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# YOLOv5 🚀 by Ultralytics, GPL-3.0 license |
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""" |
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Model validation metrics |
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""" |
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import math |
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import warnings |
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from pathlib import Path |
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import matplotlib.pyplot as plt |
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import numpy as np |
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import torch |
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import torch.nn as nn |
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from ultralytics.yolo.utils import TryExcept |
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# boxes |
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def box_area(box): |
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# box = xyxy(4,n) |
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return (box[2] - box[0]) * (box[3] - box[1]) |
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def bbox_ioa(box1, box2, eps=1e-7): |
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"""Returns the intersection over box2 area given box1, box2. Boxes are x1y1x2y2 |
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box1: np.array of shape(nx4) |
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box2: np.array of shape(mx4) |
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returns: np.array of shape(nxm) |
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""" |
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# Get the coordinates of bounding boxes |
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b1_x1, b1_y1, b1_x2, b1_y2 = box1.T |
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b2_x1, b2_y1, b2_x2, b2_y2 = box2.T |
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# Intersection area |
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inter_area = (np.minimum(b1_x2[:, None], b2_x2) - np.maximum(b1_x1[:, None], b2_x1)).clip(0) * \ |
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(np.minimum(b1_y2[:, None], b2_y2) - np.maximum(b1_y1[:, None], b2_y1)).clip(0) |
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# box2 area |
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box2_area = (b2_x2 - b2_x1) * (b2_y2 - b2_y1) + eps |
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# Intersection over box2 area |
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return inter_area / box2_area |
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def box_iou(box1, box2, eps=1e-7): |
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# https://github.com/pytorch/vision/blob/master/torchvision/ops/boxes.py |
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""" |
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Return intersection-over-union (Jaccard index) of boxes. |
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Both sets of boxes are expected to be in (x1, y1, x2, y2) format. |
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Arguments: |
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box1 (Tensor[N, 4]) |
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box2 (Tensor[M, 4]) |
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Returns: |
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iou (Tensor[N, M]): the NxM matrix containing the pairwise |
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IoU values for every element in boxes1 and boxes2 |
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""" |
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# inter(N,M) = (rb(N,M,2) - lt(N,M,2)).clamp(0).prod(2) |
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(a1, a2), (b1, b2) = box1[:, None].chunk(2, 2), box2.chunk(2, 1) |
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inter = (torch.min(a2, b2) - torch.max(a1, b1)).clamp(0).prod(2) |
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# IoU = inter / (area1 + area2 - inter) |
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return inter / (box_area(box1.T)[:, None] + box_area(box2.T) - inter + eps) |
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def bbox_iou(box1, box2, xywh=True, GIoU=False, DIoU=False, CIoU=False, eps=1e-7): |
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# Returns Intersection over Union (IoU) of box1(1,4) to box2(n,4) |
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# Get the coordinates of bounding boxes |
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if xywh: # transform from xywh to xyxy |
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(x1, y1, w1, h1), (x2, y2, w2, h2) = box1.chunk(4, 1), box2.chunk(4, 1) |
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w1_, h1_, w2_, h2_ = w1 / 2, h1 / 2, w2 / 2, h2 / 2 |
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b1_x1, b1_x2, b1_y1, b1_y2 = x1 - w1_, x1 + w1_, y1 - h1_, y1 + h1_ |
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b2_x1, b2_x2, b2_y1, b2_y2 = x2 - w2_, x2 + w2_, y2 - h2_, y2 + h2_ |
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else: # x1, y1, x2, y2 = box1 |
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b1_x1, b1_y1, b1_x2, b1_y2 = box1.chunk(4, 1) |
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b2_x1, b2_y1, b2_x2, b2_y2 = box2.chunk(4, 1) |
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w1, h1 = b1_x2 - b1_x1, b1_y2 - b1_y1 + eps |
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w2, h2 = b2_x2 - b2_x1, b2_y2 - b2_y1 + eps |
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# Intersection area |
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inter = (torch.min(b1_x2, b2_x2) - torch.max(b1_x1, b2_x1)).clamp(0) * \ |
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(torch.min(b1_y2, b2_y2) - torch.max(b1_y1, b2_y1)).clamp(0) |
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# Union Area |
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union = w1 * h1 + w2 * h2 - inter + eps |
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# IoU |
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iou = inter / union |
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if CIoU or DIoU or GIoU: |
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cw = torch.max(b1_x2, b2_x2) - torch.min(b1_x1, b2_x1) # convex (smallest enclosing box) width |
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ch = torch.max(b1_y2, b2_y2) - torch.min(b1_y1, b2_y1) # convex height |
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if CIoU or DIoU: # Distance or Complete IoU https://arxiv.org/abs/1911.08287v1 |
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c2 = cw ** 2 + ch ** 2 + eps # convex diagonal squared |
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rho2 = ((b2_x1 + b2_x2 - b1_x1 - b1_x2) ** 2 + (b2_y1 + b2_y2 - b1_y1 - b1_y2) ** 2) / 4 # center dist ** 2 |
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if CIoU: # https://github.com/Zzh-tju/DIoU-SSD-pytorch/blob/master/utils/box/box_utils.py#L47 |
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v = (4 / math.pi ** 2) * torch.pow(torch.atan(w2 / h2) - torch.atan(w1 / h1), 2) |
