Model of Large-format EO-IR sensor for calculating the probability of true and false detection and tracking for moving and fixed objects

摘要

A model was developed to understand the effects of spatial resolution and Signal to Noise ratio on the detection and tracking performance of wide-field, diffraction-limited electro-optic and infrared motion imagery systems. False positive detection probability and false positive rate per frame were calculated as a function of target-to-background contrast and object size. Results showed that moving objects are fundamentally more difficult to detect than stationary objects because SNR for fixed objects increases and false positive probability detection rates diminish rapidly with successive frames whereas for moving objects the false detection rate remains constant or increases with successive frames. The model specifies that the desired performance of a detection system, measured by the false positive detection rate, can be achieved by image system designs with different combinations of SNR and spatial resolution, usually requiring several pixels resolving the object; this capability to tradeoff resolution and SNR enables system design trades and cost optimization. For operational use, detection thresholds required to achieve a particular false detection rate can be calculated. Interestingly, for moderate size images the model converges to the Johnson Criteria. Johnson found that an imaging system with an SNR ＞3.5 has a probability of detection ＞50% when the resolution on the object is 4 pixels or more. Under these conditions our model finds the false positive rate is less than one per hundred image frames, and the ratio of the probability of object detection to false positive detection is much greater than one. The model was programmed into Matlab to generate simulated images frames for visualization.