibrated view-ports that physicallycompensate for the difference of refractive indices betweenthe air and water have been proven effective by [10], but arecostly and are reliant on precise alignment. The most popularmethod currently for refraction compensation is radial cor-rection by including it in the lens distortion parameters. Thismethod takes advantage of the fact that for any given depth,refraction exactly matches a radial distortion provided therefractive plane is perpendicular to the optical axis. However,this equivalent radial distortion varies with depth, creating asituation where the single view perspective (SVP) cameramodel fails [10]. For stereo vision, radial correction canfrequently be insufficient as shown in [11] and as it becomesdifficult to establish correct correspondences. This occursbecause the traditional epipolar system no longer holds: theepipolar rays through space no longer appear as lines insecond camera, but rather as curves that are dependent on theparameters of the refractive interface [11][12]. Additionally,correspondences that are accepted can display false curvaturein terms of depth.

For the application of detailed inspection a dense scenereconstruction is required. Dense SLAM has become an in-creasingly prominent field, driven significantly by the desirefor real time augmented reality, and inexpensive RGB-Dcameras but has clear practical implications to many roboticsapplications. Recently new methods for performing denseSLAM have emerged particularly for real time applications.Dense Tracking and Map (DTAM) [13] is monocular cameramethod which estimates detailed depth maps using selectkeyframes and minimizes a novel global energy functionto generate dense models. Although DTAM can generateexceptional quality models it is highly dependent on con-sistent light which is not optimal in underwater conditions.RGB-D SLAM [14] is another SLAM algorithm whichconstructs dense 3-D models using an RGB-D camera suchas the Microsoft Kinect. RGB-D SLAM uses scale invariantfeatures such as SIFT or SURF to perform frame to framematching and optimizes over the global network. The mapsare generated by projecting the data from all frames into 3-D space. This method is also sustainable to degradation dueto lighting and contrast effects underwater. In contrast tothe above methods KinectFusion [15] does not rely on RGBinformation to construct dense 3-D models but instead usesonly the depth map information. KinectFusion aligns famesto a global map representation using an iterative closestpoint optimization and refines the map by averaging newinformation over time. This gives KinectFusion the abilityto generate a detailed map even from noisy input data andto be unaffected by changes in lighting conditions. The orig-inal KinectFusion algorithm is limited in the reconstructionvolume due to memory constraints but improved version,Kintinuous [16], allows for continuous volumes by pagingmap information in and out of memory as needed.

The contribution of this work is the application of theexact refraction compensation demonstrated by Gedge [11]to the generation if dense geometrically accurate maps ofunderwater environments. The precise refraction parametersare found using an optimization technique over a set ofcalibration images with a standard calibration target. Oncefound, the refraction parameters are used to calculate thenon-linear epipolar geometry present in underwater stereosetups. These epipolar curves are then used with a sumof absolute differences stereo block matching algorithm togenerate improved, high quality depth maps which can beused passed to the SLAM algorithm. The SLAM algorithmuses is derived from the KinectFusion [15] approach as itprovides many beneficial qualities for use in the underwaterenvironment and can be modified to explicitly account forthe effects of refraction.

II. REFRACTION CALIBRATION

To correct for refraction, the method of Gedge et al.[11] isimplemented. This method follows a ray-tracing approach togenerate the epipolar curves of the system that has alreadybeen calibrated in air. These curves are traversed to establishstereo correspondences and then a refractive triangulation isperformed to locate the point beyond the refractive medium.

Generating the curves are generated offline using previouslycaptured calibration images and are stored in lookup tablesfor later use.

The epipolar curves are determined by first casting a raythrough the refractive interface using the same method as[17] and as illustrated in Figure ??, where the refractive planeP is defined by the plane normal Np and the distance to theplane dp . A pixel, u ∈ R2, in homogeneous coordinates u =[uT , 1]T is projected to a ray in space r from the camera’sorigin by applying the inverse of the air intrinsic cameramatrix of the left reference camera Kl:

r = K−1l u

The ray r is then scaled to intersect the refractive interfaceP at the point p0 given by

p0 =d

rT (−Np)r

The direction of the ray is then altered at the interface byrefraction according to Snell’s Law:

ni sin θi = nr sin θr

where θi is the incident angle between the ray and thesurface normal, θr is the angle between the refracted rayand the surface normal, and ni and nr are the refractiveindices of the incident medium and the refractive mediumrespectively. Computing the unit vector r of r allows us toapply Snell’s Law and yields the the distorted ray direction:

