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.
# 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:
"""
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.

Posted by ltd on Mon, 22 Nov 2021 07:22:42 -0800