Grouping Dominant Orientations for Ill-Structured Road Following

Christopher Rasmussen

Dept. Computer & Information SciencesUniversity of Delaware

Newark, DE 19716

Abstract

Many rural roads lack sharp, smoothly curving edgesand a homogeneous surface appearance, hampering tra-ditional vision-based road-following methods. However,they often have strong texture cues parallel to the roaddirection in the form of ruts and tracks left by other ve-hicles. In this paper, we describe an algorithm for fol-lowing ill-structured roads in which dominant textureorientations computed with multi-scale Gabor waveletfilters vote for a consensus road vanishing point loca-tion. In-plane road curvature and out-of-plane undula-tion are estimated in each image by tracking the van-ishing point indicated by a horizontal image strip asit moves up toward the putative vanishing line. Par-ticle filtering is also used to track the vanishing pointsequence induced by road curvature from image to im-age. Results are shown for vanishing point localizationon a variety of road scenes ranging from gravel roadsto dirt trails to highways.

1 Introduction

Many complementary strategies for visual road follow-ing have been developed based on certain assumptionsabout the characteristics of the road scene. For ex-ample, edge-based methods such as those described in[1, 2, 3] are often used to identify lane lines or roadborders, which are fit to a model of the road curvature,width, and so on. These algorithms typically work beston well-engineered roads such as highways which arepaved and/or painted, resulting in a wealth of high-contrast contours suited for edge detection. Anotherpopular set of methods for road tracking are region-based [3, 4, 5, 6]. These approaches use characteristicssuch as color or texture measured over local neighbor-hoods in order to formulate and threshold on a likeli-hood that pixels belong to the road area vs. the back-ground. When there is a good contrast for the cuechosen, there is no need for the presence of sharp or

(a)

(b)

Figure 1: (a) Desert road from DARPA Grand Chal-lenge example set (with vanishing point computed asin Section 2.2); (b) Canny edges of same scene

unbroken edges, which tends to make these methodsmore appropriate for unpaved rural roads. Of course,the contrast between, for example, the road color andthe background color tends to change over time, neces-sitating adaptation of the discriminant function [7]

Most road images can be successfully interpretedusing a variant of one of the two above approaches.Nonetheless, there are some scenes that possess neitherstrong edges nor contrasting local characteristics. Fig-

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ure 1(a) shows one such road (the cross has been addedby our algorithm and is explained in Section 2.2). Thisimage is from a set of “course examples” made avail-able to entrants in the 2004 DARPA Grand Challenge,an autonomous cross-country driving competition [8][DARPA air-brushed part of the image near the hori-zon to obscure location-identifying features]. There isno color difference between the road surface and off-road areas and no strong edges delimiting it, as the out-put of Matlab’s Canny function shows in Figure 1(b).The one characteristic that seems to define the roadis texture, but not in a locally measurable sense, be-cause there are pebbles, shadows, and stripes every-where. Rather, one seems to apprehend the road easilybecause of its overall banding pattern. This banding,presumably due to ruts and tire tracks left by previ-ous vehicles driven by humans who knew the way, isaligned with the road direction and thus most appar-ent because of the strong grouping cue imposed by itsvanishing point.

A number of researchers have used vanishing pointsas global constraints for road following or identificationof painted features on roads (such as so-called “zebracrossings,” or crosswalks) [9, 10, 11, 12]. Broadly, thekey to the approach is to use a voting procedure likea Hough transform on edge-detected line segments tofind points where many intersect. Peaks in the votingfunction are good candidates for vanishing points. Thisis sometimes called a “cascaded” Hough transform [13]because the lines themselves may have first been iden-tified via a Hough transform. Similar grouping strate-gies have also been investigated outside the context ofroads, such as in urban and indoor environments rich instraight lines, in conjunction with a more general anal-ysis of repeated elements and patterns viewed underperspective [14, 15].