r′ =ninrr − (−ni

nrcos θi + cos θr)Np

The direction r′ and the point p0 define the ray projectedfrom pixel p through the refractive plane P . This processcan be used to cast rays from each camera given a pixelcorrespondence long as the transform linking the local cam-era frames, EL→R = [R|t] is known, where R ∈ R3x3

represents the rotation matrix converting the left frame tothe right frame, and t ∈ R3x1 represents the translation fromthe left frame to the right frame. The points on each raypl, pr that are the minimum distance from the other ray canthen be found and the midpoint of pl and pr can then betaken as the estimate of the 3D triangulated point in space.

While this ray-casting approach allows the triangulationof 3D points, it requires a feature correspondence whichin turn requires the location of the epipolar curves. Thesecurves are obtained by casting a ray through a pixel, u, fromthe reference image and then finding the set of the ray’sreprojections, Qu = {q(1)u , q

(2)u , ...q

(m)u }, to the image in the

second camera. This set Qu defines the epipolar curve ofpixel u and contains the possible correspondence points inthe second image for pixel p in the reference image. Theray points generating Qu are obtained by sampling pointspk = r0 + kr′ for step lengths, k = {s1...sn}, along therefracted ray, converting them to the second camera’s frameusing EL→R, and finding the reprojections of the points pkto the image in the second camera. The reprojection of a

point pk into the second camera as in Figure ?? is found bythe following process. First, we project pk to the refractiveinterface’s normal to obtain p′k. Using this point, we can thencompute

z = ‖p′k‖ − dx = ‖p′k − pk‖

Now, using z and x and the refractive indices ni and nrwe can find u by solving the following quartic:

[(nrni

)2(d2p + u2)− u2](x− u)2 − u2z2 = 0

In this application, there only exists one valid root u andit is found in the interval [0, x]. The point, C, where thenormal passing through the camera origin meets the plane isfound by

C = −dpNp

and the point r where the ray from the camera origin tothe object would pass through the interface if no refractionoccurred is found by

r =dp

pTk (−n)pk

The point, pk, where the actual refracted ray from the objectto the camera origin intersects the interface is finally givenby

pk = ur − C‖r − C‖

The point pk can now be projected into the second imagewithout concern for the refractive plane by using the secondcamera’s camera matrix Kr to find the pixel correspondingto the epipolar curve at the depth determined by ki:

pr = Krpk

Using this procedure, we can iteratively search for pointspr within Qu in order to populate the set of points wesearch along for correspondences. While Gedge takes limitedsamples and then uses interpolation to obtain the other pixelsin the curve, we chose to exhaustively sample the curve toobtain all of the relevant elements of Qu within a specifiedrange of depths. An example of an epipolar curve is shownbelow in Figure ??.

These procedures allow us to generate the epipolar curvesto be searched for correspondences, and to determine depthgiven those correspondences, but only if the parametersof the refractive interface(s) are known. To estimate thoseparameters, we perform a calibration routine where thestereo camera configuration is already calibrated in air. Usingthis system, we capture images of a known 8x6 checker-board to establish the corners as a set of known featurecorrespondences {i, j} we can then perform a nonlinearminimization to determine the refractive parameters φ ={ni, nr, dp,L, dp,R, Np,L, Np,R} that produce the smallestsum of the minimum distances between the points pl, pr

used in triangulation for each of the known feature corre-spondences:

minimizeφ

∑{i,j}

‖pl − pr‖22

With estimates of the parameters, the epipolar curves cannow be generated offline for each pixel in the reference imageand reactive triangulation can be performed for given featurecorrespondences.

III. STEREO BLOCK MATCHING

To perform stereo matching between the cameras a sumof absolute differences (SAD) block matching algorithmis used. The sum of absolute differences block matchingapproach is an efficient local matching technique. It isperformed by taking the absolute difference of each pixel in areference block and its corresponding pixel in a target blockthen attempting to minimize the sum of these differences fora given reference point. Performing this 1-D optimizationalong a search path for each pixel in the reference imagegenerates a stereo disparity map. Normally this algorithmsearches along horizontal, straight epipolar lines to attemptto match a pixel in the reference image to the target image;however, in an underwater environment the epipolar geome-try is no longer linear and as such the block matching searchproceeds along the epipolar curves defined previously foreach pixel. The algorithm also employs several prefilterigsteps, such as image rectification and image intensity nor-malization, as well as postfiltering steps including unique-ness thresholding and speckle filtering, as implemented inthe Open Source Computer Vision Library (OpenCV) [18].Finally, depths for each of the corresponding pixel pairs canbe determined by using pixel raycasting threw the refractiveinterface and finding the point of intersection between theleft and right image ray. The block matching approach can beperform relatively quickly particularly for linear search pathsand can be easily parallelized. The use of non-linear epipolarcurves negates some of the optimization which can normal beperformed but still allows for parallelized implementations.

