2. It is given that there is an object in an image, whose location is represented by a bounding box. An object detector is used to detect the object in the image. In the object detector, a bounding box regressor is trained. To train the bounding box regressor, training pairs of predicted bounding boxes and ground-truth bounding boxes are used. Assume that a training pair is denoted as follows: Prediction: P = (Px, Py, Pw, Ph), and Ground Truth: G = (9x, gy, 9w, 9h), where a bounding box is represented by the x and y coordinates of its upper left corner, and its width and height. To train the regressor is to learn a transformation that maps the proposed bounding box P to the ground-truth bounding box G. The transformation is parameterized in terms of four functions, dx (P), dy (P), dw(P), and d(P), for the x coordinate, y coordinate, width, and height, respectively. After learning the functions, P can be transformed into a predicted ground-truth box using the following transformation: x = Pwdx (P) + Px, y = Pndy (P) + Py, w W = Pw exp(dw(P)), n = Ph exp(dn(p)). (a) Determine the targets for learning the four functions, dx (P), dy (P), dw(P), and d (P). (b) Assume that the predicted bounding box of the object is P = (80, 60, 100, 100). It is given that the ground-truth bounding box of the object is G = (85, 55, 110, 110). (i) Compute the Intersection over Union (loU) of the predicted and ground-truth bounding boxes. (ii) Assume that the output of the bounding box regressor for the predicted bounding box P is (0.05, -0.1, 0.1, 0.15). Determine the new predicted bounding box and its loU with the ground truth.