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This paper studies the evaluation of learning-based object detection models in conjunction with model-checking of formal specifications defined on an abstract model of an autonomous system and its environment. In particular, we define two metrics – proposition-labeled and class-labeled confusion matrices – for evaluating object detection, and we incorporate these metrics to compute the satisfaction probability of system-level safety requirements. While confusion matrices have been effective for comparative evaluation of classification and object detection models, our framework fills two key gaps. First, we relate the performance of object detection to formal requirements defined over downstream high-level planning tasks. In particular, we provide empirical results that show that the choice of a good object detection algorithm, with respect to formal requirements on the overall system, significantly depends on the downstream planning and control design. Secondly, unlike the traditional confusion matrix, our metrics account for variations in performance with respect to the distance between the ego and the object being detected. We demonstrate this framework on a car-pedestrian example by computing the satisfaction probabilities for safety requirements formalized in Linear Temporal Logic (LTL). 

Object classification is a key element that enables effective decision-making in many autonomous systems. A more sophisticated system may also utilize the probability distribution over the classes instead of basing its decision only on the most likely class. This paper introduces new performance metrics: the absolute class error (ACE), expectation of absolute class error (EACE) and variance of absolute class error (VACE) for evaluating the accuracy of such probabilities. We test this metric using different neural network architectures and datasets. Furthermore, we present a new task-based neural network for object classification and compare its performance with a typical probabilistic classification model to show the improvement with threshold-based probabilistic decision-making.