Vision-based ACC with a Single Camera: Bounds on ... - Mobileye

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We have built a monocular visual processing system targetedfor mass production over a wide range of applications.Fig. 1 shows the camera mounted near the rear-view mirror.The prototype processing box used at this stage of developmentis <strong>based</strong> on the PPC7410 processor. 2 . The systemruns at 10 frames per second and performs target detection(vehicles and motorcycles) in the lane and adjacent lanes,lane mark detection and following, lane departure warningand cut-in calculation using optic-flow analysis. Finally, tobe used for control, it determines the range and range rateinformation about the target vehicles.Of the many task required by the vision sensor this paperwill focus on the issue of determining the range and rangerate. After discussing the methods for computing range andrange rate we provide an analysis of the accuracy of thosemeasurements. Finally we show some results taken duringclosed loop operation and we compare those results to measurementsusing Radar.2 RangeSince we have only a single camera we must estimate therange using perspective. There are two cues which can beused: size of the vehicle in the image and position of the bottomof the vehicle in the image. Since the width of a vehicleof unknown type (car, van, truck etc) can vary anywherebetween 1.5m and 3m a range estimate <strong>based</strong> on width willonly be about 30% accurate. It can be used as a sanity checkand possibly to check out-of-calibration but it is not goodenough for actuation control.A much better estimate can be achieved using the road geometryand the point of contact of the vehicle and the road.We will at first assume a planar road surface and a cameramounted so that the optical axis is parallel to the road surface.A point on the road at a distance Z in front of thecamera will project to the image at a height y, where y isgiven by the equation:y = f H Zwhere H is the camera height in meters.Figure 2 shows a diagram of a schematic pinhole cameracomprised of a pinhole (P) and an imaging plane (I) placedat a focal distance (f) from the pinhole. The camera ismounted on vehicle (A) at a height (H). The rear of vehicle(B) is at a distance (Z 1 ) from the camera. The point ofcontact between the vehicle and the road projects onto theimage plane at a position (y 1 ). The focal distance ( f ) andthe image coordinates (y) are typically in mm and are drawnhere not to scale.2 The serial production hardware is <strong>based</strong> on a system-on-chip calledEyeQ — more details in http://www.mobileye.com(1)Figure 1: Two pictures of the compact monocular cameramounted near the rear-view mirror.Equation 1 can be derived directly from the similarity of triangles:y f= H Z. The point of contact between a more distantvehicle (C) and the road projects onto the image plane at aposition (y 2 ) which is smaller than (y 1 ).The camera electronics converts the image coordinates frommm to pixels and inverts the image back to the upright positionfor processing. Figure 3 shows an example sequence ofa truck at various distances. The distance from the horizonline to the bottom of the truck is smaller when the truck ismore distant (a) than when it is close (b and c).To determine the distance to a vehicle we must first detectthe point of contact between the vehicle and the road (i.e.the wheels) and then we can compute the distance to thevehicle:Z = f H y . (2)In practice the camera optical axis is not aligned parallel tothe road surface. Thus the horizon line is not in the center
Iy1y20A B CPfHHHZ1Z2Figure 2: Schematic diagram of the imaging geometry (see text).of the image. Both the mounting angle and the change inpitch angle due to vehicle motion can be determined by themethod described in [5]. The non-planarity can be compensatedfor to a first order by analyzing the lane markings [6].After compensating for the camera angle and road slope themain source of error is in determining the image coordinatesof contact point between the vehicle and the road. In practice,this point can be found to <strong>with</strong>in 1 pixel.The error in range Z err due to an error of n pixels in locationof the contact point is:Z err = Z n − Z =f Hy + n − Z =Typically n ≈ 1 and f H >> nZ so we get:Z err ≈ nZ2f Hf Hf HZ + n = nZ2f H + nZWe see that the error increases quadratically and as the distanceto the target increases the percentage error in depth) increases linearly.( Z errZExample: In our case a 640x480 image <strong>with</strong> a horizontalFOV of 47 o gives f = 740pixels. The camera height at H =1.2m. Thus assuming 1 pixel error, a 5% error in depth isexpected at a distance of:Z = Z errZ(3)(4)f H = 0.05 ∗ 740 ∗ 1.2 = 44m. (5)The error at 90m will be around 10%. These values aresufficient for <strong>ACC</strong>. The headway distance depends on thevehicle speed and the driver comfort setting and is typicallyless than 45m. A 5% error at 45m is well below the errorof a human driver and is not significant. What is importantis the range rate or relative velocity. In layman’s terms, itis not important whether the target is at 45m or 42m. It isimportant to know whether we are maintaining a constantdistance.3 Range RateWith a radar system range rate or relative velocity can bemeasured using doppler effect. With a vision system it iscomputed from the discrete differencing:v = ∆Z∆t . (6)Subtracting two noisy values for Z at two different timepoints cannot produce accurate measurements. We will firstshow (in sec. 3.1) how ∆Z can be computed from the scalechange (s), that is the change in image size, and the range(Z). We will then show (in sec. 3.2) how the discrete differenceintroduces an error for non infinitesimal ∆t whichlimits our accuracy. We also show how to achieve the optimalvalue for ∆t.3.1 Computing Range Rate from Scale ChangeLet W be the width (or height) of the target vehicle in meters,and let w and w ′ be the width (or height) in the imagein pixels when the target vehicle is at distances Z and Z ′respectively. As in equation (1):Then:v = ∆Z∆t = Z′ − Z=∆tLet us define:and we get:w = fW Zw ′ = fW Z ′ .f HZ ′− f H Z∆t= f H w−w′w ′ w∆t= Z w−w′w ′∆t(7)(8)s = w − w′w ′ (9)v = Zs∆t(10)
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Vision-based ACC with a Single Camera: Bounds on ... - Mobileye

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