All of the voting methods for localizing a road’s van-ishing point that we have identified in the literatureappear to be based on a prior step of finding line seg-ments via edge detection. Moreover, with the exceptionof [12] (discussed below), vanishing-point-centric algo-rithms appear not to deal explicitly with the issue ofroad curvature and/or undulation, which remove thepossibility of a unique vanishing point associated withthe road direction. Both of these limitations are prob-lematic if vanishing point methods are to be appliedto bumpy back-country roads like the desert scene dis-cussed above.

In this paper we present a straightforward methodfor locating the road’s vanishing point in such difficultscenes through texture analysis. Specifically, we re-place the edge-detection step, which does not work onmany such images because the road bands are too low-

frequency to be detected, with estimates of the domi-nant orientation at each location in the image. Thesesuffice to conduct voting in a similar fashion and finda vanishing point.

We also add a second important step to deal withroad curvature (both in- and out-of-plane), which isthe notion of tracking the vanishing points associatedwith differential segments of the road as they are tracedfrom the viewer into the distance. By integrating thissequence of directions, we can recover shape informa-tion about the road ahead to aid in driving control.The method is easily extended to temporal tracking ofthe vanishing point over sequences of images.

A related idea was proposed for planar texture anal-ysis using “spectral voting” in [16], but only tested onsynthetic images with no curvature. Another relatedpiece of work is the CMU RALPH road follower [17].Their system also exploits texture within the road in-cluding tracks, drips, and lane lines, but it works bya different mechanism: for every frame, a small set ofin-plane curvatures are hypothesized and one is chosenthat best fits the image.

2 Methods

There are three significant components to the roadfollowing algorithm, which we describe in the follow-ing subsections. First, a dominant texture orientationis computed at every image pixel. Second, assuminga straight, planar road, all dominant orientations inthe image vote for a single best road vanishing point.Third, if the road curves or undulates a series of van-ishing points for each tangent direction along the roadmust be estimated. For a sequence of road images wemust also estimate the deformation of this vanishingpoint contour from image to image.

2.1 Dominant orientation estimation

The dominant orientation θ(p) at pixel p = (x, y) of animage is the direction that describes the strongest localparallel structure or texture flow. This is of course ascale-dependent measure. As we will explain in moredetail in the next subsection, precise estimates of thedominant orientations are crucial in order to obtainsharp peaks in the voting objective function and henceaccurately localize the vanishing point. There is a con-siderable body of work on estimating dominant orien-tations. For example, we may apply a bank of multi-scale, oriented filters such as steerable filters [18] andanalyze the maximum responses. Another approachis to generate a Gaussian pyramid of the image, useprincipal components analysis on the set of gradients

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within a small window to obtain a consensus directionat each scale, and then interpolate [19].

We experimented with several approaches to localorientation estimation, including that of [19], and ob-served the most qualitatively accurate results on a widevariety of road images with a bank of Gabor waveletfilters [20]. Gabor wavelet filters essentially perform aGaussian-windowed Fourier analysis on the image viaconvolution with a set of kernels parametrized by ori-entation θ, wavelength λ, and odd or even phase. Togenerate a k × k Gabor kernel (we use k = b 10λπ c), wecalculate:

ĝodd(x, y, θ, λ) = exp[−1

8σ2(4a2 + b2)] sin(2πa/λ) (1)

where x = y = 0 is the kernel center, a = x cos θ +y sin θ, b = −x sin θ + y cos θ, σ = k9 , and the “sin”changes to “cos” for ĝeven. The actual convolution ker-nel g is then obtained by subtracting ĝ’s DC component(i.e., mean value) from itself and normalizing the resultso that g’s L2 norm is 1.

To best characterize local texture properties includ-ing step and roof edge elements at an image pixelI(x, y), we examine the standard “complex response”of the Gabor filter given by Icomplex(x, y) = (godd ∗I)(x, y)2 +(geven ∗ I)(x, y)2 for a set of n evenly spacedGabor filter orientations. The dominant orientationθ(x, y) is chosen as the filter orientation which elicitsthe maximum complex response at that location.

