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Post-processing

In object detection models like YOLO, post-processing is essential to refine the raw predictions made by the network. As we have seen in Lesson 2, these models tend to produce a large number of predictions.

This behavior is due to the model architecture, where:

  • Each grid cell predicts multiple anchor boxes.
  • Neighboring cells can detect the same object.

As a result, several overlapping boxes may represent the same object. If we keep all predicted boxes, the output would contain many duplicates.

To address this, post-processing includes:

  • Confidence thresholding: Filters out low-confidence detections.
  • Non-Maximum Suppression (NMS): Removes redundant overlapping boxes, keeping only the most confident one.

This step ensures cleaner and more accurate results.

The objective of this lesson is to learn how to implement post-processing filters and understand how they can help us improve our results.

Add Help Module Path

First, we add the help module:

addpath('help-module');

Loading a model

Next, we load the model to which we will apply the post-processing techniques:

modelPath = fullfile(pwd, 'runs', 'detect', 'train10', 'weights');
configFile = fullfile(pwd, 'datasets', 'fruits_3_4998', 'data.yaml');

yolov8Det = utils.loadModel(modelPath, configFile);

Exercise 1 - Confidence filter

Implement a confidence filter that removes detections with a confidence level below the threshold.

function filteredDetections  = filterByConfidence(detections, threshold)
    % Removes detections with confidence below a threshold.
    % Inputs:
    %   detections - Array of structs, each representing a detection result with fields:
    %                .boxes (Nx4): bounding boxes [x1 y1 x2 y2]
    %                .conf  (Nx1): confidence scores
    %                .cls   (Nx1): class labels
    %   threshold  - Scalar value specifying the minimum confidence score required to keep a detection
    %
    % Output:
    %   filteredDetections - Array of structs with low-confidence detections removed.

end

Solution

function filteredDetections  = filterByConfidence(detections, threshold)
    % Removes detections with confidence below a threshold.
    % Inputs:
    %   detections - Array of structs, each representing a detection result with fields:
    %                .boxes (Nx4): bounding boxes [x1 y1 x2 y2]
    %                .conf  (Nx1): confidence scores
    %                .cls   (Nx1): class labels
    %   threshold  - Scalar value specifying the minimum confidence score required to keep a detection
    %
    % Output:
    %   filteredDetections - Array of structs with low-confidence detections removed.

    n = numel(detections);
    filteredDetections = [];
    for i = 1:n
        detection = detections(i);
        conf = detection.conf;
        keep = conf >= threshold;
        if keep
           filteredDetections = [filteredDetections, detection];
        else
            fprintf('Filtered: removed low-confidence detection\n');
        end
    end
end

In the following code, we define an anonymous function for the filter we implemented in the previous exercise, which we then use to create a post-processing component.

ScoreThreshold = 0.73;

removeLowScore = @(detections) filterByConfidence(detections, ScoreThreshold);
postprocessing = utils.PostProcessing(yolov8Det, {removeLowScore});

This post-processing component is used in the following code to apply our filter to the detections, which we can control using the ScoreThreshold variable.

utils.displayFilteredDetections(yolov8Det, 'pear.jpg', postprocessing);

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Exercise 2 - Confidence filter by classes

As in the previous exercise, you must implement a confidence filter that removes detections with a confidence score below a threshold. However, this time, each class should have its own custom threshold.

function filteredDetection = filterByClassConfidence(detection, thresholds)
   % Filters detections using a confidence threshold specific to each class.
    % Inputs:
    %   detections  - Array of structs, each representing detection results with fields:
    %                 .boxes (Nx4): bounding boxes
    %                 .conf  (Nx1): confidence scores
    %                 .cls   (Nx1): class labels (as integers starting from 1)
    %
    %   thresholds  - Vector of class-specific confidence thresholds.
    %                 thresholds(i) is the minimum confidence required for class i.
    %
    % Output:
    %   filteredDetections - Array of structs with low-confidence detections removed,
    %                        where filtering is applied per class using corresponding thresholds.

end 

function filteredDetections = filterByClassConfidence(detections, thresholds)
    % Filters detections using a confidence threshold specific to each class.
    % Inputs:
    %   detections  - Array of structs, each representing detection results with fields:
    %                 .boxes (Nx4): bounding boxes
    %                 .conf  (Nx1): confidence scores
    %                 .cls   (Nx1): class labels (as integers starting from 1)
    %
    %   thresholds  - Vector of class-specific confidence thresholds.
    %                 thresholds(i) is the minimum confidence required for class i.
    %
    % Output:
    %   filteredDetections - Array of structs with low-confidence detections removed,
    %                        where filtering is applied per class using corresponding thresholds.