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with torch.no_grad(): |
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alpha = v / (v - iou + (1 + eps)) |
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return iou - (rho2 / c2 + v * alpha) # CIoU |
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return iou - rho2 / c2 # DIoU |
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c_area = cw * ch + eps # convex area |
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return iou - (c_area - union) / c_area # GIoU https://arxiv.org/pdf/1902.09630.pdf |
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return iou # IoU |
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def mask_iou(mask1, mask2, eps=1e-7): |
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""" |
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mask1: [N, n] m1 means number of predicted objects |
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mask2: [M, n] m2 means number of gt objects |
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Note: n means image_w x image_h |
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return: masks iou, [N, M] |
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""" |
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intersection = torch.matmul(mask1, mask2.t()).clamp(0) |
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union = (mask1.sum(1)[:, None] + mask2.sum(1)[None]) - intersection # (area1 + area2) - intersection |
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return intersection / (union + eps) |
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def masks_iou(mask1, mask2, eps=1e-7): |
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""" |
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mask1: [N, n] m1 means number of predicted objects |
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mask2: [N, n] m2 means number of gt objects |
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Note: n means image_w x image_h |
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return: masks iou, (N, ) |
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""" |
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intersection = (mask1 * mask2).sum(1).clamp(0) # (N, ) |
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union = (mask1.sum(1) + mask2.sum(1))[None] - intersection # (area1 + area2) - intersection |
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return intersection / (union + eps) |
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def smooth_BCE(eps=0.1): # https://github.com/ultralytics/yolov3/issues/238#issuecomment-598028441 |
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# return positive, negative label smoothing BCE targets |
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return 1.0 - 0.5 * eps, 0.5 * eps |
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# losses |
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class FocalLoss(nn.Module): |
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# Wraps focal loss around existing loss_fcn(), i.e. criteria = FocalLoss(nn.BCEWithLogitsLoss(), gamma=1.5) |
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def __init__(self, loss_fcn, gamma=1.5, alpha=0.25): |
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super().__init__() |
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self.loss_fcn = loss_fcn # must be nn.BCEWithLogitsLoss() |
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self.gamma = gamma |
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self.alpha = alpha |
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self.reduction = loss_fcn.reduction |
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self.loss_fcn.reduction = 'none' # required to apply FL to each element |
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def forward(self, pred, true): |
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loss = self.loss_fcn(pred, true) |
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# p_t = torch.exp(-loss) |
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# loss *= self.alpha * (1.000001 - p_t) ** self.gamma # non-zero power for gradient stability |
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# TF implementation https://github.com/tensorflow/addons/blob/v0.7.1/tensorflow_addons/losses/focal_loss.py |
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pred_prob = torch.sigmoid(pred) # prob from logits |
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p_t = true * pred_prob + (1 - true) * (1 - pred_prob) |
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alpha_factor = true * self.alpha + (1 - true) * (1 - self.alpha) |
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modulating_factor = (1.0 - p_t) ** self.gamma |
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loss *= alpha_factor * modulating_factor |
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if self.reduction == 'mean': |
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return loss.mean() |
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elif self.reduction == 'sum': |
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return loss.sum() |
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else: # 'none' |
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return loss |
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class ConfusionMatrix: |
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# Updated version of https://github.com/kaanakan/object_detection_confusion_matrix |
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def __init__(self, nc, conf=0.25, iou_thres=0.45): |
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self.matrix = np.zeros((nc + 1, nc + 1)) |
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self.nc = nc # number of classes |
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self.conf = conf |
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self.iou_thres = iou_thres |
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def process_batch(self, detections, labels): |
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""" |
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Return intersection-over-union (Jaccard index) of boxes. |
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Both sets of boxes are expected to be in (x1, y1, x2, y2) format. |
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Arguments: |
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detections (Array[N, 6]), x1, y1, x2, y2, conf, class |
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labels (Array[M, 5]), class, x1, y1, x2, y2 |
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Returns: |
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None, updates confusion matrix accordingly |
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""" |
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if detections is None: |
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gt_classes = labels.int() |
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for gc in gt_classes: |
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self.matrix[self.nc, gc] += 1 # background FN |
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return |
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detections = detections[detections[:, 4] > self.conf] |
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gt_classes = labels[:, 0].int() |
