# 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
import torch.nn as nn
from ultralytics.yolo.utils import TryExcept
# boxes
def box_area(box):
# box = xyxy(4,n)
return (box[2] - box[0]) * (box[3] - box[1])
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(nx4)
box2: np.array of shape(mx4)
returns: np.array of shape(nxm)
"""
# Get the coordinates of bounding boxes
b1_x1, b1_y1, b1_x2, b1_y2 = box1.T
b2_x1, b2_y1, b2_x2, b2_y2 = box2.T
# Intersection area
inter_area = (np.minimum(b1_x2[:, None], b2_x2) - np.maximum(b1_x1[:, None], b2_x1)).clip(0) * \
(np.minimum(b1_y2[:, None], b2_y2) - np.maximum(b1_y1[:, None], 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 box_iou(box1, box2, eps=1e-7):
# 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
"""
# inter(N,M) = (rb(N,M,2) - lt(N,M,2)).clamp(0).prod(2)
(a1, a2), (b1, b2) = box1[:, None].chunk(2, 2), box2.chunk(2, 1)
inter = (torch.min(a2, b2) - torch.max(a1, b1)).clamp(0).prod(2)
# IoU = inter / (area1 + area2 - inter)
return inter / (box_area(box1.T)[:, None] + box_area(box2.T) - inter + eps)
def bbox_iou(box1, box2, xywh=True, GIoU=False, DIoU=False, CIoU=False, eps=1e-7):
# Returns Intersection over Union (IoU) of box1(1,4) to box2(n,4)
# Get the coordinates of bounding boxes
if xywh: # transform from xywh to xyxy
(x1, y1, w1, h1), (x2, y2, w2, h2) = box1.chunk(4, 1), box2.chunk(4, 1)
w1_, h1_, w2_, h2_ = w1 / 2, h1 / 2, w2 / 2, h2 / 2
b1_x1, b1_x2, b1_y1, b1_y2 = x1 - w1_, x1 + w1_, y1 - h1_, y1 + h1_
b2_x1, b2_x2, b2_y1, b2_y2 = x2 - w2_, x2 + w2_, y2 - h2_, y2 + h2_
else: # x1, y1, x2, y2 = box1
b1_x1, b1_y1, b1_x2, b1_y2 = box1.chunk(4, 1)
b2_x1, b2_y1, b2_x2, b2_y2 = box2.chunk(4, 1)
w1, h1 = b1_x2 - b1_x1, b1_y2 - b1_y1 + eps
w2, h2 = b2_x2 - b2_x1, b2_y2 - b2_y1 + eps
# 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
union = w1 * h1 + w2 * h2 - inter + eps
# IoU
iou = inter / union
if CIoU or DIoU or GIoU:
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 dist ** 2
if 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
return iou - rho2 / c2 # DIoU
c_area = cw * ch + eps # convex area
return iou - (c_area - union) / c_area # GIoU https://arxiv.org/pdf/1902.09630.pdf
return iou # IoU
def mask_iou(mask1, mask2, eps=1e-7):
"""
mask1: [N, n] m1 means number of predicted objects
mask2: [M, n] m2 means number of gt objects
Note: n means image_w x image_h
return: masks iou, [N, M]
"""
intersection = torch.matmul(mask1, mask2.t()).clamp(0)
union = (mask1.sum(1)[:, None] + mask2.sum(1)[None]) - intersection # (area1 + area2) - intersection
return intersection / (union + eps)
def masks_iou(mask1, mask2, eps=1e-7):
"""
mask1: [N, n] m1 means number of predicted objects
mask2: [N, n] m2 means number of gt objects
Note: n means image_w x image_h
return: masks iou, (N, )
"""
intersection = (mask1 * mask2).sum(1).clamp(0) # (N, )
union = (mask1.sum(1) + mask2.sum(1))[None] - intersection # (area1 + area2) - intersection
return intersection / (union + eps)
def smooth_BCE(eps=0.1): # https://github.com/ultralytics/yolov3/issues/238#issuecomment-598028441
# return positive, negative label smoothing BCE targets
return 1.0 - 0.5 * eps, 0.5 * eps
# losses
class FocalLoss(nn.Module):
# Wraps focal loss around existing loss_fcn(), i.e. criteria = FocalLoss(nn.BCEWithLogitsLoss(), gamma=1.5)
def __init__(self, loss_fcn, gamma=1.5, alpha=0.25):
super().__init__()
self.loss_fcn = loss_fcn # must be nn.BCEWithLogitsLoss()
self.gamma = gamma
self.alpha = alpha
self.reduction = loss_fcn.reduction
self.loss_fcn.reduction = 'none' # required to apply FL to each element
def forward(self, pred, true):
loss = self.loss_fcn(pred, true)
# p_t = torch.exp(-loss)
# loss *= self.alpha * (1.000001 - p_t) ** self.gamma # non-zero power for gradient stability
# TF implementation https://github.com/tensorflow/addons/blob/v0.7.1/tensorflow_addons/losses/focal_loss.py
pred_prob = torch.sigmoid(pred) # prob from logits
p_t = true * pred_prob + (1 - true) * (1 - pred_prob)
alpha_factor = true * self.alpha + (1 - true) * (1 - self.alpha)
modulating_factor = (1.0 - p_t) ** self.gamma
loss *= alpha_factor * modulating_factor
if self.reduction == 'mean':
return loss.mean()
elif self.reduction == 'sum':
return loss.sum()
else: # 'none'
return loss
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
"""
if detections is None:
gt_classes = labels.int()
for gc in gt_classes:
self.matrix[self.nc, gc] += 1 # background FN
return
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(int)
