官方网站：https://www.uco.es/investiga/grupos/ava/node/68
Fractal Markers: a new approach for long-range camera pose estimation under occlusion
Author. Francisco José Romero Ramírez
License and how to cite 31. Introduction 42. Fractal Markers 4Default markers 5Custom markers 5Printing markers 63. Fractal marker detection and pose estimation 74. Using Fractal Markers in your project 8
License and how to citeThe library is released under GPLv3. Please cite if you use it for research:
FRACTAL MARKERS “Fractal Markers: a new approach for long-range camera pose estimation under occlusion”. Please cite our paper.https://ieeexplore.ieee.org/document/8890613[[DOWNLOAD PDF]](https://www.researchgate.net/publication/337024999_Fractal_Markers_a_new_approach_for_long-range_marker_pose_estimation_under_occlusion)
ARUCO Main Paper of Aruco version 3:"Speeded Up Detection of Squared Fiducial Markers"https://www.sciencedirect.com/science/article/pii/S0262885618300799[[DOWNLOAD PDF]](https://www.researchgate.net/publication/325787310_Speeded_Up_Detection_of_Squared_Fiducial_Markers)[[DOWNLOAD Bibtex]](https://www.uco.es/investiga/grupos/ava/sites/default/files/salinas/aruco3.bib) Paper that started Aruco project:"Automatic generation and detection of highly reliable fiducial markers under occlusion"http://www.sciencedirect.com/science/article/pii/S0031320314000235[[DOWNLOAD PDF]](https://www.researchgate.net/publication/325787310_Speeded_Up_Detection_of_Squared_Fiducial_Markers)[[DOWNLOAD Bibtex]](http://www.uco.es/investiga/grupos/ava/sites/default/files/aruco_reference.bib) Paper explaining the default dictionary of markers:"Generation of fiducial marker dictionaries using mixed integer linear programming"http://www.sciencedirect.com/science/article/pii/S0031320315003544[[DOWNLOAD PDF]](https://www.researchgate.net/publication/282426080_Generation_of_fiducial_marker_dictionaries_using_mixed_integer_linear_programming)[[DOWNLOAD Bibtex]](http://www.uco.es/investiga/grupos/ava/sites/default/files/markermip_ref.bib)
\1. Introduction
Fractal markers are a new concept of marker, which is composed of several fiducial square markers of different size inside. Unlike traditional fiducial markers, the structure of this marker can be detected from a large number of distances, as well as solve problems of partial or total occlusion of the marker.
The features of this marker, together with the tools developed make it a powerful tool for camera pose estimation in a large number of applications such as robots, unmanned vehicles and augmented reality.
Fractal Marker is integrated inside ArUco's libraries, allowing a fast, robust and precise detection of the markers. ArUco is a widely used OpenSource library for detecting squared fiducial.2. Fractal MarkersA fractal marker is a square fiducial marker composed of m markers recursively, see Figure 1. In a fractal marker, each internal marker is composed of a black region that facilitates the detection of the marker (s(f)), a region that identifies the marker (n(f)), and a white region where its immediate inner marker is located (k(f)).
**a)** **b)** **c)** **d)****Figure 2**. Default Fractal Marker configurations included in the library.
Printing markersNow you can print the marker you want. The tool utils_fractal/fractal_print_marker has been provided. ./fractal_print_marker [-c configuration] [-bs bitsize] [-noborder] Where:output. Path of the output image (jpg|png|ppm|bmp)configuration. Name of the marker configuration in case you want to print a default marker (If this is not specified the system uses by default FRACTAL_2L_6), or the configuration path of the file generated by the fractal_create tool.bitsize. Number of pixels occupied by each bit of the innermost marker (75px. by default) Examples:./fractal_print_marker fractalMarker.png./fractal_print_marker fractalMarker.png -c FRACTAL_3L_6 -bs 50./fractal_print_marker fractalMarker.png -c configuration.yml \3. Fractal marker detection and pose estimation Fractal Marker System uses ArUco to perform markers detection. The process of calling ArUco is completely transparent to the user, and carried out using the FractalDetector class. If the extrinsic parameters of the camera are known (camera matrix and distortion coefficients obtained by calibration, for more details on how to perform the camera calibration), then the library will be able to calculate the relative position of the fractal marker and the camera. The system will give you the rotation and translation vectors (Rvec and Tvec), which represent the transformation of the marker to the camera. The Rvec and Tvec transformation vectors are provided by performing the poseEstimation() implemented in the FractalDetector class. The Rvec and Tvec vectors can be used by cv::projectPoints() to project points on the image using the fractal marker reference system. Notice, that the fractal marker is normalized during the tracking process indicating that (0,0) will be the shared center of all the markers and (-1,1),(1,1),(1,-1),(-1,-1),(-1,-1) correspond to the four external corners of the fractal marker. The program utils_fractal/fractal_tracker allows in an easy and automatic way the detection of markers in the scene, as well as the camera pose estimation. It is also possible to track the marker in a video sequence.
./fractal_tracker [-cam cameraParams] [-c configuration] Where:input. Path of the input videocameraParams. *Camera calibration parameters.*configuration. Name of the marker configuration in case you want to print a default marker (If this is not specified the system uses by default FRACTAL_2L_6), or the configuration path of the file generated by the fractal_create tool.
Example./fractal_tracker video.avi -cam cameraParams.yml -c FRACTAL_3L_6
Example1: Then, create the program file sample_detection.cpp. We will be able to detect fractal markers (eg. FRACTAL_5L_6) at the scene. #include <opencv2/highgui.hpp>#include <aruco.h>using namespace std;int main(int argc,char **argv){ cv::Mat im=cv::imread(argv[1]); aruco::FractalDetector FDetector; FDetector.setConfiguration("FRACTAL_3L_6"); if(FDetector.detect(im)){ FDetector.drawMarkers(im); } cv::imshow("image",im); cv::waitKey(0);}
Finally, create a directory for building (e.g. build), go in, compile and execute
mkdir buildcd buildcmake .. -Daruco_DIR=<path2arucoConfig.cmake> -DOpenCV_DIR=<path2OpenCVConfig.cmake>make./sample_detection image_with_markers.jpg
./sample_landing landing.mov landingPad.png
