The Principle and Application of NMS (Non-Maximum Suppression) Algorithm in YOLOv8

# An Overview of the NMS Algorithm in YOLOv8

NMS (Non-Maximum Suppression) is a widely used post-processing technique in object detection aimed at filtering out the optimal detection results from candidate detection boxes, eliminating overlapping or redundant detection boxes. In the YOLOv8 object detection framework, the NMS algorithm plays a crucial role, responsible for filtering the network's predicted boxes and generating the final object detection results.

# The Principle of the NMS Algorithm

### 2.1 Mathematical Derivation of the NMS Algorithm

#### 2.1.1 IoU Calculation

Intersection over Union (IoU) is a measure of the degree of overlap between two rectangular boxes, calculated by the formula:

IoU = (Area of Overlap) / (Area of Union)

where the area of overlap is:

Area of Overlap = min(box1_width, box2_width) * min(box1_height, box2_height)

and the area of union is:

Area of Union = box1_width * box1_height + box2_width * box2_height - Area of Overlap

#### 2.1.2 Confidence Threshold and IoU Threshold

The NMS algorithm has two key parameters:

- **Confidence Threshold**: Detection boxes below this threshold are filtered out.
- **IoU Threshold**: If the IoU between two detection boxes is greater than this threshold, the detection box with the smaller IoU is filtered out.

### 2.2 Implementation Steps of the NMS Algorithm

The implementation steps of the NMS algorithm are as follows:

1. Sort all detection boxes in descending order by confidence.
2. Iterate through the list of detection boxes:
- Skip if the confidence of the current detection box is below the confidence threshold.
- Otherwise, mark the current detection box as "kept".
- For the remaining detection boxes in the list:
- Calculate the IoU between the current detection box and the remaining detection boxes.
- If the IoU is greater than the IoU threshold, mark the remaining detection box as "discarded".
3. Return all detection boxes marked as "kept".

**Code Block:**

def nms(boxes, scores, iou_threshold=0.5, confidence_threshold=0.5):
     """
     Non-Maximum Suppression Algorithm (NMS)

     Args:
         boxes: List of detection boxes, each element is [x1, y1, x2, y2]
         scores: List of detection box confidences
         iou_threshold: IoU threshold
         confidence_threshold: Confidence threshold

     Returns:
         List of detection boxes marked as 'kept'
     """

     # Sort the detection boxes
     sorted_indices = np.argsort(scores)[::-1]
     boxes = boxes[sorted_indices]
     scores = scores[sorted_indices]

     # Initialize the list of detection boxes marked as 'kept'
     keep_boxes = []

     # Iterate through the detection boxes
     while boxes.size > 0:
         # Get the detection box with the highest confidence
         box = boxes[0]
         score = scores[0]

         # If confidence is below the threshold, break
         if score < confidence_threshold:
             break

         # Mark the current detection box as 'kept'
         keep_boxes.append(box)

         # Calculate the IoU of the current detection box with the remaining detection boxes
         ious = compute_ious(box, boxes[1:])

         # Mark detection boxes with an IoU greater than the threshold as 'discarded'
         boxes = boxes[1:][ious < iou_threshold]
         scores = scores[1:][ious < iou_threshold]

     return keep_boxes

**Code Logic Analysis:**

This code block implements the NMS algorithm. It first sorts the detection boxes in descending order of confidence. Then, it iterates through the list of detection boxes and performs the following operations for each:

- If confidence is below the threshold, skip.
- Otherwise, mark the current detection box as "kept."
- Calculate the IoU of the current detection box with the remaining detection boxes.
- If IoU is greater than the threshold, mark the remaining detection boxes as "discarded."

Finally, the code block returns all detection boxes marked as "kept."

**Parameter Explanation:**

- `boxes`: List of detection boxes, each element is [x1, y1, x2, y2].
- `scores`: List of detection box confidences.
- `iou_threshold`: IoU threshold (default value is 0.5).
- `confidence_threshold`: Confidence threshold (default value is 0.5).

# The Application of the NMS Algorithm in YOLOv8

### 3.1 YOLOv8 Object Detection Framework

#### 3.1.1 YOLOv8 Networ