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 # true background
if n:
for i, dc in enumerate(detection_classes):
if not any(m1 == i):
self.matrix[dc, self.nc] += 1 # predicted background
def matrix(self):
return self.matrix
def tp_fp(self):
tp = self.matrix.diagonal() # true positives
fp = self.matrix.sum(1) - tp # false positives
# fn = self.matrix.sum(0) - tp # false negatives (missed detections)
return tp[:-1], fp[:-1] # remove background class
@TryExcept('WARNING ⚠️ ConfusionMatrix plot failure')
def plot(self, normalize=True, save_dir='', names=()):
import seaborn as sn
array = self.matrix / ((self.matrix.sum(0).reshape(1, -1) + 1E-9) if normalize else 1) # normalize columns
array[array < 0.005] = np.nan # don't annotate (would appear as 0.00)
fig, ax = plt.subplots(1, 1, figsize=(12, 9), tight_layout=True)
nc, nn = self.nc, len(names) # number of classes, names
sn.set(font_scale=1.0 if nc < 50 else 0.8) # for label size
labels = (0 < nn < 99) and (nn == nc) # apply names to ticklabels
ticklabels = (names + ['background']) if labels else "auto"
with warnings.catch_warnings():
warnings.simplefilter('ignore') # suppress empty matrix RuntimeWarning: All-NaN slice encountered
sn.heatmap(array,
ax=ax,
annot=nc < 30,
annot_kws={
"size": 8},
cmap='Blues',
fmt='.2f',
square=True,
vmin=0.0,
xticklabels=ticklabels,
yticklabels=ticklabels).set_facecolor((1, 1, 1))
ax.set_ylabel('True')
ax.set_ylabel('Predicted')
ax.set_title('Confusion Matrix')
fig.savefig(Path(save_dir) / 'confusion_matrix.png', dpi=250)
plt.close(fig)
def print(self):
for i in range(self.nc + 1):
print(' '.join(map(str, self.matrix[i])))
def fitness_detection(x):
# Model fitness as a weighted combination of metrics
w = [0.0, 0.0, 0.1, 0.9] # weights for [P, R, mAP@0.5, mAP@0.5:0.95]
return (x[:, :4] * w).sum(1)
def fitness_segmentation(x):
# Model fitness as a weighted combination of metrics
w = [0.0, 0.0, 0.1, 0.9, 0.0, 0.0, 0.1, 0.9]
return (x[:, :8] * w).sum(1)
def smooth(y, f=0.05):
# Box filter of fraction f
nf = round(len(y) * f * 2) // 2 + 1 # number of filter elements (must be odd)
p = np.ones(nf // 2) # ones padding
yp = np.concatenate((p * y[0], y, p * y[-1]), 0) # y padded
return np.convolve(yp, np.ones(nf) / nf, mode='valid') # y-smoothed
def plot_pr_curve(px, py, ap, save_dir=Path('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 mAP@0.5' % ap[:, 0].mean())
ax.set_xlabel('Recall')
ax.set_ylabel('Precision')
ax.set_xlim(0, 1)
ax.set_ylim(0, 1)
ax.legend(bbox_to_anchor=(1.04, 1), loc="upper left")
ax.set_title('Precision-Recall Curve')
fig.savefig(save_dir, dpi=250)
plt.close(fig)
def plot_mc_curve(px, py, save_dir=Path('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 = smooth(py.mean(0), 0.05)
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)
ax.legend(bbox_to_anchor=(1.04, 1), loc="upper left")
ax.set_title(f'{ylabel}-Confidence Curve')
fig.savefig(save_dir, dpi=250)
plt.close(fig)
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
def ap_per_class(tp, conf, pred_cls, target_cls, plot=False, save_dir='.', names=(), eps=1e-16, prefix=""):
""" 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 mAP@0.5
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, nt = np.unique(target_cls, return_counts=True)
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 = nt[ci] # number of labels
n_p = i.sum() # number of predictions
if n_p == 0 or n_l == 0:
continue
# Accumulate FPs and TPs
fpc = (1 - tp[i]).cumsum(0)
tpc = tp[i].cumsum(0)
# Recall
recall = tpc / (n_l + eps) # 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 mAP@0.5
# Compute F1 (harmonic mean of precision and recall)
f1 = 2 * p * r / (p + r + eps)
names = [v for k, v in names.items() if k in unique_classes] # list: only classes that have data
names = dict(enumerate(names)) # to dict
if plot:
plot_pr_curve(px, py, ap, Path(save_dir) / f'{prefix}PR_curve.png', names)
plot_mc_curve(px, f1, Path(save_dir) / f'{prefix}F1_curve.png', names, ylabel='F1')
plot_mc_curve(px, p, Path(save_dir) / f'{prefix}P_curve.png', names, ylabel='Precision')
plot_mc_curve(px, r, Path(save_dir) / f'{prefix}R_curve.png', names, ylabel='Recall')
i = smooth(f1.mean(0), 0.1).argmax() # max F1 index
p, r, f1 = p[:, i], r[:, i], f1[:, i]
tp = (r * nt).round() # true positives
fp = (tp / (p + eps) - tp).round() # false positives
return tp, fp, p, r, f1, ap, unique_classes.astype(int)
def ap_per_class_box_and_mask(
tp_m,
tp_b,
conf,
pred_cls,
target_cls,
plot=False,
save_dir=".",
names=(),
):
"""
Args:
tp_b: tp of boxes.
