REAL-TIME DISPARITY MAPSFOR IMMERSIVE 3-D TELECONFERENCING

BY HYBRID RECURSIVE MATCHING AND CENSUS TRANSFORM

E. Trucco1, K Plakas1, Nicole Brandenburg2, Peter Kauff2, Michael Karl2, Oliver Schreer2

(1) Dept. of Computing and Electrical Engin.Heriot-Watt UniversityEdinburgh EH14 4AS

UK{mtc,costas}@cee.hw.ac.uk

(2) Heinrich-Hertz-InstitutEinsteinufer 3710587 Berlin

Germany{kauff, brandenburg, karl, schreer}@hhi.de

Corresponding author: K. Plakas, costas@cee.hw.ac.uk

REAL TIME DISPARITY MAPSFOR IMMERSIVE 3-D TELECONFERENCINGBY HYBRID RECURSIVE MATCHING AND CENSUS TRANSFORM

ABSTRACT

This paper presents a novel, real-time disparity algorithm developed for immersiveteleconferencing. The algorithm combines the Census transform with a hybrid block- and pixel-recursive matching scheme. Computational effort is minimised by the efficient selection of asmall number of candidate vectors, guaranteeing both spatial and temporal consistency ofdisparities. The latter aspect is crucial for 3-D videoconferencing applications, where novelviews of the remote conferees must be synthesised with the correct motion parallax. Thisapplication requires video processing at ITU-Rec. 601 resolution. The algorithm generatesdisparity maps in real time and for both directions (left-to-right and right-to-left) on a PentiumIII, 800 MHz processor with good quality.

KeywordsReal-time disparity analysis, teleconferencing, recursive block-matching, pixel-recursivematching, Census.

1.� INTRODUCTION

This paper presents a novel, real-time disparityalgorithm developed for an immersiveteleconferencing system.Immersive teleconferencing subtends a class ofteleconferencing systems enabling confereeslocated in different geographical places to meetaround a virtual table, appearing at each stationin such a way to create a convincing impressionof presence [Kalawsky 00]. In particular,immersive indicates a setup which completelycovers the angle of view of the visual systemsuch that the boundaries of the station are notvisible. Figure 1 shows an artist’s rendering ofsuch a system. The purpose is to enable theparticipants to make use of rich communicationmodalities as similar as possible to those usedin a face-to-face meeting (e.g., gestures, eyecontact, realistic images, correct sounddirection, etc) and eliminate the limits of non-immersive teleconferencing, which impoverishcommunication (e.g., face-only images inseparate windows, unrealistic avatars, no eyecontact) or skew the participants’ balance (e.g.,some participants appearing larger than others,or in privileged positions on screen. Such asystem is the target of the European IST projectVIRTUE [Schreer00,VIRTUEweb]. The firstdemonstrator, currently under development, is

limited to semi-immersive displays like 60’’plasma monitor or 80’’ rear Projector.

Figure 1. An artist’s rendering of a -immersiveteleconferencing setup.

In the teleconferencing system we aredeveloping, the realism of the images of remoteconferees is maximised through view synthesis[Avidan97]. Two stereo pairs collect images ofeach conferee in each station; from these, 3-Ddisparity maps are computed at frame rate, andused to generate synthetic views of remoteparticipants in the remote stations, adapted tothe viewpoints of the local participants. In thisway, and using physically-plausible viewsynthesis, the image generated is a true image,not an avatar carrying unrealistic artifacts.

A key ingredient in such a system is a modulecomputing reliable disparity maps at frame rate.Requirements are exacting: full resolution videoprocessing according to ITU-Rec. 601;disparity maps in real time; no constraints onparticipants (e.g., clothes, visual markers); andcameras mounted around a wide screen,yielding a wide-baseline stereo geometry, thatis, significant image differences caused by largecamera displacement and different orientations.Figure 2 shows an example.

Figure 2. Example of stereo pair typical for ourapplication. Notice the large viewpoint difference(wide baseline) between the two images.

These requirements are not met in toto byexisting approaches, typically based onhierachical block-matching [Faugeras93] oroptic flow [Barron94]. Wide-baseline stereo hasbeen investigated [Intille94,Pritchett98] but notnecessarily in real-time applicative contexts. Onthe other hand, several real-time stereo systemshave been built around the parallel-cameraconfiguration to minimise computationalcomplexity (see e.g. [Bertozzi97, Faugeras93,Konolige97, Ohm98], [Redert97] for ateleconferencing application, and [Kanade96,Triclops] for other real-time stereo systems).The algorithm proposed in this paper combinesan optimised implementation of Census-basedmatching [Zabih94] with a new, hybridrecursive matching algorithm (HRM). Weachieve real-time disparity maps reduced by afactor of 8 with respect to full-size CCIR601.The attraction of Census-based matching is itslow cost, as only shifts and integer operationsare performed, and improved performance indiscontinuity regions.HRM reaps the advantages of both block-recursive matching and pixel-recursive opticalflow estimation. This algorithm has alreadybeen used successfully for fast motionestimation for format conversion and MPEGcoding [Kauff00,Ohm97] and has recently beenapplied to disparity estimation [Kauff 01].This paper is organised as follows: Section 2reviews briefly the HRM algorithm; Section 3

presents Census-based block matching; Section4 sketches the issues of consistency and post-processing; Section 5 presents someexperimental results; Section 6 summarises anddiscusses our work, and suggests some futuredevelopments.

