box_utils.py

""" Helper functions for calculating 2D and 3D bounding box IoU.
Collected by Charles R. Qi
Date: September 2017
"""
from __future__ import print_function

import numpy as np
from scipy.spatial import ConvexHull


def polygon_clip(subjectPolygon, clipPolygon):
    """ Clip a polygon with another polygon.
    Ref: https://rosettacode.org/wiki/Sutherland-Hodgman_polygon_clipping#Python
    Args:
      subjectPolygon: a list of (x,y) 2d points, any polygon.
      clipPolygon: a list of (x,y) 2d points, has to be *convex*
    Note:
      **points have to be counter-clockwise ordered**
    Return:
      a list of (x,y) vertex point for the intersection polygon.
    """

    def inside(p):
        return (cp2[0] - cp1[0]) * (p[1] - cp1[1]) > (cp2[1] - cp1[1]) * (p[0] - cp1[0])

    def computeIntersection():
        dc = [cp1[0] - cp2[0], cp1[1] - cp2[1]]
        dp = [s[0] - e[0], s[1] - e[1]]
        n1 = cp1[0] * cp2[1] - cp1[1] * cp2[0]
        n2 = s[0] * e[1] - s[1] * e[0]
        n3 = 1.0 / (dc[0] * dp[1] - dc[1] * dp[0])
        return [(n1 * dp[0] - n2 * dc[0]) * n3, (n1 * dp[1] - n2 * dc[1]) * n3]

    outputList = subjectPolygon
    cp1 = clipPolygon[-1]

    for clipVertex in clipPolygon:
        cp2 = clipVertex
        inputList = outputList
        outputList = []
        s = inputList[-1]

        for subjectVertex in inputList:
            e = subjectVertex
            if inside(e):
                if not inside(s):
                    outputList.append(computeIntersection())
                outputList.append(e)
            elif inside(s):
                outputList.append(computeIntersection())
            s = e
        cp1 = cp2
        if len(outputList) == 0:
            return None
    return (outputList)


def poly_area(x, y):
    """ Ref: http://stackoverflow.com/questions/24467972/calculate-area-of-polygon-given-x-y-coordinates """
    return 0.5 * np.abs(np.dot(x, np.roll(y, 1)) - np.dot(y, np.roll(x, 1)))


def convex_hull_intersection(p1, p2):
    """ Compute area of two convex hull's intersection area.
        p1,p2 are a list of (x,y) tuples of hull vertices.
        return a list of (x,y) for the intersection and its volume
    """
    inter_p = polygon_clip(p1, p2)
    if inter_p is not None:
        hull_inter = ConvexHull(inter_p)
        return inter_p, hull_inter.volume
    else:
        return None, 0.0


def box3d_vol(corners):
    ''' corners: (8,3) no assumption on axis direction '''
    a = np.sqrt(np.sum((corners[0, :] - corners[1, :]) ** 2))
    b = np.sqrt(np.sum((corners[1, :] - corners[2, :]) ** 2))
    c = np.sqrt(np.sum((corners[0, :] - corners[4, :]) ** 2))
    return a * b * c


def is_clockwise(p):
    x = p[:, 0]
    y = p[:, 1]
    return np.dot(x, np.roll(y, 1)) - np.dot(y, np.roll(x, 1)) > 0


def box3d_iou(corners1, corners2):
    ''' Compute 3D bounding box IoU.
    Input:
        corners1: numpy array (8,3), assume up direction is negative Y
        corners2: numpy array (8,3), assume up direction is negative Y
    Output:
        iou: 3D bounding box IoU
        iou_2d: bird's eye view 2D bounding box IoU
    todo (rqi): add more description on corner points' orders.
    '''
    # corner points are in counter clockwise order
    rect1 = [(corners1[i, 0], corners1[i, 2]) for i in range(3, -1, -1)]
    rect2 = [(corners2[i, 0], corners2[i, 2]) for i in range(3, -1, -1)]
    area1 = poly_area(np.array(rect1)[:, 0], np.array(rect1)[:, 1])
    area2 = poly_area(np.array(rect2)[:, 0], np.array(rect2)[:, 1])
    inter, inter_area = convex_hull_intersection(rect1, rect2)
    iou_2d = inter_area / (area1 + area2 - inter_area)
    ymax = min(corners1[0, 1], corners2[0, 1])
    ymin = max(corners1[4, 1], corners2[4, 1])
    inter_vol = inter_area * max(0.0, ymax - ymin)
    vol1 = box3d_vol(corners1)
    vol2 = box3d_vol(corners2)
    iou = inter_vol / (vol1 + vol2 - inter_vol)
    return iou, iou_2d


def get_iou(bb1, bb2):
    """
    Calculate the Intersection over Union (IoU) of two 2D bounding boxes.
    Parameters
    ----------
    bb1 : dict
        Keys: {'x1', 'x2', 'y1', 'y2'}
        The (x1, y1) position is at the top left corner,
        the (x2, y2) position is at the bottom right corner
    bb2 : dict
        Keys: {'x1', 'x2', 'y1', 'y2'}
        The (x, y) position is at the top left corner,
        the (x2, y2) position is at the bottom right corner
    Returns
    -------
    float
        in [0, 1]
    """
    assert bb1['x1'] < bb1['x2']
    assert bb1['y1'] < bb1['y2']
    assert bb2['x1'] < bb2['x2']
    assert bb2['y1'] < bb2['y2']

    # determine the coordinates of the intersection rectangle
    x_left = max(bb1['x1'], bb2['x1'])
    y_top = max(bb1['y1'], bb2['y1'])
    x_right = min(bb1['x2'], bb2['x2'])
    y_bottom = min(bb1['y2'], bb2['y2'])

    if x_right < x_left or y_bottom < y_top:
        return 0.0

    # The intersection of two axis-aligned bounding boxes is always an
    # axis-aligned bounding box
    intersection_area = (x_right - x_left) * (y_bottom - y_top)

    # compute the area of both AABBs
    bb1_area = (bb1['x2'] - bb1['x1']) * (bb1['y2'] - bb1['y1'])
    bb2_area = (bb2['x2'] - bb2['x1']) * (bb2['y2'] - bb2['y1'])

    # compute the intersection over union by taking the intersection
    # area and dividing it by the sum of prediction + ground-truth
    # areas - the interesection area
    iou = intersection_area / float(bb1_area + bb2_area - intersection_area)
    assert iou >= 0.0
    assert iou <= 1.0
    return iou


def box2d_iou(box1, box2):
    ''' Compute 2D bounding box IoU.
    Input:
        box1: tuple of (xmin,ymin,xmax,ymax)
        box2: tuple of (xmin,ymin,xmax,ymax)
    Output:
        iou: 2D IoU scalar
    '''
    return get_iou({'x1': box1[0], 'y1': box1[1], 'x2': box1[2], 'y2': box1[3]}, \
                   {'x1': box2[0], 'y1': box2[1], 'x2': box2[2], 'y2': box2[3]})