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detection_classes = detections[:, 5].int() |
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iou = box_iou(labels[:, 1:], detections[:, :4]) |
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x = torch.where(iou > self.iou_thres) |
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if x[0].shape[0]: |
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matches = torch.cat((torch.stack(x, 1), iou[x[0], x[1]][:, None]), 1).cpu().numpy() |
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if x[0].shape[0] > 1: |
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matches = matches[matches[:, 2].argsort()[::-1]] |
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matches = matches[np.unique(matches[:, 1], return_index=True)[1]] |
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matches = matches[matches[:, 2].argsort()[::-1]] |
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matches = matches[np.unique(matches[:, 0], return_index=True)[1]] |
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else: |
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matches = np.zeros((0, 3)) |
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n = matches.shape[0] > 0 |
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m0, m1, _ = matches.transpose().astype(int) |
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for i, gc in enumerate(gt_classes): |
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j = m0 == i |
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if n and sum(j) == 1: |
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self.matrix[detection_classes[m1[j]], gc] += 1 # correct |
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else: |
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self.matrix[self.nc, gc] += 1 # true background |
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if n: |
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for i, dc in enumerate(detection_classes): |
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if not any(m1 == i): |
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self.matrix[dc, self.nc] += 1 # predicted background |
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def matrix(self): |
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return self.matrix |
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def tp_fp(self): |
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tp = self.matrix.diagonal() # true positives |
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fp = self.matrix.sum(1) - tp # false positives |
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# fn = self.matrix.sum(0) - tp # false negatives (missed detections) |
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return tp[:-1], fp[:-1] # remove background class |
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@TryExcept('WARNING ⚠️ ConfusionMatrix plot failure') |
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def plot(self, normalize=True, save_dir='', names=()): |
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import seaborn as sn |
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array = self.matrix / ((self.matrix.sum(0).reshape(1, -1) + 1E-9) if normalize else 1) # normalize columns |
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array[array < 0.005] = np.nan # don't annotate (would appear as 0.00) |
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fig, ax = plt.subplots(1, 1, figsize=(12, 9), tight_layout=True) |
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nc, nn = self.nc, len(names) # number of classes, names |
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sn.set(font_scale=1.0 if nc < 50 else 0.8) # for label size |
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labels = (0 < nn < 99) and (nn == nc) # apply names to ticklabels |
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ticklabels = (names + ['background']) if labels else "auto" |
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with warnings.catch_warnings(): |
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warnings.simplefilter('ignore') # suppress empty matrix RuntimeWarning: All-NaN slice encountered |
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sn.heatmap(array, |
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ax=ax, |
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annot=nc < 30, |
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annot_kws={ |
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"size": 8}, |
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cmap='Blues', |
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fmt='.2f', |
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square=True, |
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vmin=0.0, |
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xticklabels=ticklabels, |
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yticklabels=ticklabels).set_facecolor((1, 1, 1)) |
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ax.set_ylabel('True') |
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ax.set_ylabel('Predicted') |
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ax.set_title('Confusion Matrix') |
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fig.savefig(Path(save_dir) / 'confusion_matrix.png', dpi=250) |
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plt.close(fig) |
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def print(self): |
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for i in range(self.nc + 1): |
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print(' '.join(map(str, self.matrix[i]))) |
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def fitness_detection(x): |
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# Model fitness as a weighted combination of metrics |
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w = [0.0, 0.0, 0.1, 0.9] # weights for [P, R, mAP@0.5, mAP@0.5:0.95] |
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return (x[:, :4] * w).sum(1) |
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def fitness_segmentation(x): |
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# Model fitness as a weighted combination of metrics |
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w = [0.0, 0.0, 0.1, 0.9, 0.0, 0.0, 0.1, 0.9] |
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return (x[:, :8] * w).sum(1) |
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def smooth(y, f=0.05): |
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# Box filter of fraction f |
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nf = round(len(y) * f * 2) // 2 + 1 # number of filter elements (must be odd) |
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p = np.ones(nf // 2) # ones padding |
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yp = np.concatenate((p * y[0], y, p * y[-1]), 0) # y padded |
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return np.convolve(yp, np.ones(nf) / nf, mode='valid') # y-smoothed |
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def compute_ap(recall, precision): |
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""" Compute the average precision, given the recall and precision curves |
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# Arguments |
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recall: The recall curve (list) |
