VERNIER: an open-source software pushing marker pose estimation down to the micrometer and nanometer scales

TL;DR

VERNIER addresses the challenge of $6$-DoF pose estimation at micro/nano scales by combining phase-based localization with coarse absolute decoding using pseudo-periodic markers. It introduces two marker families (small HP code/Stamp and large Megarena) and provides an open-source C++ library that computes camera-to-marker transforms with nanometer-scale precision over centimeter ranges. The approach leverages Fourier-domain phase analysis to achieve high-resolution relative positioning and robust absolute decoding, enabling applications in metrology, micro-assembly, and correlative microscopy, with guidelines to balance range, resolution, and imaging conditions. Practical results and synthetic tests demonstrate reliable performance, and the work offers actionable recommendations for marker design and optical setup to maximize robustness in microscopy settings.

Abstract

Pose estimation is still a challenge at the small scales. Few solutions exist to capture the 6 degrees of freedom of an object with nanometric and microradians resolutions over relatively large ranges. Over the years, we have proposed several fiducial marker and pattern designs to achieve reliable performance for various microscopy applications. Centimeter ranges are possible using pattern encoding methods, while nanometer resolutions can be achieved using phase processing of the periodic frames. This paper presents VERNIER, an open source phase processing software designed to provide fast and reliable pose measurement based on pseudo-periodic patterns. Thanks to a phase-based local thresholding algorithm, the software has proven to be particularly robust to noise, defocus and occlusion. The successive steps of the phase processing are presented, as well as the different types of patterns that address different application needs. The implementation procedure is illustrated with synthetic and experimental images. Finally, guidelines are given for selecting the appropriate pattern design and microscope magnification lenses as a function of the desired performance.

Figures (6)

• Figure 1: Comparison of vision-based methods dedicated to pose measurement under microscopy published in Yao2021review (courtesy of IEEE). Numbers correspond to the references of this review. The method that is implemented in VERNIER is number 122 in orange at the top of the graph.
• Figure 2: The three marker types (on the left an HP code marker, in the middle a Stamp marker, on the right a Megarena encoded pattern).
• Figure 3: Fine localization process of Megarena patterns: a) recorded image; b) Fourier spectrum; c$_{1,2}$) 1D wrapped phase maps obtained from spectral lobes $f_1$ and $f_2$, respectively, through inverse Fourier transform; d$_{1,2}$) unwrapped phase planes encode the fine position of the periodic frame of dots with respect to the image pixel frame. The red stripe identifies a single line of dots for the sake of easier understanding.
• Figure 4: Localization process of HP codes: a) corners detection in recorded image; b) image apodization; c) peaks detection in Fourier spectrum.
• Figure 5: Overview of features and metrics of the marker pose estimation with VERNIER.