IV. DENSE LOCALIZATION AND MAPPING

The localization and mapping used is adapted from aproven SLAM technique introduced by Newcombe et. al.[15], known as KinectFusion. This approach was originallyintended for use with a Microsoft Kinect RGB-D camera.The KinectFusion algorithm has many beneficial charac-teristics which make it specifically suitable for underwaterinspection tasks and can be modified to to specificallyaccount for refraction in the imaging pipeline. This method isalso ideally suited to be extended for use with stereo cameraswhich can be formatted to produce depth maps similar tothose created by the Kinect. The algorithm generates highdensity detailed maps while allowing for denoising and mapcorrection by averaging data over time. The KinectFusionalgorithm is largely lighting invariant as it does not rely coloror intensity information.

The map is represented by a single global 3-D voxel gridwhich contains discretized truncated signed distance function

(TSDF) values. The truncated signed distance function is atool used to store vertex information in space [19] . Thealgorithm proceeds by iterating through four main stages:

1) Measurement Pre-processing: New depth map mea-surements are pre-processed to generate dense vertexand a normal maps.

2) Surface Prediction: A new predicted surface is gener-ated my projecting the map into the current estimatedcamera frame.

3) Pose Estimation: The new position of the camerais estimated using an iterative closest point approachgiven the new vertex map and the predicted surface asthe reference and target points respectively.

4) Map Update: The map TSDF values are updated withthe current measurement information

One of the vital aspects of the algorithm is the ability toproject image pixels into and back from 3-D space. In thecase of a camera under normal operation in open air thisis a trivial task which is accomplished using the camera’sintrinsic parameter matrix. However, when the camera issubmerged in and underwater enclosure this task is no longertrivial. Therefore it is vital to define functions that canperform the equivalent operations for cases which includerefractive interfaces.

First denote the intrinsic camera matrix as, K ∈ R3x3, thepixel space of the camera as U ⊂ R2, and a pixel locationas u ∈ U . Let the a pixel location in homogeneous form beu = [uT , 1]T and the 6DOF camera pose in the global frame,g, at time t be represented by the transformation matrix:

Tg,t =

[Rg,t tg,t

0 1

]

where Rg,t ∈ SO3 is a rotation matrix and tg,t ∈mathbbR3 is the translation vector.

The function for calculating the projective ray from a givenpixel location through a refractive interface is then definedas:

Ψ :R2 → R3

Ψ(u) =nwnaK−1u− (

−nwna

θ + ϕ) ∗Np

θ = NTp K

−1u

ϕ = (1− nwna

2∗ (1− θ2)1/2

where Np is the normal of the refractive plane with respectto the camera, and nw and na are the refractive indices ofwater and air respectively. Additionally, unlike the standardcamera model this ray also has an offset from the cameraorigin which is calculated:

γ :R2 → R3

γ(u) = v − (NTp v)Np

v =−dp

(K−1u)TNpK−1u

where dp is the distance from the camera focal point tothe refractive plane. Calculating a pixel co-ordinate from apoint, pc ∈ R3, in a more intensive process due to the need tosolve a quartic function. This back projection to the camerapixel space can be defined as:

Φ R3 → R2

FIXME − this− is− not− rightplease− disregard− for − now− : (

. Every stage of the the algorithm uses one of theseprojection functions and as such it is important that theycorrectly account for refraction in order to produce the bestpossible mapping results.

The measurement pre-processing stage incorporates re-fraction corrections in order to correctly project depth imagepixels into 3-D space. A new measurement consists of adepth map Dt where each image pixel, u, is a raw depthmeasurement, Dt(u) ∈ R. A pixel in the vertex map canthen be defined from the corresponding pixel location andthe depth value such that the vertex point in the 3-D cameraframe, pc ∈ R3 is defined as

pc = Dt(u)Ψ(u) + γ(u)

for all u, in the depth image. This generates the vertexmap, Vc,t, in the camera frame, c such that Vc,t(u) ∈mathbbR3. Using the refraction correction the input ver-tex map correctly reflects the actual 3-D geometry of theunderwater scene. The corresponding normal map,Nc,t canbe computed by simply doing the cross product of a vertexpoint and its neighboring pixels.

