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With an aim to realizing highly accurate position estimation, we propose in this paper a method for efficiently and accurately detecting the 3D positions and poses of traditional fiducial markers with black frames in high resolution images taken by ordinary web cameras. Our tracking method can be efficiently executed utilizing GPGPU computation, and in order to realize this, we devised a connected-component labeling method suitable for GPGPU execution. In order to improve accuracy, we devised a method for detecting 2D positions of the corners of markers in subpixel accuracy. We implemented our method in Java and OpenCL, and we confirmed that the proposed method provides better detection and measurement accuracy, and recognizing from high-resolution images is beneficial for improving accuracy. We also confirmed that our method is more than two times as fast as the existing method with CPU computation.