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metrics.py
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# YOLOv5 🚀 by Ultralytics, GPL-3.0 license
"""
Model validation metrics
"""
import math
import warnings
from pathlib import Path
import matplotlib.pyplot as plt
import numpy as np
import torch
def fitness(x):
# Model fitness as a weighted combination of metrics
w = [0.0, 0.0, 0.1, 0.9] # weights for [P, R, [email protected], [email protected]:0.95]
return (x[:, :4] * w).sum(1)
def ap_per_class(tp, conf, pred_cls, target_cls, plot=False, save_dir='.', names=()):
""" Compute the average precision, given the recall and precision curves.
Source: https://github.com/rafaelpadilla/Object-Detection-Metrics.
# Arguments
tp: True positives (nparray, nx1 or nx10).
conf: Objectness value from 0-1 (nparray).
pred_cls: Predicted object classes (nparray).
target_cls: True object classes (nparray).
plot: Plot precision-recall curve at [email protected]
save_dir: Plot save directory
# Returns
The average precision as computed in py-faster-rcnn.
"""
# Sort by objectness
i = np.argsort(-conf)
tp, conf, pred_cls = tp[i], conf[i], pred_cls[i]
# Find unique classes
unique_classes = np.unique(target_cls)
nc = unique_classes.shape[0] # number of classes, number of detections
# Create Precision-Recall curve and compute AP for each class
px, py = np.linspace(0, 1, 1000), [] # for plotting
ap, p, r = np.zeros((nc, tp.shape[1])), np.zeros((nc, 1000)), np.zeros((nc, 1000))
for ci, c in enumerate(unique_classes):
i = pred_cls == c
n_l = (target_cls == c).sum() # number of labels
n_p = i.sum() # number of predictions
if n_p == 0 or n_l == 0:
continue
else:
# Accumulate FPs and TPs
fpc = (1 - tp[i]).cumsum(0)
tpc = tp[i].cumsum(0)
# Recall
recall = tpc / (n_l + 1e-16) # recall curve
r[ci] = np.interp(-px, -conf[i], recall[:, 0], left=0) # negative x, xp because xp decreases
# Precision
precision = tpc / (tpc + fpc) # precision curve
p[ci] = np.interp(-px, -conf[i], precision[:, 0], left=1) # p at pr_score
# AP from recall-precision curve
for j in range(tp.shape[1]):
ap[ci, j], mpre, mrec = compute_ap(recall[:, j], precision[:, j])
if plot and j == 0:
py.append(np.interp(px, mrec, mpre)) # precision at [email protected]
# Compute F1 (harmonic mean of precision and recall)
f1 = 2 * p * r / (p + r + 1e-16)
if plot:
plot_pr_curve(px, py, ap, Path(save_dir) / 'PR_curve.png', names)
plot_mc_curve(px, f1, Path(save_dir) / 'F1_curve.png', names, ylabel='F1')
plot_mc_curve(px, p, Path(save_dir) / 'P_curve.png', names, ylabel='Precision')
plot_mc_curve(px, r, Path(save_dir) / 'R_curve.png', names, ylabel='Recall')
i = f1.mean(0).argmax() # max F1 index
return p[:, i], r[:, i], ap, f1[:, i], unique_classes.astype('int32')
def compute_ap(recall, precision):
""" Compute the average precision, given the recall and precision curves
# Arguments
recall: The recall curve (list)
precision: The precision curve (list)
# Returns
Average precision, precision curve, recall curve
"""
# Append sentinel values to beginning and end
mrec = np.concatenate(([0.0], recall, [1.0]))
mpre = np.concatenate(([1.0], precision, [0.0]))
# Compute the precision envelope
mpre = np.flip(np.maximum.accumulate(np.flip(mpre)))
# Integrate area under curve
method = 'interp' # methods: 'continuous', 'interp'
if method == 'interp':
x = np.linspace(0, 1, 101) # 101-point interp (COCO)
ap = np.trapz(np.interp(x, mrec, mpre), x) # integrate
else: # 'continuous'
i = np.where(mrec[1:] != mrec[:-1])[0] # points where x axis (recall) changes
ap = np.sum((mrec[i + 1] - mrec[i]) * mpre[i + 1]) # area under curve
return ap, mpre, mrec
class ConfusionMatrix:
# Updated version of https://github.com/kaanakan/object_detection_confusion_matrix
def __init__(self, nc, conf=0.25, iou_thres=0.45):
self.matrix = np.zeros((nc + 1, nc + 1))
self.nc = nc # number of classes
self.conf = conf
self.iou_thres = iou_thres
def process_batch(self, detections, labels):
"""
Return intersection-over-union (Jaccard index) of boxes.
Both sets of boxes are expected to be in (x1, y1, x2, y2) format.