2.� HYBRID RECURSIVE MATCHING

The structure of the HRM algorithm isillustrated in Figure 3. The Census transformand Hamming distance correlation replace SADin calculating the Displaced Block Difference(DBD) within the block matching stage of theHRM.

update vector

block vector

3 candidate vectors

start vector

pixel-recursionand

clamping ontothe epipolar line

selection ofupdate vector

(smallest DPD)

selection of startvector

(smallest DBD)

selection of finalvector

block vectormemory

right image

left image

Figure 3: outline of HRM algorithm.

The main idea of HRM is to use neighbouringspatio-temporal candidates as input for block-recursive disparity estimation. The rationale isthat such candidate vectors are the most likelyto provide a good estimate of the disparity forthe current pixel. In addition, a further updatevector is tested against the best candidate. Thisupdate vector is computed by applying a local,pixel-recursive process to the current block,which uses the best candidate of block-recursion as a start vector. Apart from aconsiderable reduction of computational load,this method also leads to spatio-temporallyconsistent disparity maps, particularlyimportant as temporal inconsistencies indisparity sequences may cause obvious,annoying artifacts in the final virtual images ofparticipants.The whole algorithm can be divided into threestages (Figure 3):

1.� three candidate vectors (two spatial and onetemporal) are evaluated for the currentblock position by recursive block matching;

2.� the candidate vector with the best result ischosen as the start vector for the pixel-recursive algorithm, which yields an updatevector;

3.� the final vector is obtained by comparingthe update vector from the pixel recursivestage with the start vector from the block-recursive one.

Census matching is used in steps 1 and 3 forblock matching, in lieu of SAD.

2.1 BLOCK RECURSION

Block recursion is performed in the spatial andtemporal directions on the grid of a sparsedisparity vector field, usually with 8x8 or 4x4grid size. To cope with arbitrarily shaped videoobjects and to determine the spatial candidatevectors isotropically, the video frames arescanned in two interleaved, meandering paths,changing their order from frame to frame andguided by a binary mask representing the shapeof the video object [Kauff 01]. Three candidatesare tested to select the best one for the currentblock-vector position (see Figure 4):

•� A vertical predecessor, chosen from theblock above or below, depending onwhether the vertical scan-direction is top-to-bottom or bottom-to-top.

•� A horizontal predecessor, taken from theleft or right neighbour block, depending onthe current horizontal direction of the scanpath.

•� A temporal predecessor, taken from theprevious reference frame.

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The three candidates are compared to find thebest match in the right image for the currentpixel in the left image. In the HRM originalversion, the following shape-driven displacedblock difference (DBD) was taken as criterionfor this purpose, and has been replaced byCensus:

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Notice that no local search around the candidatevector is applied in the block-recursive stage.Thus, if only block-recursive matching wereused, the "best match vector" would always bechosen from the same triple of candidates. Thisworks well where disparities are spatially andtemporally consistent, but fails in the presenceof abrupt changes in the disparity map. Toobviate this problem, the output of the block-recursive stage must be updated permanently.The update is delivered by the pixel-recursivestage, explained in the next section.

2.2 PIXEL RECURSION

Pixel-recursive disparity estimation is a low-complexity method calculating densedisplacement fields using a simplified opticalflow approach. The update vector, d, iscalculated using spatial gradients in the currentframe and the displaced pixel difference DPDgiven by corresponding points in the left andright images as follows:

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where ε describes a so-called convergencefactor and di is an initial displacement. Strictlyspeaking, Eq. (1) must be iterated until aminimum DPD is reached, setting di to theoutput of the previous iteration. However, asthe pixel-recursive stage is only used for

finding an update vector, the followingapproximation is applied:

[ ]Tyxii uuyxDPDyx ,),,(),( ⋅−= ddd (2)

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Experiments have shown that there is nonotable difference between the original opticflow relation in Eq. (1) and its approximation inEq. (2). The threshold value in Eq. (3) isusually set to 2 or 3, and decreases thesensitivity of the pixel recursion to noise inunstructured image regions.

Output vector

Recursive update

Start vector

Start vector Recursion within the blockCurrent pixel

position

Figure 5: outline of the pixel-recursion scheme.