    n = numel(detections);
    filteredDetections = [];  % preallocate struct array
    for i = 1:n
        detection = detections(i);

        cls = detection.cls;
        conf = detection.conf;
        keep = conf >= thresholds(cls);

        if keep
            filteredDetections = [filteredDetections, detection];
        else
            fprintf('Filtered: removed low-confidence detections (per class)\n');
        end
    end
end 

% Threshold vector per class (index = class)
appleThreshold = 0.66;
orangeThreshold = 0.45;
pearThreshold = 0.61;

scoreThresholds = [appleThreshold, orangeThreshold, pearThreshold];
removeLowScorePerClass = @(detections) filterByClassConfidence(detections, scoreThresholds)

removeLowScorePerClass = function_handle with value:
    @(detections)filterByClassConfidence(detections,scoreThresholds)

postprocessing = utils.PostProcessing(yolov8Det, {removeLowScorePerClass});

utils.displayFilteredDetections(yolov8Det, 'multiple.jpg', postprocessing);

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figure_1.png

Intersection over Union (IoU)

In object detection, a fundamental concept is Intersection over Union (IoU). This metric quantifies the overlap between two bounding boxes: the predicted box from the model and the ground truth box. IoU is used to assess how accurate a prediction is in relation to the actual annotation.

Formally, IoU is defined as the ratio between the area of intersection and the area of union of the two boxes:

image_0.png

The value of IoU is bounded between 0 and 1:

  • IoU = 0 means there is no overlap.
  • IoU = 1 indicates a perfect match between the prediction and the ground truth.

Exercise 3 - Calculate IoU

Implement a function that calculates the Intersection over Union of two bounding boxes:

Hint

$$ \textrm{union}={\textrm{area}}_1 +{\textrm{area}}_2 -\textrm{intersection} $$ 

function iou = calculateIoU(b1, b2)
    % Calculates the Intersection over Union (IoU) between two bounding boxes.
    %
    % Inputs:
    %   b1 - 1x4 vector representing the first bounding box [x1 y1 x2 y2]
    %   b2 - 1x4 vector representing the second bounding box [x1 y1 x2 y2]
    %
    % Output:
    %   iou - Scalar value between 0 and 1 representing the IoU.
    %         IoU = 0 if there is no overlap.
    %         IoU = 1 if boxes are identical.

    iou = calculateIoUSolution(b1, b2);

end


function iou = calculateIoU(b1, b2)
    % Calculates the Intersection over Union (IoU) between two bounding boxes.
    %
    % Inputs:
    %   b1 - 1x4 vector representing the first bounding box [x1 y1 x2 y2]
    %   b2 - 1x4 vector representing the second bounding box [x1 y1 x2 y2]
    %
    % Output:
    %   iou - Scalar value between 0 and 1 representing the IoU.
    %         IoU = 0 if there is no overlap.
    %         IoU = 1 if boxes are identical.

    x1 = max(b1(1), b2(1));
    y1 = max(b1(2), b2(2));
    x2 = min(b1(3), b2(3));
    y2 = min(b1(4), b2(4));
    inter = max(0, x2-x1) * max(0, y2-y1);
    area1 = (b1(3)-b1(1))*(b1(4)-b1(2));
    area2 = (b2(3)-b2(1))*(b2(4)-b2(2));
    union = area1 + area2 - inter;
    if union>0
        iou = inter/union;
    else
        iou = 0;
    end

end

Test

utils.displayIoU([0 0 2 2], [2 2 4 4], @calculateIoU) % expected 0

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utils.displayIoU([2 2 4 4], [2 2 4 4], @calculateIoU) % expected 1

figure_3.png

utils.displayIoU([0 0 2 2], [1 1 3 3], @calculateIoU) % expected 0.1429

figure_4.png

utils.displayIoU([0 0 2 2], [1 1 2 2], @calculateIoU) % expected 0.25

figure_5.png

utils.displayIoU([0 0 3 3], [0.5 0 3 3], @calculateIoU); % Expectected 0.8333

figure_6.png

Exercise 4 - Non-Maximum Suppression

In this exercise, your goal is to implement Non-Maximum Suppression (NMS) to eliminate redundant overlapping detections of the same class.

How NMS Works

The basic NMS algorithm consists of these steps:

  1. Filter by Confidence Score: Remove all boxes with confidence (objectness × class probability) below a threshold (e.g., 0.25).
  2. Sort Boxes by Score: Arrange the remaining boxes in descending order of their confidence scores.

