Reconstructing Vehicle Motion from Conceptual Description

Conceptual Description of Vehicle Motion

Conceptual Descriptions of a visual scene result in considerable loss of quantitative data but contains valuable information which may be useful in deciding on courses of action, on generating Natural Language Descriptions, or in validating the correctness of the analysis. Earlier attempts at reconstruction (Nagel/Haag/Jeyakumar/Mukerjee:1999), used very simple assumptions leading to wide positional errors in the reconstruction. In this work, we use an improved model which permits more flexible matching with the conceptual descriptions and also uses more aspects of the data than were being used before. The following attributes are used to generate the synthetic image sequence:

• Fuzzy description of the vehicle's velocity. Six fuzzy values are used : very fast, fast, normal, small, very_small and null. Each conceptual attribute implies that velocity is most likely to be in a certain range. Conceptual attributes are available for each frame, every 1/50th of a second.
• Lane Duration: How long is the vehicle in a particular lane. This information is integrated with the lane length, which is known from the road geometry to constrain the reconstructed velocity of the vehicle.
• Validity of conceptual description. Each attribute (velocity, lane) is given a measure of confidence during conceptual description generation. This can be used to obtain more reliable reconstructions.

FUZZY MEMBERSHIP FUNCTION : In the conceptual description, velocity has been abstracted using the above graph. (For more information on the image processing and conceptual description generation process, see http://i21www.ira.uka.de/tutorium/ ) from which the above figure is taken.

TEMPORAL SMOOTHING

The current work improves on a number of deficiencies on the previous model [Jeyakumar 1999]:

• Previously, the velocity was set at the mean value in the velocity range. This led to jerky motion and led to wide errors in the reconstruction.
• The model was not using past information in reconstructing the current velocity. The current model incorporates past position and velocity information for smoother motion.
• The present model has the further option of improving the match by using future knowledge - e.g. when is the vehicle reaching the end of the lane?

As is expected, the SIS generated by the present model is closer to the OIS than the prevoius model.

FIGURE 1: Velocity Time Graph based on [Jeyakumar 99]. Here the velocity changes discontinuously based on the dominant conceptual description. This description may be changing frequently, resulting in sharp fluctuations in velocity (breaks within each interval).

FIGURE 2. Smoothed Velocity Time graph for the same data set as above. This time graph incorporates all the three temporal smoothing measures.

The Mathematical Desccription

The time period has been divided into intervals during which all conceptual attributes are the same. When the velocity transitions from one value to another, a simple model is to consider a ramp-up interval, a constant velocity interval, and a ramp-down interval to the next velocity. Here sine functions are used for the ramp intervals to ensure high-order continuity at both ends.

To find velocity during the beginning and end of the region a sine-curve is used.Thus, the continuity of velocity and acceleration is maintained (which should be as force applied cannot be discontinuous). The value of velocity, during the transision from t_(i-1)max to t_(i)min

v(t) = amplitude*sin(omega*t + phi) for t_(i-1)max < t < t_(i)max
where

amplitude = (c_i - c_i-1)/2
omega = 2*pi/((1-alpha)*(t_(i)max - t_(i)min + t_(i-1)max- t_(i-1)min))
phi = -omega*t_(i)min

Velocity-Transition Graph: Nomenclature. Velocity (along y-axis) is shown varying with time. Intervals between vertical lines are constant-attribute intervals. The velocity reconstruction (red curve) involves a constant part at the centers of each interval, and sine curves interpolating between these values. When future knowledge is to be incorporated, the curve can be shifted so that the total distance traveled matches at landmark points such as road boundaries (green lines).

Incorporating Future plans: Using The Lane Data

The velocity function which we get above has a variable c_i whose value can be adjusted better by integrating velocity over the period when the vehicle is in a given lane, and matching it to the lane length. If the integrated value does not match, a suitable shift is given to the the c_i's in this interval so as to obtain a better match.

Use of Validity

The above model leads to a problem where the actual velocity is close to a transition point so that the dominant conceptual description is switching rapidly between two ranges. Here the velocity tends to oscillate rapidly between the two reconstructions (FIGURE).

Rapid oscillations are seen where the conceptual description fluctuates rapidly (the interval can be as low as tenth of a second). This can be smoothed by smoothing such multiple-validity cases over a longer time interval.

Usually in these situations, the velocity description has non-zero validity in these two ranges. Short-duration intervals are thus integrated with the previous intervals, resulting in a smoother velocity function.

The results are presented below with superimposition of the new reconstruction on the Original Image Sequence (OIS).

Comparison Of Previous And Present Model

FIGURE. Reconstructions shown superimposed on the actual images. New reconstruction is shown in Blue and the previous model based on Jeyakumar is in purple. In the subsequent sequence (below) the previous reconstruction (purple) is seen to be shooting ahead of the original car. The new reconstruction (blue) incorporates both past and future motion history and integrates it for lane duration, it results in a much better fit. The error is still quite high near the stop line, after which the original vehicle accelerates rapidly. It is possible that this type of behaviour can be learned using human-like driving models. Data is shown for every 200th-frame (4 seconds).

CONCLUSION

The error is still quite high near the stop line, after which the original vehicle accelerates rapidly. In the next model, human driving behaviour aspects (Gupta, Chakraborty, and Mukerjee 1998) will be integrated into the reconstruction, resulting in more appropriate behaviour in relations to other cars, lanes, and special situations such as traffic lights.

REFERENCES

1. Jeyakumar, V., Generation of Synthetic Image sequences for car maneuvers extracted from image sequence evaluation, M.Tech. Thesis, April 1999.
2. Nagel, H.-H., M. Haag, V. Jeyakumar, and A. Mukerjee, Visualization of Conceptual Descriptions Derived from Image Sequences. DMGR 1999.
3. Gupta, Shami; Chakrabarty, Partha; and Amitabha Mukerjee; 1998 Microscopic simulation of vehicular traffic on congested roads Proceedings ISIRS-98, ed. M. Vidyasagar, Tata McGraw Hill, Bangalore, January 10-13, 1998.