Arguments:
detections (Array[N, 6]), x1, y1, x2, y2, conf, class
labels (Array[M, 5]), class, x1, y1, x2, y2
Returns:
None, updates confusion matrix accordingly
"""
detections = detections[detections[:, 4] > self.conf]
gt_classes = labels[:, 0].int()
detection_classes = detections[:, 5].int()
iou = box_iou(labels[:, 1:], detections[:, :4])
x = torch.where(iou > self.iou_thres)
if x[0].shape[0]:
matches = torch.cat((torch.stack(x, 1), iou[x[0], x[1]][:, None]), 1).cpu().numpy()
if x[0].shape[0] > 1:
matches = matches[matches[:, 2].argsort()[::-1]]
matches = matches[np.unique(matches[:, 1], return_index=True)[1]]
matches = matches[matches[:, 2].argsort()[::-1]]
matches = matches[np.unique(matches[:, 0], return_index=True)[1]]
else:
matches = np.zeros((0, 3))
n = matches.shape[0] > 0
m0, m1, _ = matches.transpose().astype(np.int16)
for i, gc in enumerate(gt_classes):
j = m0 == i
if n and sum(j) == 1:
self.matrix[detection_classes[m1[j]], gc] += 1 # correct
else:
self.matrix[self.nc, gc] += 1 # background FP
if n:
for i, dc in enumerate(detection_classes):
if not any(m1 == i):
self.matrix[dc, self.nc] += 1 # background FN
def matrix(self):
return self.matrix
def plot(self, normalize=True, save_dir='', names=()):
try:
import seaborn as sn
array = self.matrix / ((self.matrix.sum(0).reshape(1, -1) + 1E-6) if normalize else 1) # normalize columns
array[array < 0.005] = np.nan # don't annotate (would appear as 0.00)
fig = plt.figure(figsize=(12, 9), tight_layout=True)
sn.set(font_scale=1.0 if self.nc < 50 else 0.8) # for label size
labels = (0 < len(names) < 99) and len(names) == self.nc # apply names to ticklabels
with warnings.catch_warnings():
warnings.simplefilter('ignore') # suppress empty matrix RuntimeWarning: All-NaN slice encountered
sn.heatmap(array, annot=self.nc < 30, annot_kws={"size": 8}, cmap='Blues', fmt='.2f', square=True,
xticklabels=names + ['background FP'] if labels else "auto",
yticklabels=names + ['background FN'] if labels else "auto").set_facecolor((1, 1, 1))
fig.axes[0].set_xlabel('True')
fig.axes[0].set_ylabel('Predicted')
fig.savefig(Path(save_dir) / 'confusion_matrix.png', dpi=250)
plt.close()
except Exception as e:
print(f'WARNING: ConfusionMatrix plot failure: {e}')
def print(self):
for i in range(self.nc + 1):
print(' '.join(map(str, self.matrix[i])))
def bbox_iou(box1, box2, x1y1x2y2=True, GIoU=False, DIoU=False, CIoU=False, eps=1e-7):
# Returns the IoU of box1 to box2. box1 is 4, box2 is nx4
box2 = box2.T
# Get the coordinates of bounding boxes
if x1y1x2y2: # x1, y1, x2, y2 = box1
b1_x1, b1_y1, b1_x2, b1_y2 = box1[0], box1[1], box1[2], box1[3]
b2_x1, b2_y1, b2_x2, b2_y2 = box2[0], box2[1], box2[2], box2[3]
else: # transform from xywh to xyxy
b1_x1, b1_x2 = box1[0] - box1[2] / 2, box1[0] + box1[2] / 2
b1_y1, b1_y2 = box1[1] - box1[3] / 2, box1[1] + box1[3] / 2
b2_x1, b2_x2 = box2[0] - box2[2] / 2, box2[0] + box2[2] / 2
b2_y1, b2_y2 = box2[1] - box2[3] / 2, box2[1] + box2[3] / 2
# Intersection area
inter = (torch.min(b1_x2, b2_x2) - torch.max(b1_x1, b2_x1)).clamp(0) * \
(torch.min(b1_y2, b2_y2) - torch.max(b1_y1, b2_y1)).clamp(0)
# Union Area
w1, h1 = b1_x2 - b1_x1, b1_y2 - b1_y1 + eps
w2, h2 = b2_x2 - b2_x1, b2_y2 - b2_y1 + eps
union = w1 * h1 + w2 * h2 - inter + eps
iou = inter / union
if GIoU or DIoU or CIoU:
cw = torch.max(b1_x2, b2_x2) - torch.min(b1_x1, b2_x1) # convex (smallest enclosing box) width
ch = torch.max(b1_y2, b2_y2) - torch.min(b1_y1, b2_y1) # convex height
if CIoU or DIoU: # Distance or Complete IoU https://arxiv.org/abs/1911.08287v1
c2 = cw ** 2 + ch ** 2 + eps # convex diagonal squared
rho2 = ((b2_x1 + b2_x2 - b1_x1 - b1_x2) ** 2 +
(b2_y1 + b2_y2 - b1_y1 - b1_y2) ** 2) / 4 # center distance squared
if DIoU:
return iou - rho2 / c2 # DIoU
elif CIoU: # https://github.com/Zzh-tju/DIoU-SSD-pytorch/blob/master/utils/box/box_utils.py#L47
v = (4 / math.pi ** 2) * torch.pow(torch.atan(w2 / h2) - torch.atan(w1 / h1), 2)
with torch.no_grad():
alpha = v / (v - iou + (1 + eps))
return iou - (rho2 / c2 + v * alpha) # CIoU
else: # GIoU https://arxiv.org/pdf/1902.09630.pdf
c_area = cw * ch + eps # convex area
return iou - (c_area - union) / c_area # GIoU
else:
return iou # IoU
def box_iou(box1, box2):
# https://github.com/pytorch/vision/blob/master/torchvision/ops/boxes.py
"""
Return intersection-over-union (Jaccard index) of boxes.