Multiple pixel-recursive processes are started atevery first pixel position of the odd lines in theblock under inspection (an example is shown inFigure 5 with a 4x4 block). Each recursionworks over two lines using left-to-right scan forodd lines and right-to-left scan for even lines.Thus, the total number N of recursions perblock depends on the size of the block, and isgiven by half of the block’s height (i.e., N=2 inthe example from Figure 5, N=4 for 8x8 blocks,etc).With rectified images, pixel recursion is onlyused for the x-component of the disparity vector

in Eqs. (2), (3) and (4). With unrectifiedimages, pixel recursion is carried out for bothcomponents of the disparity vector. Here, the xand y components are processed independentlyof each other; as a consequence, the resultingupdate vector does not necessarily meet theepipolar constraint. Therefore, the update vectoris clamped to the closest pixel position at thecurrent epipolar line after each recursion step.Finally, the vector with the smallest DPDamong all pixel-recursion processes is taken asthe final update vector. After pixel recursion,the DBD is calculated for this selected updatevector and compared to the DBD of the startvector. If the latter is smaller than the one of thestart vector, the update vector is chosen as finaloutput vector, otherwise the start vector fromthe block-recursive stage is retained (see Figure3).

2.3 EPIPOLAR CONSTRAINT

As the HRM algorithm from Figure 1 is used toestimate disparities and since it can therefore beassumed that the cameras of the stereo rig areweakly calibrated, the well-known epipolarconstraint can be exploited to increase matchingrobustness in the given approach. The epipolarconstraint tells us that a pixel mr=[xr,yr,1]T ofthe right image which corresponds to a pixelml=[xl,yl,1]T of the left image, must lie on theepipolar line lr of ml [Zhang 96]:

OUU

7

U ZLWK P)OOP ⋅==⋅ 0 (5)

Here, F denotes the the fundamental matrixrepresenting a compact description of weakcamera calibration.

However, note that in the most general case thetwo components of the gradient vector in Eq.(3) are calculated independently from eachother and do not necessarily meet the epipolarconstraint. One way to correct this is to clampall vectors obtained during pixel recursion ontothe closest position of the correspondingepipolar line. Thus, the update vectors and withit all output vectors subsequently stored in theblock vector memory and used as candidatesduring block recursion (see Fig. 3) now respectthe epipolar constraint.

Another possibility is to rectify the left andright input images before applying the HRM

algorithm from Figure 3. In this case theepipolar lines always coincide with horizontalscan lines of the rectified images [Fusiello97].As a consequence, disparity estimation issimplified to a horizontal match. In this specialcase, only the horizontal component of thegradient in Eq. (3) is calculated and only thehorizontal component in Eq. (2) is updatedwhereas the vertical component is always equalto zero. The epipolar constraint is nowrespected implicitly.

A further alternative to exploit the epipolarconstraint implicitly is the so-called λ-parametrisation which has been proposed by[Alvarez00] in the framework of an anisotropicdiffusion approach to disparity estimation. It isbased on the fact that the disaprity vector can bedecomposed into independent components

71PGPP ⋅+⋅+=+= OOU(6)

Here, N and T denote normalized vectorsperpendicular and, respectively, tangential tothe corresponding epipolar line lr. γ is thedistance from ml to lr and λ is an unknownparameter along the epipolar line. Note that N,T and γ are given by epiolar geometry and canbe calculated in dependence on ml and lr. Usingthis λ-parametrisation the pixel recursion fromEq. (2) can be applied to the scalar λ instead ofdisparity vector d:

[ ] [ ]7\[\[LL XXZZ\['3' ⋅⋅−= ),,(GOO (7)

Here, wx and wy denote to weighting factorsdepending on ml and lr. After pixel recursionthe resulting update vector can be determinedusing Eq. (6).

3.� CENSUS-BASED MATCHING

The original HRM algorithm from Fig. 3 usesthe DBD to select the start vector out of thethree candidates. To combine HRM withcensus-based matching, the algorithm has beenmodified as shown in Fig. 6. For this purposethe two input images are transformed by usingthe Census Transform, and the matchingcriterion adopted is the Hamming distance(HD).

update

block vector

3 candidate vectors

start vector

pixel-recursion +clamping ontoepipolar line

selection ofupdate vector

(smallest DPD)

selection of startvector

(smallest HD)

selection of finalvector

(smallest HD)

block vectormemoryright census

transformed image

left censustransformed image

left image

right image

Figure 6: combination of HRM with CENSUS.

