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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, mAP@0.5, mAP@0.5:0.95]
- 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 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 = 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 mAP@0.5
- # 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 mAP@0.5' % 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()
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