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Pose estimation is of great importance in many computer vision applications: robot navigation, augmented reality, and many more. This process is based on finding correspondences between points in the real environment and their 2d image projection. This is usually a difficult step, and thus it is common the use of synthetic or fiducial markers to make it easier.

One of the most popular approach is the use of binary square fiducial markers. The main benefit of these markers is that a single marker provides enough correspondences (its four corners) to obtain the camera pose eur usd news. Also, the inner binary codification makes them specially robust, allowing the possibility of applying error detection and correction techniques.

The aruco module is based on the ArUco library, a popular library for detection of square fiducial markers developed by Rafael Muñoz and Sergio Garrido:

S. Garrido-Jurado, R. Muñoz-Salinas, F. J. Madrid-Cuevas, and M. J xau usd investing. Marín-Jiménez. 2014. "Automatic generation and detection of highly reliable fiducial markers under occlusion". Pattern Recogn. 47, 6 (June 2014), 2280-2292. DOI=10.1016/j.patcog.2014.01.005

An ArUco marker is a synthetic square marker composed by a wide black border and a inner binary matrix which determines its identifier (id). The black border facilitates its fast detection in the image and the binary codification allows its identification and the application of error detection and correction techniques. The marker size determines the size of the internal matrix. For instance a marker size of 4×4 is composed by 16 bits.

It must be noted that a marker can be found rotated in the environment, however, the detection process needs to be able to determine its original rotation, so that each corner is identified unequivocally. This is also done based on the binary codification.

A dictionary of markers is a set of markers that are considered in an specific application 1 usd to inr. It is simply the list of binary codifications of each of its markers.

One may think that the marker id is the number obtained from converting the binary codification to a decimal base number. However, this is not possible since for high marker sizes the number of bits is too high and managing so huge numbers is not practical. Instead, a marker id is simply the marker index inside the dictionary it belongs to. For instance, the first 5 markers inside a dictionary has the ids: 0, 1, 2, 3 and 4.

Before their detection, markers need to be printed in order to be placed in the environment. Marker images can be generated using the drawMarker() function.

Given an image where some ArUco markers are visible, the detection process has to return a list of detected markers. Each detected marker includes:

• Detection of marker candidates usd to cop exchange rate. In this step the image is analyzed in order to find square shapes that are candidates to be markers. It begins with an adaptive thresholding to segment the markers, then contours are extracted from the thresholded image and those that are not convex or do not approximate to a square shape are discarded. Some extra filtering are also applied (removing too small or too big contours, removing contours too close to each other, etc).

• After the candidate detection, it is necessary to determine if they are actually markers by analyzing their inner codification. This step starts by extracting the marker bits of each marker. To do so, first, perspective transformation is applied to obtain the marker in its canonical form. Then, the canonical image is thresholded using Otsu to separate white and black bits bloomberg stock futures market. The image is divided in different cells according to the marker size and the border size and the amount of black or white pixels on each cell is counted to determine if it is a white or a black bit. Finally, the bits are analyzed to determine if the marker belongs to the specific dictionary and error correction techniques are employed when necessary.

• The second parameter is the size of the marker side in meters or in any other unit aed to usd exchange rate history. Note that the translation vectors of the estimated poses will be in the same unit

The marker coordinate system that is assumed by this function is placed at the center of the marker with the Z axis pointing out, as in the following image. Axis-color correspondences are X:red, Y:green, Z:blue.

Apart of the marker size and the number of markers in the dictionary, there is another important dictionary parameter, the inter-marker distance. The inter-marker distance is the minimum distance among its markers and it determines the error detection and correction capabilities of the dictionary.

In general, lower dictionary sizes and higher marker sizes increase the inter-marker distance and vice-versa. However, the detection of markers with higher sizes is more complex, due to the higher amount of bits that need to be extracted from the image.

For instance, if you need only 10 markers in your application, it is better to use a dictionary only composed by those 10 markers than using one dictionary composed by 1000 markers. The reason is that the dictionary composed by 10 markers will have a higher inter-marker distance and, thus, it will be more robust to errors.