tp_m: tp of masks.
other arguments see `func: ap_per_class`.
"""
results_boxes = ap_per_class(tp_b,
conf,
pred_cls,
target_cls,
plot=plot,
save_dir=save_dir,
names=names,
prefix="Box")[2:]
results_masks = ap_per_class(tp_m,
conf,
pred_cls,
target_cls,
plot=plot,
save_dir=save_dir,
names=names,
prefix="Mask")[2:]
results = {
"boxes": {
"p": results_boxes[0],
"r": results_boxes[1],
"f1": results_boxes[2],
"ap": results_boxes[3],
"ap_class": results_boxes[4]},
"masks": {
"p": results_masks[0],
"r": results_masks[1],
"f1": results_masks[2],
"ap": results_masks[3],
"ap_class": results_masks[4]}}
return results
class Metric:
def __init__(self) -> None:
self.p = [] # (nc, )
self.r = [] # (nc, )
self.f1 = [] # (nc, )
self.all_ap = [] # (nc, 10)
self.ap_class_index = [] # (nc, )
@property
def ap50(self):
"""AP@0.5 of all classes.
Return:
(nc, ) or [].
"""
return self.all_ap[:, 0] if len(self.all_ap) else []
@property
def ap(self):
"""AP@0.5:0.95
Return:
(nc, ) or [].
"""
return self.all_ap.mean(1) if len(self.all_ap) else []
@property
def mp(self):
"""mean precision of all classes.
Return:
float.
"""
return self.p.mean() if len(self.p) else 0.0
@property
def mr(self):
"""mean recall of all classes.
Return:
float.
"""
return self.r.mean() if len(self.r) else 0.0
@property
def map50(self):
"""Mean AP@0.5 of all classes.
Return:
float.
"""
return self.all_ap[:, 0].mean() if len(self.all_ap) else 0.0
@property
def map(self):
"""Mean AP@0.5:0.95 of all classes.
Return:
float.
"""
return self.all_ap.mean() if len(self.all_ap) else 0.0
def mean_results(self):
"""Mean of results, return mp, mr, map50, map"""
return (self.mp, self.mr, self.map50, self.map)
def class_result(self, i):
"""class-aware result, return p[i], r[i], ap50[i], ap[i]"""
return (self.p[i], self.r[i], self.ap50[i], self.ap[i])
def get_maps(self, nc):
maps = np.zeros(nc) + self.map
for i, c in enumerate(self.ap_class_index):
maps[c] = self.ap[i]
return maps
def update(self, results):
"""
Args:
results: tuple(p, r, ap, f1, ap_class)
"""
p, r, f1, all_ap, ap_class_index = results
self.p = p
self.r = r
self.all_ap = all_ap
self.f1 = f1
self.ap_class_index = ap_class_index
class Metrics:
"""Metric for boxes and masks."""
def __init__(self) -> None:
self.metric_box = Metric()
self.metric_mask = Metric()
def update(self, results):
"""
Args:
results: Dict{'boxes': Dict{}, 'masks': Dict{}}
"""
self.metric_box.update(list(results["boxes"].values()))
self.metric_mask.update(list(results["masks"].values()))
def mean_results(self):
return self.metric_box.mean_results() + self.metric_mask.mean_results()
def class_result(self, i):
return self.metric_box.class_result(i) + self.metric_mask.class_result(i)
def get_maps(self, nc):
return self.metric_box.get_maps(nc) + self.metric_mask.get_maps(nc)
@property
def ap_class_index(self):
# boxes and masks have the same ap_class_index
return self.metric_box.ap_class_index