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Pedestrian detection is an important part of the perception system of autonomous vehicles. Foggy and low-light conditions are quite challenging for pedestrian detection, and several models have been proposed to increase the robustness of detections under such challenging conditions. Checking if such a model performs well is largely evaluated by manually inspecting the results of object detection. We propose a monitoring technique that uses Timed Quality Temporal Logic (TQTL) to do differential testing: we first check when an object detector (such as vanilla YOLO) fails to accurately detect pedestrians using a suitable TQTL formula on a sequence of images. We then apply a model specialized to adverse weather conditions to perform object detection on the same image sequence. We use Image-Adaptive YOLO (IA-YOLO) for this purpose. We then check if the new model satisfies the previously failing specifications. Our method shows the feasibility of using such a differential testing approach to measure the improvement in quality of detections when specialized models are used for object detection.