One class, five detections, three real dogs. Work down the list in score order: a detection whose best-overlapping ground-truth box clears IoU 0.5 and is still unclaimed takes it and counts as a true positive; anything else, including a detection whose best match is already taken, is a false positive. After each one, precision and recall are recomputed over everything seen so far, and a point joins the curve. Recall can only rise; precision falls whenever a false positive lands. Average precision is the area under the upward-interpolated curve, so where a detection sits in the ranking matters as much as whether it is right — compare right answers first with right answers last, which hold exactly the same five detections and the same three hits, and differ only in the order the detector ranked them. The three area conventions disagree on identical predictions, which is why an AP quoted without its protocol is not a comparable number.