With a priori knowledge of the distribution of actual(3-D) road texture wavelengths λroad, the camera focallength, and the pitch or tilt angle of the camera with re-spect to the ground plane, the distribution of perceivedroad texture wavelengths in the image λimage could beestablished. This information would allow a principledchoice of a range of filter wavelengths to run at eachimage location and weights for combining them, withlarger-scale filters being applied toward the bottom ofthe image and finer filters used closer to the horizonline.

However, in this work the testing images were cap-tured by a variety of uncalibrated cameras mountedwith unknown height and tilt. Furthermore, the datacontain a number of significant departures from theplanar ground assumption. Based on empirical obser-vation of performance using 4 octave-separated wave-lengths both independently and in combination, wefound that a single wavelength related to the image di-mensions by an ad hoc scaling factor gave good resultsat a significant computational savings vs. multi-scaleschemes. Thus for all of the results in this paper we usea Gabor filter wavelength of λ = 2blog2(w)c−5, where wis the width of the input image. For 720 × 480 and

Figure 2: Dominant orientations (subsampled) fordesert image

640 × 480 images, for example, this results in λ = 16and a kernel size of 50× 50.

A large number of orientations (e.g., n = 72) werenecessary to achieve superior angular resolution forθ(p) given the voting method described in the next sub-section. Performing this many convolutions per imagewith such large kernels is obviously computationallyexpensive. Nonetheless, we found that using the con-volution theorem and the FFTW Fourier transform li-brary [21] allows dominant orientations to be obtainedwith adequate speed. For example, calculating θ(p)for every pixel in a 160× 120 image with n = 72 takes∼130 ms on a 3.0 GHz Pentium IV (the same machineis used for all speed figures in this paper).

An example of the dominant orientations computedover a sparse grid of locations is shown in Figure 2 forthe desert road image.

2.2 Vanishing Point Voting

For a straight road segment on planar ground, there isa unique vanishing point associated with the dominantorientations of the pixels belonging to the road. Curvedsegments induce a set of vanishing points (discussedbelow). Though road vanishing points may lie outsidethe field of view (FOV) of the road-following camera,it is reasonable to limit our search to the area of theimage itself if the following conditions are met: (1)The camera’s optical axis heading and tilt are alignedwith the vehicle’s direction of travel and approximatelylevel, respectively; (2) Its FOV is sufficiently wide toaccomodate the maximum curvature of the road; and(3) The vehicle is roughly aligned with the road (i.e.,road following is proceeding successfully).

Furthermore, we assert that for most road scenes, es-pecially rural ones, the vanishing point due to the roadis the only one in the image. In rural scenes, there is

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very little other coherent parallel structure besides thatdue to the road. The dominant orientations of muchoff-road texture such as vegetation, rocks, etc. are ran-domly and uniformly distributed with no strong pointsof convergence. Even in urban scenes with non-roadparallel structure, such texture is predominantly hori-zontal and vertical, and hence the associated vanishingpoints are located well outside the image.

In the following subsections we describe methodsfor formulating an objective function votes(v) to eval-uate the support of road vanishing point candidatesv = (x, y) over a search region C roughly the size ofthe image itself, and how to efficiently find the globalmaximum of votes.

2.2.1 Objective function

The possible vanishing points for an image pixel p withdominant orientation θ(p) are all of the points (x, y)along the line defined by (p, θ(p)). Because our methodof computing the dominant orientations has a finiteangular resolution of nπ , uncertainty about the “true”θ(p) should spread this support over an angular inter-val. Thus, if the angle of the line joining an image pixelp and a vanishing point candidate v is α(p,v), we saythat p votes for v if the difference between α(p,v) andθ(p) is within the dominant orientation estimator’s an-gular resolution. Formally, this defines a voting func-tion as follows:

vote(p,v) ={

1 if |α(p,v)− θ(p)| ≤ n2π0 otherwise (2)

This leads to a straightforward objective functionfor a given vanishing point candidate v:

votes(v) =∑

p∈R(v)

vote(p,v) (3)

where R(v) defines a voting region. For straight, flatroads, we set R(v) to be the entire image, minus edgepixels excluded from convolution by the kernel size, andminus pixels above the current candidate v.

