I want to calculate the overlapped area "THE GRAY REGION" between red and blue rectangles.
Each rectangle is defined by its four corner coordinates. The resulted unit of the overlapped area is unit square.
I could not imagine how can I do it?
Any creative comments would be appreciated.
Two rectangles do not overlap if one of the following conditions is true. 1) One rectangle is above top edge of other rectangle. 2) One rectangle is on left side of left edge of other rectangle.
overlap noun (SAME AREA) the amount by which two things or activities cover the same area: The roof tiles will need an overlap of several centimetres.
This type of intersection is easily done by the "min of the maxes" and "max of the mins" idea. To write it out one needs a specific notion for the rectangle, and, just to make things clear I'll use a namedtuple:
from collections import namedtuple
Rectangle = namedtuple('Rectangle', 'xmin ymin xmax ymax')
ra = Rectangle(3., 3., 5., 5.)
rb = Rectangle(1., 1., 4., 3.5)
# intersection here is (3, 3, 4, 3.5), or an area of 1*.5=.5
def area(a, b): # returns None if rectangles don't intersect
dx = min(a.xmax, b.xmax) - max(a.xmin, b.xmin)
dy = min(a.ymax, b.ymax) - max(a.ymin, b.ymin)
if (dx>=0) and (dy>=0):
return dx*dy
print area(ra, rb)
# 0.5
If you don't like the namedtuple notation, you could just use:
dx = max(a[0], b[0]) - min(a[2], b[2])
etc, or whatever notation you prefer.
As this question has a shapely tag, here is a solution using it. I will use the same rectangles as in the tom10 answer:
from shapely.geometry import Polygon
polygon = Polygon([(3, 3), (5, 3), (5, 5), (3, 5)])
other_polygon = Polygon([(1, 1), (4, 1), (4, 3.5), (1, 3.5)])
intersection = polygon.intersection(other_polygon)
print(intersection.area)
# 0.5
This is much more concise than the version in the accepted answer. You don't have to construct your own Rectangle
class as Shapely already provides the ready ones. It's less error-prone (go figure out the logic in that area
function). And the code itself is self-explanatory.
References:
Docs for object.intersection(other)
method
Since the post is very related to computer vision and object detection, I thought of putting some code together that I use for finding the intersection of bounding boxes and also finding their intersection over union (IoU). This code was originally developed by Adrian Rosebrock in this blog post:
This is the module (where I named it Bbox
):
class Bbox:
def __init__(self, x1, y1, x2, y2):
self.x1 = max(x1, x2)
self.x2 = min(x1, x2)
self.y1 = max(y1, y2)
self.y2 = max(y1, y2)
self.box = [self.x1, self.y1, self.x2, self.y2]
self.width = abs(self.x1 - self.x2)
self.height = abs(self.y1 - self.y2)
@property
def area(self):
"""
Calculates the surface area. useful for IOU!
"""
return (self.x2 - self.x1 + 1) * (self.y2 - self.y1 + 1)
def intersect(self, bbox):
x1 = max(self.x1, bbox.x1)
y1 = max(self.y1, bbox.y1)
x2 = min(self.x2, bbox.x2)
y2 = min(self.y2, bbox.y2)
intersection = max(0, x2 - x1 + 1) * max(0, y2 - y1 + 1)
return intersection
def iou(self, bbox):
intersection = self.intersection(bbox)
iou = intersection / float(self.area + bbox.area - intersection)
# return the intersection over union value
return iou
And to use it:
a = Bbox([516, 289, 529, 303])
b = Bbox([487, 219, 533, 342])
result = a.intersect(b)
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