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precision: The precision curve (list) |
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# Returns |
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Average precision, precision curve, recall curve |
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""" |
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# Append sentinel values to beginning and end |
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mrec = np.concatenate(([0.0], recall, [1.0])) |
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mpre = np.concatenate(([1.0], precision, [0.0])) |
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# Compute the precision envelope |
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mpre = np.flip(np.maximum.accumulate(np.flip(mpre))) |
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# Integrate area under curve |
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method = 'interp' # methods: 'continuous', 'interp' |
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if method == 'interp': |
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x = np.linspace(0, 1, 101) # 101-point interp (COCO) |
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ap = np.trapz(np.interp(x, mrec, mpre), x) # integrate |
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else: # 'continuous' |
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i = np.where(mrec[1:] != mrec[:-1])[0] # points where x axis (recall) changes |
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ap = np.sum((mrec[i + 1] - mrec[i]) * mpre[i + 1]) # area under curve |
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return ap, mpre, mrec |
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def ap_per_class(tp, conf, pred_cls, target_cls, plot=False, save_dir='.', names=(), eps=1e-16, prefix=""): |
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""" Compute the average precision, given the recall and precision curves. |
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Source: https://github.com/rafaelpadilla/Object-Detection-Metrics. |
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# Arguments |
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tp: True positives (nparray, nx1 or nx10). |
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conf: Objectness value from 0-1 (nparray). |
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pred_cls: Predicted object classes (nparray). |
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target_cls: True object classes (nparray). |
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plot: Plot precision-recall curve at mAP@0.5 |
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save_dir: Plot save directory |
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# Returns |
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The average precision as computed in py-faster-rcnn. |
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""" |
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# Sort by objectness |
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i = np.argsort(-conf) |
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tp, conf, pred_cls = tp[i], conf[i], pred_cls[i] |
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# Find unique classes |
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unique_classes, nt = np.unique(target_cls, return_counts=True) |
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nc = unique_classes.shape[0] # number of classes, number of detections |
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# Create Precision-Recall curve and compute AP for each class |
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px, py = np.linspace(0, 1, 1000), [] # for plotting |
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ap, p, r = np.zeros((nc, tp.shape[1])), np.zeros((nc, 1000)), np.zeros((nc, 1000)) |
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for ci, c in enumerate(unique_classes): |
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i = pred_cls == c |
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n_l = nt[ci] # number of labels |
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n_p = i.sum() # number of predictions |
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if n_p == 0 or n_l == 0: |
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continue |
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# Accumulate FPs and TPs |
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fpc = (1 - tp[i]).cumsum(0) |
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tpc = tp[i].cumsum(0) |
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# Recall |
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recall = tpc / (n_l + eps) # recall curve |
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r[ci] = np.interp(-px, -conf[i], recall[:, 0], left=0) # negative x, xp because xp decreases |
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# Precision |
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precision = tpc / (tpc + fpc) # precision curve |
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p[ci] = np.interp(-px, -conf[i], precision[:, 0], left=1) # p at pr_score |
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# AP from recall-precision curve |
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for j in range(tp.shape[1]): |
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ap[ci, j], mpre, mrec = compute_ap(recall[:, j], precision[:, j]) |
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if plot and j == 0: |
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py.append(np.interp(px, mrec, mpre)) # precision at mAP@0.5 |
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# Compute F1 (harmonic mean of precision and recall) |
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f1 = 2 * p * r / (p + r + eps) |
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names = [v for k, v in names.items() if k in unique_classes] # list: only classes that have data |
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names = dict(enumerate(names)) # to dict |
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# TODO: plot |
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''' |
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if plot: |
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plot_pr_curve(px, py, ap, Path(save_dir) / f'{prefix}PR_curve.png', names) |
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plot_mc_curve(px, f1, Path(save_dir) / f'{prefix}F1_curve.png', names, ylabel='F1') |
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plot_mc_curve(px, p, Path(save_dir) / f'{prefix}P_curve.png', names, ylabel='Precision') |
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plot_mc_curve(px, r, Path(save_dir) / f'{prefix}R_curve.png', names, ylabel='Recall') |
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''' |
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|
|
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], |
|
|
"ap": results_boxes[3], |
|
|
"f1": results_boxes[2], |
|
|
"ap_class": results_boxes[4]}, |
|
|
"masks": { |
|
|
"p": results_masks[0], |
|
|
"r": results_masks[1], |
|
|
"ap": results_masks[3], |
|
|
"f1": results_masks[2], |
|
|
"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, all_ap, f1, 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
|
|
|
|