Only pixels below the vanishing line l implied byv are allowed to vote because support is only soughtfrom features in the plane of the road (though in urbanscenes out-of-plane building features, etc. may corrob-orate this decision [11]). This reduces ambiguity in thevoting objective function and speeds the voting com-putation somewhat. A possible effect of this choice is abias of votes toward higher image locations (since lowerones have fewer voters “eligible” to support them), butwe have not found this to be an issue in practice.

Figure 3: Votes for vanishing point candidates (top 3/4of image in Figure 1(a))

In this work, we assume that l is approximatelyhorizontal. Other researchers have inferred l for roadand urban scenes by computing a second vanishingpoint obtained with either another set of parallel lines[13, 10, 16] or the cross ratio of equally spaced lines[10]. The road scenes we are considering have insuffi-cient structure to carry out such computations.

We did not find that variations on the voting func-tion vote such as weighting p’s vote by the strength ofthe filter response at θ(p) or the anisotropy of the fil-ter response over all angles at p improved the accuracyof vanishing point localization. An obvious alternativecriterion, the point-to-line distance between a candi-date v and the ray defined by θ(p), was considered,but it performed poorly when there were few votersnear the candidate. This occurred, for example, whenthe vanishing point was occluded by a vehicle furtheralong the road.

An example of votes computed at a 1-pixel resolu-tion over C = the top three-fourths of the image inFigure 1(a) (where the maximum vote-getter vmax isindicated with a cross) is shown in Figure 3.

2.2.2 Computational considerations

An efficient alternative to arithmetic computation ofEquation 2 results from noting that the voting proce-dure is equivalent to rasterizing one thin isosceles “tri-angle of votes” per voter defined by p, θ(p), and n in anadditive accumulation buffer A in which each pixel is avanishing point candidate v. After drawing every votetriangle, the pixel in A (which represents C at a fixedresolution) with the maximum value is vmax . This kindof raster voting can be conducted very quickly (espe-cially on graphics hardware) vs. the slower dot productvoting method described above. For example, votingcan be carried out (given the dominant orientations)with every pixel in a 160×120 image as a voter in ∼35

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ms even with no graphics card acceleration1.For dot product voting, an exhaustive search over C

for the global maximum of votes of the type necessaryto generate Figure 3 is costly and unnecessary. Rather,a hierarchical scheme is indicated in order to limit thenumber of evaluations of votes and control the preci-sion with which vmax is localized. Because it integrateseasily with the tracking methods described in the nextsubsection, we perform a randomized search by carry-ing out a few iterations of a particle filter [22] initializedto a uniform, grid-like distribution over C (with spac-ing ∆x = ∆y = 10). Exhaustive search adds little tothe cost of raster voting, however. Overall, the van-ishing point can be robustly estimated for 160 × 120images with raster voting at roughly 6 fps, making ve-hicle control at the moderate speeds appropriate on ill-structured roads viable. For a slight accuracy penaltythe frame rate can be pushed up to real-time with votersubsampling, smaller n, etc.

2.3 Tracking the Vanishing Point

Road curvature and/or non-planarity result in a setof different apparent vanishing points associated withdifferent tangents along the section of road seen bythe camera. Therefore the procedure of the precedingsubsection, which assumes a unique vanishing point,must be modified to estimate the sequence of vanish-ing points which correspond to differential segments ofroad at increasing distances from the camera. Further-more, over a sequence of images gathered as the cam-era moves along the road, the vanishing point contourthus traced for a single image must itself be trackedfrom frame to frame.

2.3.1 Road curvature in one image

Suppose the spine of the approaching road section thatis visible to the camera is parametrically defined by anonlinear space curve x(u), with increasing u indicat-ing greater distance along the road. If x(u) lies entirelyin one plane then the image of these vanishing pointsv(u) is a 1-D curve on the vanishing line l. If x(u) isnot in the plane, then the vanishing line varies with dis-tance according to l(u) (still assumed to be horizontal)and v(u) is a 2-D curve.

