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metrics.py
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metrics.py
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import numpy as np
from pathlib import Path
import matplotlib.pyplot as plt
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 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 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 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)