Merge pull request #28289 from JonasPerolini:pr-aruco-identification

Identify ArUco markers based on threshold to reduce false positives #28289

**Goal:** parametrize the current marker identification process (pixel-based majority count) to reduce the number of false positives while maintaining high recall. Useful in high risk scenarios in which false positives are not acceptable. 

**Context:** This PR builds on top of https://github.com/opencv/opencv/pull/23190 in which we've introduced a pixel-based confidence in the marker detection.

**Solution:** Include a new parameter: `validBitIdThreshold` used to identify markers based on the pixel count of each cell. Set the parameter default either to 50% which is equivalent to the current majority count implementation or to 49% which already singnificantly reduces the number of false positives (see details below). 

**Test coverage:** 
- Unit tests: `CV_ArucoDetectionThreshold`, `CV_InvertedArucoDetectionThreshold`
- The impact of `validBitIdThreshold` on false positives was also tested using the benchmark dataset: `MIRFLICKR-25k` https://www.kaggle.com/datasets/skfrost19/mirflickr25k which contains random images without any markers. Every marker detection is a false positive. 

Example of images in the dataset:

![im2048](https://github.com/user-attachments/assets/3e38796b-67ce-44be-a91d-2fd268414515)

![im17627](https://github.com/user-attachments/assets/37253b9f-829d-4bac-b9fc-c844d16f546e)

**Results:** A threshold of 49% already allows to significantly reduce the number of false positives for the dict `DICT_4X4_1000`: 
- `5942` false positives for `validBitIdThreshold = 0.5`
- `629` false positives for `validBitIdThreshold = 0.49` and `0.46` 
   - number of false positives divided by `9.5` when compared to `validBitIdThreshold = 0.5`
- `139` false positives for `validBitIdThreshold = 0.43` and `0.4` 
   - number of false positives divided by `42` when compared to `validBitIdThreshold = 0.5`

Dicts with a higher number of cells are not as impacted since it's much harder to obtain false positives. However, the less cells in a marker the further away it can be reliably detected, so the dict `DICT_4X4_1000` is commonly used.

<img width="1280" height="800" alt="false_positive_image_rate" src="https://github.com/user-attachments/assets/1a0ee16a-221d-443e-835b-022ed6dea6b0" />

In the image attached, the values of `validBitIdThreshold` tested are:  `0.10f, 0.20f, 0.30f, 0.40f, 0.43f, 0.46f, 0.49f, 0.50f, 0.53f, 0.56f, 0.60f, 0.70f, 0.80f, 0.90f`

Summary of the results: [summary.csv](https://github.com/user-attachments/files/24315662/summary.csv)

Note that we can also analyse the number of false positives per marker `id`. For example, here's the histogram for the dict `DICT_4X4_1000`. (The CSV attached contains all the results)

<img width="1440" height="640" alt="false_positive_ids_DICT_4X4_1000_thr0 50" src="https://github.com/user-attachments/assets/af4f3ff8-9b8f-4682-9d51-a090c2610d8c" />

For example, the marker id 17 is detected 252 times with  `validBitIdThreshold = 0.5` and only 34 times with `validBitIdThreshold = 0.49`. Looking at marker 17 (see below), we understand that this simple pattern randomly occurs in images.

<img width="447" height="441" alt="Marker17" src="https://github.com/user-attachments/assets/f5d09227-b39b-4598-94f9-b529f8300703" />

Results for every dict and every `validBitIdThreshold` [per_id.csv](https://github.com/user-attachments/files/24315667/per_id.csv)

**Missing coverage:** there is no labeled dataset with images containing markers to analyse the impact of on the recall  (i.e. look at the true positive rate). For my specific use case (drones) any threshold above `0.4` allows to maintain a high recall in all conditions.

### Pull Request Readiness Checklist


- [x] I agree to contribute to the project under Apache 2 License.
- [x] To the best of my knowledge, the proposed patch is not based on a code under GPL or another license that is incompatible with OpenCV
- [ ] The PR is proposed to the proper branch
- [ ] There is a reference to the original bug report and related work
- [ ] There is accuracy test, performance test and test data in opencv_extra repository, if applicable
      Patch to opencv_extra has the same branch name.
- [ ] The feature is well documented and sample code can be built with the project CMake

modules/objdetect/include/opencv2/objdetect/aruco_detector.hpp

@@ -20,6 +20,8 @@ enum CornerRefineMethod{
     CORNER_REFINE_APRILTAG, ///< Tag and corners detection based on the AprilTag 2 approach @cite wang2016iros
 };
 
+static constexpr float DEFAULT_VALID_BIT_ID_THRESHOLD{0.49f};
+
 /** @brief struct DetectorParameters is used by ArucoDetector
  */
 struct CV_EXPORTS_W_SIMPLE DetectorParameters {
@@ -49,7 +51,7 @@ struct CV_EXPORTS_W_SIMPLE DetectorParameters {
         aprilTagQuadSigma = 0.0;
         aprilTagMinClusterPixels = 5;
         aprilTagMaxNmaxima = 10;
-        aprilTagCriticalRad = (float)(10* CV_PI /180);
+        aprilTagCriticalRad = (float)(10 * CV_PI / 180);
         aprilTagMaxLineFitMse = 10.0;
         aprilTagMinWhiteBlackDiff = 5;
         aprilTagDeglitch = 0;
@@ -57,6 +59,7 @@ struct CV_EXPORTS_W_SIMPLE DetectorParameters {
         useAruco3Detection = false;
         minSideLengthCanonicalImg = 32;
         minMarkerLengthRatioOriginalImg = 0.0;
+        validBitIdThreshold = DEFAULT_VALID_BIT_ID_THRESHOLD;
     }
 
     /** @brief Read a new set of DetectorParameters from FileNode (use FileStorage.root()).
@@ -231,6 +234,9 @@ struct CV_EXPORTS_W_SIMPLE DetectorParameters {
 
     /// range [0,1], eq (2) from paper. The parameter tau_i has a direct influence on the processing speed.
     CV_PROP_RW float minMarkerLengthRatioOriginalImg;
+
+    /// range [0,1], define the acceptable threshold when comparing the detected marker to the dictionary during marker identification.
+    CV_PROP_RW float validBitIdThreshold;
 };
 
 /** @brief struct RefineParameters is used by ArucoDetector

modules/objdetect/include/opencv2/objdetect/aruco_dictionary.hpp

@@ -65,6 +65,12 @@ class CV_EXPORTS_W_SIMPLE Dictionary {
      */
     CV_WRAP bool identify(const Mat &onlyBits, CV_OUT int &idx, CV_OUT int &rotation, double maxCorrectionRate) const;
 
+    /** @brief Given a matrix of pixel ratio raging from 0 to 1. Returns whether if marker is identified or not.
+     *
+     * Returns reference to the marker id in the dictionary (if any) and its rotation.
+     */
+    CV_WRAP bool identify(const Mat &onlyCellPixelRatio, CV_OUT int &idx, CV_OUT int &rotation, double maxCorrectionRate, float validBitIdThreshold) const;
+
     /** @brief Returns Hamming distance of the input bits to the specific id.
      *
      * If `allRotations` flag is set, the four possible marker rotations are considered
@@ -84,6 +90,10 @@ class CV_EXPORTS_W_SIMPLE Dictionary {
     /** @brief Transform list of bytes to matrix of bits
       */
     CV_WRAP static Mat getBitsFromByteList(const Mat &byteList, int markerSize, int rotationId = 0);
+
+    /** @brief Get ground truth bits float
+      */
+     CV_WRAP Mat getMarkerBits(int markerId, int rotationId = 0) const;
 };