Both sets of boxes are expected to be in (x1, y1, x2, y2) format.
Arguments:
box1 (Tensor[N, 4])
box2 (Tensor[M, 4])
Returns:
iou (Tensor[N, M]): the NxM matrix containing the pairwise
IoU values for every element in boxes1 and boxes2
"""
def box_area(box):
# box = 4xn
return (box[2] - box[0]) * (box[3] - box[1])
area1 = box_area(box1.T)
area2 = box_area(box2.T)
# inter(N,M) = (rb(N,M,2) - lt(N,M,2)).clamp(0).prod(2)
inter = (torch.min(box1[:, None, 2:], box2[:, 2:]) - torch.max(box1[:, None, :2], box2[:, :2])).clamp(0).prod(2)
return inter / (area1[:, None] + area2 - inter) # iou = inter / (area1 + area2 - inter)
def bbox_ioa(box1, box2, eps=1E-7):
""" Returns the intersection over box2 area given box1, box2. Boxes are x1y1x2y2
box1: np.array of shape(4)
box2: np.array of shape(nx4)
returns: np.array of shape(n)
"""
box2 = box2.transpose()
# Get the coordinates of bounding boxes
b1_x1, b1_y1, b1_x2, b1_y2 = box1[0], box1[1], box1[2], box1[3]
b2_x1, b2_y1, b2_x2, b2_y2 = box2[0], box2[1], box2[2], box2[3]
# Intersection area
inter_area = (np.minimum(b1_x2, b2_x2) - np.maximum(b1_x1, b2_x1)).clip(0) * \
(np.minimum(b1_y2, b2_y2) - np.maximum(b1_y1, b2_y1)).clip(0)
# box2 area
box2_area = (b2_x2 - b2_x1) * (b2_y2 - b2_y1) + eps
# Intersection over box2 area
return inter_area / box2_area
def wh_iou(wh1, wh2):
# Returns the nxm IoU matrix. wh1 is nx2, wh2 is mx2
wh1 = wh1[:, None] # [N,1,2]
wh2 = wh2[None] # [1,M,2]
inter = torch.min(wh1, wh2).prod(2) # [N,M]
return inter / (wh1.prod(2) + wh2.prod(2) - inter) # iou = inter / (area1 + area2 - inter)
# Plots ----------------------------------------------------------------------------------------------------------------
def plot_pr_curve(px, py, ap, save_dir='pr_curve.png', names=()):
# Precision-recall curve
fig, ax = plt.subplots(1, 1, figsize=(9, 6), tight_layout=True)
py = np.stack(py, axis=1)
if 0 < len(names) < 21: # display per-class legend if < 21 classes
for i, y in enumerate(py.T):
ax.plot(px, y, linewidth=1, label=f'{names[i]} {ap[i, 0]:.3f}') # plot(recall, precision)
else:
ax.plot(px, py, linewidth=1, color='grey') # plot(recall, precision)
ax.plot(px, py.mean(1), linewidth=3, color='blue', label='all classes %.3f [email protected]' % ap[:, 0].mean())
ax.set_xlabel('Recall')
ax.set_ylabel('Precision')
ax.set_xlim(0, 1)
ax.set_ylim(0, 1)
plt.legend(bbox_to_anchor=(1.04, 1), loc="upper left")
fig.savefig(Path(save_dir), dpi=250)
plt.close()
def plot_mc_curve(px, py, save_dir='mc_curve.png', names=(), xlabel='Confidence', ylabel='Metric'):
# Metric-confidence curve
fig, ax = plt.subplots(1, 1, figsize=(9, 6), tight_layout=True)
if 0 < len(names) < 21: # display per-class legend if < 21 classes
for i, y in enumerate(py):
ax.plot(px, y, linewidth=1, label=f'{names[i]}') # plot(confidence, metric)
else:
ax.plot(px, py.T, linewidth=1, color='grey') # plot(confidence, metric)
y = py.mean(0)
ax.plot(px, y, linewidth=3, color='blue', label=f'all classes {y.max():.2f} at {px[y.argmax()]:.3f}')
ax.set_xlabel(xlabel)
ax.set_ylabel(ylabel)
ax.set_xlim(0, 1)
ax.set_ylim(0, 1)
plt.legend(bbox_to_anchor=(1.04, 1), loc="upper left")
fig.savefig(Path(save_dir), dpi=250)
plt.close()