The Census transform [Zabih94] captures thelocal grey-level structure. It maps theneighbourhood of a pixel to a bit stringidentifying the pixels with smaller intensityvalues than the central one. As no intensityvalue is encoded, the representation is largelyimmune to photometric and projectivedistortion, image gain or bias (whether local orglobal) and gamma correction.Assume that the image region to transform is asquare of side , and W is the square correlation(matching) window. Each pixel P in W will bereplaced with the value of the local transform,computed in the region of radius centered atP. Note that the transform is applied to Wseparately in I1 and I2, then the transformedwindows are compared via correlation.If ⊕ denotes concatenation, the Censustransform of a pixel P of image I is defined as

[ ] ),,(,),(

PPIPITPWP

′⊕=∈′

ξβ

,

where

′<

=′otherwise 0

)()( if 1),,(

PIPIPPIξ

and I(P) and I(P’) are, respectively, the intensityvalues at points P and P’. The correlation of thewindow W between the two images I1 and I2 isgiven by

∑ ∑∈ ′∈′

′=WP PWP

PPErrWC),(

),()(β

where the error (dissimilarity) criterion is

),,(),,(),( 21 PPIPPIPPErr ′−′=′ ξξ

Note that the value of Err can be 0, 1 or -1, andthat Err(P,P’) is nonzero just in case P and P’

switch their relative ordering between the twoimages. If ⊗ denotes the Hamming distancebetween two bit strings, i.e., the number of bitsthat differ, the Census transform correlation canbe written as

[ ] [ ]PITPITWC ,,)( 21 ⊗= .

Both steps of this algorithm (Census transform,correlation) are spatially uniform. However,when combined, the resulting method is not: theinfluence of a particular pixel varies dependingon its location, and the farther a pixel is fromthe center of the window, the lower itsinfluence.The attraction of Census-based matching is itslow cost, as only shifts and integer operationsare performed. Our implementation [Zini99]adopts various optimisations to minimise thenumber of operations performed.

4.� CONSISTENCY CHECK

The matching procedure described above isperformed twice (left-to-right and right-to-left),then left-right consistency is applied. Disparityvectors failing the test are rejected and areinterpolated using the surrounding, consistentdisparity vectors.The holes created by this consistency analysisare firstly filled by a 3x3 median filter. Thisprocedure also smooths the disparity map andfilters out outliers. Obviously, the median filtercannot be applied to holes larger than the filtermask. To fill these, a linear interpolation filteris applied in the horizontal direction.Subsequently, a bilinear filter is used togenerate a dense disparity vector field out of thesparse field.

5.� EXPERIMENTAL RESULTS

The benefits of the Census transform within theHRM framework have been tested on the basisof a segmented and rectified input sequence, ofwhich a stereo pair is shown in Figure 7.

Figure 7: input stereo pair after figure-background segmentation and rectification.

Figure 8 shows the disparity maps obtainedfrom the combined HRM and Census algorithm(Figure 6). The black regions show areas ofinconsistent disparities.

Figure 8: left-to-right and right-to-left disparitymaps after consistency check.

Figure 9 shows the same disparity maps aftermedian filtering and interpolation. The holesc\aused by the inconsistency check are nowfilled. Note that the disparity maps are spatially(and temporally) consistent in areas ofhomogeneous depth, and rapid depth transitionsaround the arms have been found accurately.Synthesis results based on this disparity mapsshow good quality.

Figure 10: Final disparity maps after medianfiltering and interpolation.

To quantify the benefit of Census Transform inthe given framework, we compared the HRMwith and without CT on the basis of computersimulations. Two criteria have been used forthis comparison: the percentage of consistent

disparities and the delta of the consistencycheck. Figures 11 and 12 plot the two criteria,respectively, against frame number. The greycircles refer to the original HRM algorithm(called SAD here), the black squares to theCensus matching version. Both graphs showthat CENSUS matching improves performance.More detailed comparisons (not reported here)also show that the combination of HRM withCensus matching gives better results especiallyin critical regions, such as areas of low textureor close to borders of segmented objects (e.g.,arm contours in Figure 7).

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6.� CONCLUSIONS AND FUTURE WORK

We have presented a real-time matchingalgorithm combining Census matching with ahighly efficient pixel-recursive scheme.Experiments with stereo sequences from thetarget application (immersive teleconferencing)indicate that the combined algorithm performsbetter than the original pixel-recursive one. Thealgorithm is being incorporated in the firstdemonstrator of an immersive teleconferencingsystem developed for by EU VIRTUE project.

As to future technical work, we areinvestigating a different kind of parametrisationfor estimating the epipolar geometry, calledlambda parametrisation. Experiments are alsounder way with a novel, robust detector ofocclusion contours using registered disparitymaps and intensity data.

ACKNOWLEDGMENTSThis work is partially supported by the Ministryof Science and Technology of the FederalRepublic of Germany, Grant-No.01 AK 022,and by the EU project VIRTUE (Framework V,IST). Thanks to Emile Hendriks, FrancescoIsgro‘ and Bang-Jun Lei for many usefuldiscussions.

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