PuzzlePoles: Cylindrical Fiducial Markers Based on the PuzzleBoard Pattern

TL;DR

PuzzlePole introduces cylindrical fiducial markers built from the PuzzleBoard pattern to achieve robust 360° recognition and precise pose estimation. The method uses quasiperiodic sub-patterns to wrap around cylinders seamlessly, enabling reliable decoding even at low image resolutions and under occlusion. Detection combines corner localization, grid decoding, and a Perspective-n-Point solver to recover position and orientation, with support for multiple poles. The approach offers potential for loop-closure in SLAM and improved localization in GPS-denied environments, with strong applicability to robotics and tangible interfaces.

Abstract

Reliable perception of the environment is a key enabler for autonomous systems, where calibration and localization tasks often rely on robust visual markers. We introduce the PuzzlePole, a new type of fiducial markers derived from the recently proposed PuzzleBoard calibration pattern. The PuzzlePole is a cylindrical marker, enabling reliable recognition and pose estimation from 360° viewing direction. By leveraging the unique combinatorial structure of the PuzzleBoard pattern, PuzzlePoles provide a high accuracy in localization and orientation while being robust to occlusions. The design offers flexibility for deployment in diverse autonomous systems scenarios, ranging from robot navigation and SLAM to tangible interfaces.

Figures (6)

• Figure 1: A sub-pattern of the PuzzleBoard pattern, which starts at $y=73$ (and $x=0$). As can be seen, the last row of puzzle pieces is identical to the first one. By wrapping the pattern onto a vertical cylinder and placing the first and last row exactly onto each other, one gets a seamless cyclic pattern.
• Figure 2: Repetition of a quasiperiodic sub-pattern. First row: The code stripe $B$ from the PuzzleBoard patternstelldinger2024. Second row: Separation of the stripe into three sub-patterns with the second (12 bit wide) sub-pattern being the quasi-periodic one starting at position 73. It starts with the same 2x6 bits as the following pattern. Third row: Repetition of the quasi-periodic sub-pattern. Fourth row: Stitching the sub-patterns together results in a pattern where every 3x3-sub-pattern does not generate new 3x3-sub-patterns at the stitching positions.
• Figure 3: Localization of a partially occluded PuzzlePole
• Figure 4: Localization of a multiple unique PuzzlePoles
• Figure 5: Experimental setup to measure the localization error between two PuzzlePoles, measured by the localization algorithm. The colors of the coordinate systems are: blue=x, green=y, red=z.