The surface prediction stage generates a predicted vertexmap, Vg,t, and surface normal map, Ng,t, by raycasting fromthe current estimate of the camera position into the map.Raycasting is performed by sequentially stepping through theTSDF map along the rays projected from each pixel until thatray intersects with the map. The TSDF representation of themap enables efficient raycasting since the step size, α alongeach ray can be, α ≥ µ, where µ is the TSDF truncationdistance, and once a positive TSDF value is found single unitsteps are taken. The location of intersection is the predictedvertex, pg ∈ R3, which is determined when the TSDF valuebecomes negative. The camera rays used for raycasting arealso affected by refraction in water. A ray in the global frameat pixel u, denoted rg(u) ∈ R3, can be computed as

rg(u) = Rg,t−1Ψ(u)

however it must also be offset initially by γ(u). Byaccounting for refraction in the surface prediction stage thepredicted surface more accurately represents what the rawcamera measurements will produce and as such the poseestimation stage will provide more accurate matching resultswhich will in turn improve the resulting map.

The pose estimation process is performed by employingpoint to plane iterative closest point (ICP) optimization[20] and the fast projective data association algorithm forcorrespondences. Vertex correspondences are computed bycalculating the predicted pixel location

u = Φ(T kg,tVc,t)

where T kg,t is the current transform estimate at ICP it-eration k. For the vertex to be a valid correspondencethe measured and predicted vertex maps must contain avalid value at u, and the variation in corresponding surfacenormals and point to plane distances must be below a definedthreshold. The ICP alignment then processed iteratively usingand updating these correspondences om each iteration. Badcorrespondences are not included in the map update stagesuch that outliers are rejected from distorting the map.In this manner the alignment of of the measured surface(Vc,t,Nc,t) and the predicted surface (Vg,t,Ng,t) is performedand generates the new camera pose Tg,t.

The map update stage takes the aligned measurementinformation and fuses it into the global map using the TSDFvalues. For a signed distance function the function gives thevalue corresponding to the distance from the closest vertexsuch that a negative value represents space within a surfaceand positive values represent free space. The TSDF simplytruncates the function at a maximum distance value, µ. TheTSDF is implemented as a discrete voxel grid where eachcell has both the TSDF value, F ∈ R, and a confidenceweighting W ∈ R. The new TSDF value of a point, pg ∈ R3,is calculated by projecting pg to a specific camera pixel,u, and calculating the difference between the the measureddepth, Dt(u), and the distance to pg . The depth differenced ∈ R is calculated as

d = ||T−1g,t pg||2 −Dt(Φ(T−1g,t pg))

The difference value, d, is then truncated and normalizedby µ to get the measured value of Fm. The new value of theTSDF, Ft is the weighted average between the measured,Fm, and current, Ft−1 values. The weight value, Wt, isthe summation of the previous weighting with the constantmeasurement weight, Wm = 1. Using the weighted averagefor multiple noisy TSDF measurements over time producesa de-noising effect and results in a much smoother map.The maximum weight for a cell is also truncated whichallows for control over how quickly the map reacts to dy-namic changes. applied The original Kinect fusion algorithmleveraged GPU parallelization to vastly increase performanceand allow for high frame rates and real time operation.The modified algorithm still maintains the same ability tobe parallelised but increase computation by a non-trivial

factor due to the increased number of operations needed toaccount for refraction. However, since the bottle neck forthis type of GPU programming has generally been memoryand not computation the modified algorithm should still beable to be run at a reasonable rate on most high end graphicsprocessors.

V. EXPERIMENTAL RESULTS

The proposed method was evaluated using a custom stereocamera setup which included a Point Grey Bumblebee2stereo camera mounted in a custom waterproof enclosure.The data was collected at the University of Waterloo poolwith the addition of artificial submerged objects of varioussizes and shapes to generate a known static environment.The camera was moved manually by an operator throughthe environment for the various test cases. Two main resultsof system are presented. First the improvement in the rawstereo depth map generation is demonstrated and evaluatedbased on pixel correspondences and curvature minimizationon a flat surface. Second, the results of the overall mappingand demonstrates the improvements to the localization andmapping accuracy over time.