As a consequence, the aruco module includes several ways to select your dictionary of markers, so that you can increase your system robustness:

This is the easiest way to select a dictionary. The aruco module includes a set of predefined dictionaries of a variety of marker sizes and number of markers decimal places chart. For instance:

These parameters determine the minimum and maximum size of a marker, concretely the maximum and minimum marker perimeter. They are not specified in absolute pixels values, instead they are specified relative to the maximum dimension of the input image.

For instance, a image with size 640×480 and a minimum relative marker perimeter of 0.05 will lead to a minimum marker perimeter of 640×0.05 = 32 pixels, since 640 is the maximum dimension of the image. The same applies for the maxMarkerPerimeterRate parameter.

If the minMarkerPerimeterRate is too low, it can penalize considerably the detection performance since many more contours would be considered for future stages. This penalization is not so noticeable for the maxMarkerPerimeterRate parameter, since there are usually many more small contours than big contours. A minMarkerPerimeterRate value of 0 and a maxMarkerPerimeterRate value of 4 (or more) will be equivalent to consider all the contours in the image, however this is not recommended for the performance reasons.

A polygonal approximation is applied to each candidate and only those that approximate to a square shape are accepted. This value determines the maximum error that the polygonal approximation can produce (see approxPolyDP() function for more information).

This parameter is relative to the candidate length (in pixels). So if the candidate has a perimeter of 100 pixels and the value of polygonalApproxAccuracyRate is 0.04, the maximum error would be 100×0.04=5.4 pixels.

Minimum distance between any pair of corners in the same marker define futures market. It is expressed relative to the marker perimeter. Minimum distance in pixels is Perimeter * minCornerDistanceRate.

Minimum distance between any pair of corners from two different markers. It is expressed relative to the minimum marker perimeter of the two markers. If two candidates are too close, the smaller one is ignored.

Minimum distance to any of the marker corners to the image border (in pixels). Markers partially occluded by the image border can be correctly detected if the occlusion is small. However, if one of the corner is occluded, the returned corner is usually placed in a wrong position near the image border.

If the position of marker corners is important, for instance if you want to do pose estimation, it is better to discard markers with any of their corners are too close to the image border. Elsewhere, it is not necessary.

Before analyzing the binary code itself, the bits need to be extracted. To do so, the perspective distortion is removed and the resulting image is thresholded using Otsu threshold to separate black and white pixels.

only the pixels inside the green squares are considered. It can be seen in the right image that the resulting pixels contain a lower amount of noise from neighbor cells rmb to usd calculator. The perspectiveRemoveIgnoredMarginPerCell parameter indicates the difference between the red and the green squares.

This parameter is relative to the total size of the cell. For instance if the cell size is 40 pixels and the value of this parameter is 0.1, a margin of 40*0.1=4 pixels is ignored in the cells. This means that the total amount of pixels that would be analyzed on each cell would actually be 32×32, instead of 40×40.

After the bits have been extracted, the next step is checking if the extracted code belongs to the marker dictionary and, if necessary, error correction can be performed.

The bits of the marker border should be black usd jpy exchange rate. This parameter specifies the allowed number of erroneous bits in the border, i.e. the maximum number of white bits in the border. It is represented relative to the total number of bits in the marker.

Each marker dictionary has a theoretical maximum number of bits that can be corrected ( Dictionary.maxCorrectionBits). However, this value can be modified by the errorCorrectionRate parameter.

For instance, if the allowed number of bits that can be corrected (for the used dictionary) is 6 and the value of errorCorrectionRate is 0.5, the real maximum number of bits that can be corrected is 6*0.5=3 bits.

After markers have been detected and identified, the last step is performing subpixel refinement in the corner positions (see OpenCV cornerSubPix() and cv::aruco::CornerRefineMethod)

Note that this step is optional and it only makes sense if the position of the marker corners have to be accurate, for instance for pose estimation. It is usually a time consuming step and it is disabled by default.

High values can produce the effect that close image corners are included in the window region, so that the marker corner moves to a different and wrong location during the process. Furthermore it can affect to performance.

These two parameters determine the stop criterion of the subpixel refinement process. The cornerRefinementMaxIterations indicates the maximum number of iterations and cornerRefinementMinAccuracy the minimum error value before stopping the process.

If the number of iterations is too high, it can affect the performance. On the other hand, if it is too low, it can produce a poor subpixel refinement.

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