CACLR (cumulative ACLR)

CACLR (cumulative ACLR) stands for Cumulative Absolute Category-wise Localisation Error. It is a performance metric used in the field of object detection and image classification to evaluate the accuracy of the localization of an object in an image. CACLR is an extension of the widely used Average Precision (AP) metric, and it is widely used in research papers and competitions to evaluate the performance of object detection algorithms.

In this article, we will discuss the concept of CACLR, its calculation, and how it is used in evaluating the performance of object detection algorithms.

Object Detection and Localization

Object detection is a field of computer vision that involves identifying the presence of objects in an image and drawing a bounding box around them. Object localization is a related task that involves not only detecting objects but also precisely localizing them within an image. Object detection and localization are critical tasks in various applications such as self-driving cars, robotics, and security systems.

The accuracy of object detection and localization can be evaluated using several performance metrics such as precision, recall, and average precision. In addition to these metrics, object detection algorithms are also evaluated based on their ability to accurately localize objects within an image.

Average Precision (AP)

The average precision (AP) is a widely used performance metric for object detection algorithms. AP is used to evaluate the accuracy of object detection by calculating the precision and recall of the algorithm at different intersection over union (IoU) thresholds.

The precision is the fraction of true positives (TP) among the total number of detections (TP + false positives (FP)). Recall is the fraction of true positives (TP) among the total number of ground truth objects (TP + false negatives (FN)). IoU is a measure of how well the predicted bounding box overlaps with the ground truth bounding box.

To calculate AP, the precision and recall are first calculated for each IoU threshold. The precision-recall curve is then calculated by plotting the precision values against the recall values for each IoU threshold. The area under the precision-recall curve (AUC) is then calculated to obtain the AP score.

Cumulative Absolute Category-wise Localisation Error (CACLR)

The Average Precision (AP) metric does not take into account the accuracy of the localization of the predicted bounding box. Therefore, an extension of AP called Cumulative Absolute Category-wise Localisation Error (CACLR) was proposed to evaluate the accuracy of object localization.

CACLR is a performance metric that measures the cumulative error of the predicted bounding boxes with respect to the ground truth bounding boxes. CACLR is computed by calculating the absolute distance between the center point of the predicted bounding box and the ground truth bounding box for each object category.

The CACLR metric is computed as the average of the absolute distance between the center point of the predicted bounding box and the ground truth bounding box for each object category over all images in the dataset. The distance between the center point of the predicted bounding box and the ground truth bounding box is calculated using the Euclidean distance formula.

CACLR is calculated as follows:

CACLR = (1 / N) * Σ(ci / ni)

where N is the total number of object categories, ci is the sum of the distances between the center point of the predicted bounding box and the ground truth bounding box for category i, and ni is the total number of objects in category i.

Calculating CACLR

To calculate CACLR, the predicted bounding boxes and ground truth bounding boxes are first matched based on their IoU values. The predicted bounding boxes with the highest IoU values with the ground truth bounding boxes are considered as true positives.

For each true positive, the distance between the center point of the predicted bounding box and the ground truth bounding box is calculated using the Euclidean distance formula. The distance values for each object category are then summed up, and the total distance for each category is divided by the total number of objects in that category to obtain the average distance for that category. The average distance for each category is then summed up and divided by the total number of categories to obtain the CACLR score.

CACLR provides a measure of the accuracy of the localization of the predicted bounding box for each object category. A low CACLR score indicates that the algorithm is accurately localizing the objects in the image. A high CACLR score indicates that the algorithm is not accurately localizing the objects in the image.

Limitations of CACLR

CACLR has some limitations. First, it does not consider the size of the object in the image. For example, an object that is small in size may have a larger localization error than an object that is larger in size, even if the actual distance between the predicted and ground truth bounding boxes is the same.

Second, CACLR does not consider the orientation of the object in the image. If an object is rotated, the center point of the predicted bounding box may be far from the center point of the ground truth bounding box, even if the predicted bounding box accurately encompasses the object.

Conclusion

CACLR is an important performance metric used in evaluating the accuracy of object detection algorithms. It measures the cumulative error of the predicted bounding boxes with respect to the ground truth bounding boxes for each object category. CACLR provides a measure of the accuracy of the localization of the predicted bounding box for each object category, and a low CACLR score indicates that the algorithm is accurately localizing the objects in the image.

However, CACLR has some limitations, including not considering the size and orientation of the object in the image. Despite these limitations, CACLR is still widely used in research papers and competitions to evaluate the performance of object detection algorithms.