A. Stereo Depth Image CorrectionThe quality of the final map is directly correlated to the

quality of the depth maps that can be produced by the stereocamera setup. In the case where the refraction distortion isnot correctly compensated for the depth maps can be heavilydegraded. In Figure 1 two representative depth maps arepresented. The top row shows a depth map of a flat surfaceand the bottom row shows and example scene containingvarious miscellaneous objects objects.

The figure shows that in the case of the flat surfacethere are significant errors in the standard case winch arecausing the false impression of curvature on the surface. Therefraction corrected image does not show the false curvatureand correct calculates a constant depth across the wholeimage. It can also be clearly seen from the images that thenumber of incorrect correspondences is significantly higherin the standard case particularly in the corners of the images.The image corners are the most effected by the effects ofrefraction and as such the standard case fails must often inthese regions.

The curvature of the flat wall in each of the images can becalculated quantitatively by sampling the depths and fittinga quadratic approximation, Q(x) : x ∈ R2. We can thencalculate a curvature value, κ ∈ R, by taking, κ = || 52

Q(x)||2. As such a flat surface should have a curvature valueof zero while higher curvature will have larger values.

Correspondence can also be quantitatively accessed by tak-ing the percent of the image which has a correct correspon-dence. In this case we will assume that any correspondencewhich was not filtered is correct and will be included in thetotal.

Table I shows the results of the curvature and corre-spondence calculations. It demonstrates that the refractioncorrected depth map has resulted in significant improvementsof the standard case.

(a) Standard radial correction on a flat textured surface (b) Our full refraction correction on a flat textured surface

(c) Standard radial correction on an example scene (d) Our full refraction correction on an example scene

Fig. 1. Comparison of standard radial correction versus our full refraction correction technique on depth map quality and density. False coloring is appliedto the images based on depth values scaled such that purple is less then 0.2m from the camera and ranges to red representing greater then 5m. Greyrepresents a point which failed to be corresponded.

TABLE ISUMMARY CURVATURE AND CORRESPONDENCE PERCENTAGES FOR THE

RADIAL AND FULL CORRECTION CASES.

Radial Correction Full CorrectionCurvature (κ) ?? ??

Correspondence Percentage ?? ??

B. Map Reconstruction Quality

To evaluate the overall map reconstruction quality thepresented method was performed on an underwater datasetin which an artificial scene of interest was constructed out ofplastic bins containers of various sizes and dive weights. Themain characteristics of interest when evaluating the map arethat of erroneous curvature of flat surfaces as well as generalgeometric consistency in size and shape of objects. Figure2 shows the comparison of the map generated with standard

radial correction versus the map generated using our fullrefraction correction method.

The refraction corrected map has significantly smootherfeatures and the flat surface shows much less curvature. Thisis due to the fact that consecutive frames have much betterglobal consistency and thus align much better to the globalmap. This allows for the mapping to better average measure-ments over time and create a higher quality approximation ofthe accrual surface. It should also be noted that the standardversion has significantly worse convergence properties sincethe ICP has much worse correspondence information to usewhen aligning the frames. The global consistency and ICPalignment of the map can be demonstrated quantitatively bycomparing the average error in the ICP minimization andthe number of rejected correspondences. This informationshows how closely the current depth image matches to theglobal map. If a given depth image matches the global map

(a) Map of a flat surface generated using standard radial correc-tion !!This is just a place holder image for now!!

(b) Map of a flat surface generated using our full refractioncorrection

Fig. 2. Comparison of standard radial correction versus our full refraction correction technique on depth map quality and density

with very little error and has a high number of correctcorrespondences the map can be considered to be an accuraterepresentation of the scene. Table II summarizes the resultsof the ICP alignment quality.

TABLE IISUMMARY OF ICP ERROR AND CORRESPONDENCE REJECTION.

Radial Correction Full CorrectionAverage ICP error ?? ??

Average Correspondences ?? ??

The ICP matching results on the refraction correctedmap are significantly better indicating that the generatedreconstruction is a better match to the actual measured scene.

VI. CONCLUSION

This work demonstrates that visual SLAM results forunderwater applications can be improved by specificallyaccounting for refraction in the stereo matching and SLAMalgorithms. A method for refraction compensated SLAM ispresented and shown to improve both depth map quality fromstereo camera sensors as well as the overall resulting 3-Dreconstruction. Future work in this area includes optimizationof implementation for real time performance as well asoutdoor field trials in different environmental conditions.

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