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# import the necessary packages
import numpy as np
def non_max_suppression(boxes, probs=None, overlapThresh=0.3):
# if there are no boxes, return an empty list
if len(boxes) == 0:
return []
# if the bounding boxes are integers, convert them to floats -- this
# is important since we'll be doing a bunch of divisions
if boxes.dtype.kind == "i":
boxes = boxes.astype("float")
# initialize the list of picked indexes
pick = []
# grab the coordinates of the bounding boxes
x1 = boxes[:, 0]
y1 = boxes[:, 1]
x2 = boxes[:, 2]
y2 = boxes[:, 3]
# compute the area of the bounding boxes and grab the indexes to sort
# (in the case that no probabilities are provided, simply sort on the
# bottom-left y-coordinate)
area = (x2 - x1 + 1) * (y2 - y1 + 1)
idxs = y2
# if probabilities are provided, sort on them instead
if probs is not None:
idxs = probs
# sort the indexes
idxs = np.argsort(idxs)
# keep looping while some indexes still remain in the indexes list
while len(idxs) > 0:
# grab the last index in the indexes list and add the index value
# to the list of picked indexes
last = len(idxs) - 1
i = idxs[last]
pick.append(i)
# find the largest (x, y) coordinates for the start of the bounding
# box and the smallest (x, y) coordinates for the end of the bounding
# box
xx1 = np.maximum(x1[i], x1[idxs[:last]])
yy1 = np.maximum(y1[i], y1[idxs[:last]])
xx2 = np.minimum(x2[i], x2[idxs[:last]])
yy2 = np.minimum(y2[i], y2[idxs[:last]])
# compute the width and height of the bounding box
w = np.maximum(0, xx2 - xx1 + 1)
h = np.maximum(0, yy2 - yy1 + 1)
# compute the ratio of overlap
overlap = (w * h) / area[idxs[:last]]
# delete all indexes from the index list that have overlap greater
# than the provided overlap threshold
idxs = np.delete(idxs, np.concatenate(([last],
np.where(overlap > overlapThresh)[0])))
# return only the bounding boxes that were picked
return boxes[pick].astype("int")
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