  3. Suppress Overlapping Boxes:

  4. Take the box with the highest confidence, call it B1.

  5. Compute the IoU (Intersection over Union) of B1 with all other boxes:IoU
  6. IoUThreshold (e.g., 0.5), discard those boxes since they likely represent the same object.
  7. Repeat with the next remaining box.

Hint

Use the following function to convert bounding boxes into the format required by the calculateIoU function:

function boxXYXY = xywh2xyxy(boxXYWH)
    % Convert [x y w h] into [x1 y1 x2 y2]
    boxXYXY = [boxXYWH(1), ...
               boxXYWH(2), ...
               boxXYWH(1) + boxXYWH(3), ...
               boxXYWH(2) + boxXYWH(4)];
end

function filteredDetections = filterByOverlapping(detections, iouThreshold, calculateIoU)
    % Removes overlapping detections based on Intersection over Union (IoU).
    % Inputs:
    %   detections    - Array of Struct containing detection results with fields:
    %                  .boxes (Nx4): bounding boxes [x1 y1 x2 y2]
    %                  .conf  (Nx1): confidence scores
    %                  .cls   (Nx1): class labels
    %   iouThreshold - Scalar threshold for IoU. Detections with IoU above this 
    %                  value (and same class) are considered duplicates.
    %   calculateIoU  - Function handle to compute IoU between two boxes.
    %
    % Output:
    %   filteredDetection - Detection struct with overlapping boxes removed,
    %                       keeping the one with higher confidence.
end

function filteredDetections = filterByOverlapping(detections, iouThreshold, calculateIoU)
    % Removes overlapping detections based on Intersection over Union (IoU).
    % Inputs:
    %   detections    - Array of Struct containing detection results with fields:
    %                  .boxes (Nx4): bounding boxes [x1 y1 x2 y2]
    %                  .conf  (Nx1): confidence scores
    %                  .cls   (Nx1): class labels
    %   iouThreshold - Scalar threshold for IoU. Detections with IoU above this 
    %                  value (and same class) are considered duplicates.
    %   calculateIoU  - Function handle to compute IoU between two boxes.
    %
    % Output:
    %   filteredDetection - Detection struct with overlapping boxes removed,
    %                       keeping the one with higher confidence.


    % Extract individual detection components
    boxes = vertcat(detections.boxes);  % Nx4
    conf  = vertcat(detections.conf);   % Nx1
    cls   = vertcat(detections.cls);    % Nx1

    N = size(boxes, 1);         % Total number of detections

    % Sort detections by descending confidence
    [~, order] = sort(conf, 'descend');

    keep = false(N,1);          % Boolean mask to track which boxes to keep

    % Iterate over detections in sorted order
    for k = 1:N
        idx = order(k);         % Index of the current detection
        keepThis = true;        % Flag indicating whether to keep the current box

        % Compare with previously kept boxes
        for j = find(keep)'     % Indices of already kept boxes
            if cls(idx) == cls(j)   % Only compare boxes of the same class
                iou = calculateIoU(xywh2xyxy(boxes(idx,:)), xywh2xyxy(boxes(j,:)));
                if iou > iouThreshold
                    keepThis = false;
                    break;
                end
            end
        end

        if keepThis
            keep(idx) = true;
        end
    end

    % Keep only selected detections
    filteredDetections.boxes = boxes(keep,:);
    filteredDetections.conf  = conf(keep);
    filteredDetections.cls   = cls(keep);

    removed = sum(~keep);
    if removed > 0
        fprintf('Filtered: removed %d overlapping detections\n', removed);
    end
end

ScoreThreshold = 0.5;
removeLowScore = @(detections) filterByConfidence(detections, ScoreThreshold);

iouThreshold = 0.5;
removeOverlapping = @(detections) filterByOverlapping(detections, iouThreshold, @calculateIoU);

filters = {removeLowScore, removeOverlapping};
postprocessing = utils.PostProcessing(yolov8Det, filters);
utils.displayFilteredDetections(yolov8Det, 'pear.jpg', postprocessing);

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figure_7.png

utils.displayFilteredDetections(yolov8Det, 'orange.jpg', postprocessing);

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figure_8.png

utils.displayFilteredDetections(yolov8Det, 'orange2.jpg', postprocessing);

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figure_9.png

utils.displayFilteredDetections(yolov8Det, 'apple.jpg', postprocessing);

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figure_10.png

utils.displayFilteredDetections(yolov8Det, 'apple2.jpg', postprocessing);

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figure_11.png

utils.displayFilteredDetections(yolov8Det, 'multiple.jpg', postprocessing);

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figure_12.png

Now, after filtering the predictions, we obtain good results; however, we have no idea how good the model actually is.

In the next lesson, we will address this question.