We cannot directly recover v(u) since x(u) is un-known. However, u is a monotonically increasing func-tion of the image scanline s, where s = 0 is the bottomrow of pixels, so we can attempt to estimate the closely

1For the raster voting results in this paper, the vote trianglesare approximated by lines, and A has a bit-depth of 8, both ofwhich can lead to some artifacts

related curve v(s). This implies modifying Equation 3to

votes(v(s)) =∑

p∈R(v,s±∆)

vote(p,v) (4)

where R(v, s±∆) is now a differential horizontal stripof voting pixels centered on scanline s. Smaller valuesof the height of the strip 2∆ yield a more accurate butless precise approximation of the road tangent (∆ ≈0.1h, where h is the image height, for the results in thispaper). s is iterated from 0 until vmax (s) ∈ R(v, s±∆)(roughly the point where the strip crosses the vanishingline).

A strip-based approach to vanishing point detectionfor curvature estimation was also used in [12] for edge-detected road boundaries and lane lines, but with onlya few non-overlapping strips. The resolution of theirapproach would be improved with overlapping strips,as we use.

Furthermore, we do not simply estimate a best van-ishing point fit vmax (s) for every s independently byrerunning the full randomized search over C as de-scribed in the previous subsection. Rather, we trackthe vanishing point by continuing to run the particlefilter with weak dynamics p(v(s) |v(s−1)) (e.g., a low-variance, circular Gaussian). This allows a more accu-rate estimate of vmax (s) because of the concentrationof particles already in the solution area, and reducesthe chance of misidentification of the vanishing pointdue to a false peak somewhere else in the image.

The vanishing point of each strip s implies a tangentto the image of the road curve at s. By hypothesiz-ing an arbitrary point on the road, we can integratethis tangent function over s (i.e., with Euler steps) andthereby trace a curve or “flow line” followed by theroad point. This procedure is illustrated in the nextsection.

2.3.2 Image sequences

As the vehicle travels down the road, the perceivedroad shape changes over time t according to x(u, t). Asimplification that nonetheless works fairly well is toignore road curvature within a single image and justtrack the global vanishing point vmax of the entire im-age from frame to frame.

However, following the analysis from the precedingsubsection, we are interested how the vanishing pointcontour v(s, t) depends on its shape v(s, t − 1) at theprevious time step. A straightforward approach is tocarry forward the start of the curve v(0, t−1) with sometemporal dynamics to “seed” the tracker in the next

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(a) (b)

(c) (d)

(e) (f)

Figure 4: Computed vanishing points using the entireimage as the voting region (dot product voting)

frame at v(0, t) and then track points along the van-ishing point contour as described above. It is much lessefficient and effective to track the state of the vanish-ing point contour as a whole by sampling entire curvesbecause of the high dimensionality of the state space.

3 Results

Straight roads Vanishing point localization bydominant texture orientation voting worked robustlyon predominantly straight roads with a wide varietyof surface characteristics. Results on 720 × 480 DVcamera images captured on a variety of roads at Ft.Indiantown Gap, PA (the “FITG” data) are shownin Figure 4. Here dot product voting was used, thevoters were decimated by half vertically and horizon-tally within R, and the particle filter-based search used∼600 particles. None of the dirt road examples in Fig-ures 4(a)-(d) are truly straight or level, so some appar-ent discrepancies are due to these departures from theassumption. Although the algorithm was formulatedespecially for heavily banded roads, as Figures 4(e) and(f) show, it also works with mostly homogeneous as-phalt roads by utilizing the few edges that are present

in a manner similar to the edge-based methods de-scribed in the introduction.

