def METHOD_NAME(boxes: dict, start, end):
    idxs = sorted([int(i) for i in boxes.keys()])
    bbox = [boxes[str(i)] for i in idxs]
    new_bboxes = []
    for i in range(4):
        f = interp1d(idxs, [b[i] for b in bbox])
        new_b = f(list(range(start, end + 1)))
        new_bboxes.append(new_b)
    new_bboxes = np.stack(new_bboxes, axis=1)
    return new_bboxes