Atmospheric Image Formation Model | Detection Methods and Collision Avoidance
Atmospheric Image Formation Model:
A Sense and Avoid system which is capable of operating in Visual Flight Rules (VFR) conditions must be capable of operating under a variety of atmospheric conditions like haze, fog and also against the sun. Atmospheric conditions affect the image of the aircraft in the image and hence also the detectability of the aircraft by the vision based algorithms. We chose signal-to-background ratio (SBR) as a measure of contrast and hence detectability in the image. In order to determine the minimum resolution requirement to obtain reliable detecton performance upto a certain range we use our image formation model to predict the signal to background ratio that will be obtained under anygiven atmospheric condition. We found empirically that a SBR of 1dB results in a detection rate of above 95%. This implies that an appropriate sensor must be able to provide a SBR of 1 dB in the image of an aircraft that is at a range of 3 miles from the sensor.
The figure shows an image of a target which we pick manually for the purpose of groundtruth and then fit a Gaussian to it to determine the signal-to-background ratio
The figure shows the overview of the atmospheric image model. The input to the system are the weather conditions and the geometry of the intruder aircraft and the output is the required resolution in milliradian/pixel. Having knowledge of the geometry allows the model to account for point of view of the intruding aircraft.
The model accounts for the fact that under haze the image of the aircraft is actually lighter than the background as the airlight between the camera and target contributes to the image of the aircraft.
A few examples of the image of the aircraft in the image.
We acquired imagery of the flying intruder aircraft at ranges upto 6 miles. We picked out the image of the aircraft manually in thousands of images and extracted the 11 x 11 windows around the intruder aircraft from these images. After calculating the signal-to-background ratio (SBR) by fitting Gaussians to them we plotted the SBR as a function of range and compared the general trend to the trend that our atmospheric image modelling system predicted. We found that the predicted trends were pretty close to the experimental data. We did observe some biases in the trends that seem to point towards a systematic bias rather than any inaccuracy in the image modelling system.
The above images shows the predicted trend of the SBR (blue) and the trend from the experimental data (red) for 4 different camera/lens pairs. The predicted and the empirical trends are close to each other.
Minimum Resolution Requirement:
The atmospheric image formation model allows us to determine the minimum resolution required to detect aircraft reliably at 3 miles as required by the FAA regulations.
The above image shows the SBR vs range for various sensor resolutions. The resolution of the two sensors whose curves lie below the 1 dB and 3 miles intersection are inadequate for the purpose of Sense and Avoid and hence are rejected. The rest of the curves can produce a SBR greater than 1 dB at 3 miles and hence enable the reliable ( greater than 95% ) detection of the intruder aircraft.