from __future__ import absolute_import, division
import numpy as np
from shapely.geometry import box, Polygon
def center_error(rects1, rects2):
r"""Center error.
Args:
rects1 (numpy.ndarray): An N x 4 numpy array, each line represent a rectangle
(left, top, width, height).
rects2 (numpy.ndarray): An N x 4 numpy array, each line represent a rectangle
(left, top, width, height).
"""
centers1 = rects1[..., :2] + (rects1[..., 2:] - 1) / 2
centers2 = rects2[..., :2] + (rects2[..., 2:] - 1) / 2
errors = np.sqrt(np.sum(np.power(centers1 - centers2, 2), axis=-1))
return errors
def normalized_center_error(rects1, rects2):
r"""Center error normalized by the size of ground truth.
Args:
rects1 (numpy.ndarray): prediction box. An N x 4 numpy array, each line represent a rectangle
(left, top, width, height).
rects2 (numpy.ndarray): groudn truth box. An N x 4 numpy array, each line represent a rectangle
(left, top, width, height).
"""
centers1 = rects1[..., :2] + (rects1[..., 2:] - 1) / 2
centers2 = rects2[..., :2] + (rects2[..., 2:] - 1) / 2
errors = np.sqrt(np.sum(np.power((centers1 - centers2)/np.maximum(np.array([[1.,1.]]), rects2[:, 2:]), 2), axis=-1))
return errors
def rect_iou(rects1, rects2, bound=None):
r"""Intersection over union.
Args:
rects1 (numpy.ndarray): An N x 4 numpy array, each line represent a rectangle
(left, top, width, height).
rects2 (numpy.ndarray): An N x 4 numpy array, each line represent a rectangle
(left, top, width, height).
bound (numpy.ndarray): A 4 dimensional array, denotes the bound
(min_left, min_top, max_width, max_height) for ``rects1`` and ``rects2``.
"""
assert rects1.shape == rects2.shape
if bound is not None:
# bounded rects1
rects1[:, 0] = np.clip(rects1[:, 0], 0, bound[0])
rects1[:, 1] = np.clip(rects1[:, 1], 0, bound[1])
rects1[:, 2] = np.clip(rects1[:, 2], 0, bound[0] - rects1[:, 0])
rects1[:, 3] = np.clip(rects1[:, 3], 0, bound[1] - rects1[:, 1])
# bounded rects2
rects2[:, 0] = np.clip(rects2[:, 0], 0, bound[0])
rects2[:, 1] = np.clip(rects2[:, 1], 0, bound[1])
rects2[:, 2] = np.clip(rects2[:, 2], 0, bound[0] - rects2[:, 0])
rects2[:, 3] = np.clip(rects2[:, 3], 0, bound[1] - rects2[:, 1])
rects_inter = _intersection(rects1, rects2)
areas_inter = np.prod(rects_inter[..., 2:], axis=-1)
areas1 = np.prod(rects1[..., 2:], axis=-1)
areas2 = np.prod(rects2[..., 2:], axis=-1)
areas_union = areas1 + areas2 - areas_inter
eps = np.finfo(float).eps
ious = areas_inter / (areas_union + eps)
ious = np.clip(ious, 0.0, 1.0)
return ious
def _intersection(rects1, rects2):
r"""Rectangle intersection.
Args:
rects1 (numpy.ndarray): An N x 4 numpy array, each line represent a rectangle
(left, top, width, height).
rects2 (numpy.ndarray): An N x 4 numpy array, each line represent a rectangle
(left, top, width, height).
"""
assert rects1.shape == rects2.shape
x1 = np.maximum(rects1[..., 0], rects2[..., 0])
y1 = np.maximum(rects1[..., 1], rects2[..., 1])
x2 = np.minimum(rects1[..., 0] + rects1[..., 2],
rects2[..., 0] + rects2[..., 2])
y2 = np.minimum(rects1[..., 1] + rects1[..., 3],
rects2[..., 1] + rects2[..., 3])
w = np.maximum(x2 - x1, 0)
h = np.maximum(y2 - y1, 0)
return np.stack([x1, y1, w, h]).T
def poly_iou(polys1, polys2, bound=None):
r"""Intersection over union of polygons.
Args:
polys1 (numpy.ndarray): An N x 4 numpy array, each line represent a rectangle
(left, top, width, height); or an N x 8 numpy array, each line represent
the coordinates (x1, y1, x2, y2, x3, y3, x4, y4) of 4 corners.
polys2 (numpy.ndarray): An N x 4 numpy array, each line represent a rectangle
(left, top, width, height); or an N x 8 numpy array, each line represent
the coordinates (x1, y1, x2, y2, x3, y3, x4, y4) of 4 corners.
bound (numpy.ndarray, optional): A 2 dimensional array, denotes the image bound
(width, height) for ``rects1`` and ``rects2``.
"""
assert polys1.ndim in [1, 2]
if polys1.ndim == 1:
polys1 = np.array([polys1])
polys2 = np.array([polys2])
assert len(polys1) == len(polys2)
polys1 = _to_polygon(polys1)
polys2 = _to_polygon(polys2)
if bound is not None:
bound = box(0, 0, bound[0], bound[1])
polys1 = [p.intersection(bound) for p in polys1]
polys2 = [p.intersection(bound) for p in polys2]
eps = np.finfo(float).eps
ious = []
for poly1, poly2 in zip(polys1, polys2):
area_inter = poly1.intersection(poly2).area
area_union = poly1.union(poly2).area
ious.append(area_inter / (area_union + eps))
ious = np.clip(ious, 0.0, 1.0)
return ious
def _to_polygon(polys):
r"""Convert 4 or 8 dimensional array to Polygons
Args:
polys (numpy.ndarray): An N x 4 numpy array, each line represent a rectangle
(left, top, width, height); or an N x 8 numpy array, each line represent
the coordinates (x1, y1, x2, y2, x3, y3, x4, y4) of 4 corners.
"""
def to_polygon(x):
assert len(x) in [4, 8]
if len(x) == 4:
return box(x[0], x[1], x[0] + x[2], x[1] + x[3])
elif len(x) == 8:
return Polygon([(x[2 * i], x[2 * i + 1]) for i in range(4)])
if polys.ndim == 1:
return to_polygon(polys)
else:
return [to_polygon(t) for t in polys]
