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 #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:

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.

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

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)

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.

Results for every dict and every validBitIdThreshold 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

• I agree to contribute to the project under Apache 2 License.
• 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