2021SC@SDUSC

preface

This analysis measures.py file is used to calculate evaluation indicators, including mAP, confusion matrix and IOU related functions.

fitness function

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)

This function is used to calculate the final map by comparing P, R mAP@0.5 , mAP@0.5 : weighted average calculation map of 0.95

ap_per_class function

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')

Calculate the average precision of each class and draw the P-R curve

Parameters:

tp: true positive

Conf: conf of prediction box

pred_cls: class of prediction box

target_cls: class of GT

plot: whether to draw PR curve

save_dir: save path

Return value:

p: precision of each category at maximum average f1

r: recall of each category at maximum average f1

ap: mAP of each category under 10 iou thresholds

f1: f1 of each category at maximum average f1

unique_classes: index of all categories in the dataset

i = np.argsort(-conf)

Sort by conf from large to small, and return the index corresponding to the data

tp, conf, pred_cls = tp[i], conf[i], pred_cls[i]

Get the corresponding tp, conf and PRED after reordering_ cls

unique_classes = np.unique(target_cls)
nc = unique_classes.shape[0]

De duplication of categories. nc is the number of categories

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))

initialization

    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

Calculate fp, tp, recall, precision

f1 = 2 * p * r / (p + r + 1e-16)

Calculate f1

    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')

Draw the pr curve

compute_ap function

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

Calculate the mAP of a category under a iou threshold

Return value:

ap: average precision

mpre: precision for adding protection values

mrec: add recall of protection value

This function calculates the mAP according to the precision and recall under different thresholds

Fusionmatrix class

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])))

Calculate confusion matrix

init method

 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

Initialization, nc: number of categories, conf: prediction frame confidence threshold, iou_thres: iou threshold

process_batch method

detections: prediction results

labels: target results

detections = detections[detections[:, 4] > self.conf]

Screen out prediction frames with low confidence

gt_classes = labels[:, 0].int()

All gt box categories

detection_classes = detections[:, 5].int()

All forecast box categories

iou = box_iou(labels[:, 1:], detections[:, :4])

Find the iou of all gt boxes and all prediction boxes

x = torch.where(iou > self.iou_thres)

Select a value greater than the threshold

        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))

Get the largest iou in each prediction box and all gt boxes

        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

Calculation of mixing matrix

matrix method

    def matrix(self):
        return self.matrix

Returns the mixture matrix

plot and print methods

plot is used to visualize the mixed food matrix, and print is used to output and print the mixed food matrix. I won't talk about it carefully

summary

A lot of numpy matrix operations are used. They are complex and need to be debug ged carefully to understand. The rest will continue in the next article.