Results on a more extensive group of scenes areshown in Figure 5. 16 illustrative images (the “Mojave”data) were chosen from a large set of high-resolutiondigital photographs taken on a scouting trip along apossible Grand Challenge route in the Southern Cal-ifornia desert. The algorithm was run on resampled320×240 versions of the images using raster voting andparticle-based search; the figure shows the computedvmax for 12 of the 16 images with a green cross. To as-sess the algorithm’s performance vs. human perceptionof the vanishing point location, we invited ∼ 30 mem-bers of the UD computer science department to partic-ipate in a web-based study. Subjects were given a shortdefinition of road vanishing points, shown two differentexample images with the vanishing point marked, andasked to click where they thought the vanishing pointwas in 640 × 480 versions of each of the 16 Mojaveimages. 16 subjects completed the study; 11 of their256 choices (4.3%) were manually removed as obviousmisclick outliers. The figure indicates the distributionof human choices with red 3σ error ellipses, most ofwhich were fairly tight. The mean (median) positionaldifference at the 320×240 scale between our algorithm’sestimates and the human choices was 7.8 pixels hori-zontally (5.3) and 8.0 pixels vertically (4.6).

Curved roads Examples of tracking the vanishingpoint for curved, non-planar roads from the FITG dataare shown in Figures 6(a) and (b) (again using dotproduct voting). The yellow contour indicates the traceof the estimated vanishing point positions as the scan-line s was incremented and the set of voters changedto points farther along the road. Horizontal movementof the vanishing point is of course proportional to left-right road curvature, and vertical movement indicatesa rise or dip in the road. Thus we see that the road inFigure 6(a) is relatively level with a slight dip in themiddle, which is correct. On the other hand, the van-ishing point for the road in Figure 6(b) rises, indicatingan approaching hill.

A more intuitive interpretation of the vanishingpoint motion can be obtained by simply integrating theimplied tangent to the image of the road curve (the linejoining any point on scanline s with its vanishing pointv(s)) for a few sample points. These are the green con-tours, or “flow lines,” in the images in Figures 6. Thesecurves are not meant to indicate the width of the road,for no segmentation has been carried out, but ratheronly to illustrate the structure of the terrain that theroad ahead traverses.

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Figure 5: Computed vanishing points (raster voting) are shown as crosses, with Gaussian fits of a set of humanresponses marked with ellipses

Image sequences Vanishing point samples from theparticle filter tracking a global vanishing point over adifficult sequence of images from the FITG data areshown in Figure 7 (the images were subsampled to360× 240 and dot product voting was used for this se-quence). Near the start of the sequence, in Figure 7(a),the particles are coalescing around a consensus vanish-ing point after starting in a uniform distribution overthe image. The cluster of particles tightly follows theroad vanishing point despite a number of turns andbumps, and continues to track it even in the poorlydefined area of Figure 7(d).

4 Conclusion

We have presented an algorithm for road following thatat its most basic level relies on road texture to identifya global road vanishing point for steering control. Byspatially partitioning the voting procedure into stripsparallel to the vanishing line and tracking the results,we can estimate a sequence of vanishing points forcurved road and recover road structure through inte-gration. With no training, the system is robust to avariety of road surface materials and geometries, andit runs quickly enough for real vehicle control.

One algorithmic component that we have not dis-cussed here regards road segmentation. The estimatedroad curvature alone does not provide informationabout the vehicle’s lateral displacement that would al-low centering–for this we need estimates of the leftand right road boundaries. The ”flow lines” describedabove provide a powerful constraint by indicating theshapes these edges might take at hypothetical image lo-cations. This allows the road segmentation task to beformulated as simply a 2-D search for a pair of flow lineswhich maximize the difference of some visual discrimi-nant function inside the road region vs. outside it. Weare currently experimenting with using this constraintwith discriminant functions based on color as well asthe local density of pixels that voted for vmax .

5 Acknowledgments

Portions of this work were supported by a grant fromthe National Institute of Standards & Technology. TheMojave data was generously provided by Caltech’sGrand Challenge team.

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(a)

(b)

Figure 6: Tracks of vanishing point (yellow) for curvedroad and induced road “flow lines” (green)

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IntroductionMethodsDominant orientation estimationVanishing Point VotingObjective functionComputational considerations

Tracking the Vanishing PointRoad curvature in one imageImage sequences

ResultsConclusionAcknowledgments