We investigate the application of the common circle method for estimating sample motion in optical diffraction tomography (ODT) of sub-millimeter sized biological tissue. When samples are confined via contact-free acoustical force fields, their motion must be estimated from the captured images. The common circle method identifies intersections of Ewald spheres in Fourier space to determine rotational motion. This paper presents a practical implementation, incorporating temporal consistency constraints to achieve stable reconstructions. Our results on both simulated and real-world data demonstrate that the common circle method provides a computationally efficient alternative to full optimization methods for motion detection.
Figures & tables
Figure 1: Illustration of the common circles as intersections of the Ewald spheres. Left: Two hemispheres H0 (green) and Ht (red) intersect in a common circle. The north pole of both hemispheres is at 0 . Right: For real-valued (lossless) interactions, a dual common circle at the intersection of H0 (green) and −Ht (red) exists. Data must agree on the two intersections.
Figure 2: (a) Ground truth refractive index n(x) of the phantom. (b) Absolute value of the preprocessed data ∣mt(x)∣ for t=1 simulated with the BPM with added noise. (c) Reconstruction of the refractive index n(x) for noisy simulated data using the Rytov approximation and the rotations reconstructed via the common circle method.
Figure 3: Error of the reconstructed rotation (in degree) at each frame t for the neuroblastoma phantom of Figure 2 with exact (a) or noisy data (b), (c).
Figure 4: Absolute value of the transformed and preprocessed measurements ∣mt(x)∣ for the three-beads object dataset for time steps t∈{0,5,10} (left to right).
Figure 5: Reconstructed rotations for three-beads object. The four plots are the components of the quaternions. Blue: Common circle method. Red: Optimization approach [ 27 ] .
Figure 6: Three-beads object. Left: Rotation angle ∠(RtR0⊤) in degrees. Right: Angle d(RtCC,RtOpt) in degrees between the rotation RtCC reconstructed with the common circle method and the Optimization approach RtOpt [ 27 ] . The average over all time steps is 10.3 °.
Figure 7: Reconstructed refractive index n(x) for the Three-Beads object. Left: Rytov reconstruction with rotations from common circle method (PSNR 21.3, SSIM 0.669). Center: Rytov reconstruction with rotations from [ 27 ] (PSNR 21.3, SSIM 0.682). Right: Reconstruction with the optimization approach.
Figure 8: Reconstructed refractive index n(x) for the Three-Beads object incorporating the reconstructed translations from [ 27 ] . Left: Rytov reconstruction with rotations from common circle method (PSNR 24.3, SSIM 0.704). Right: Rytov reconstruction with rotations from [ 27 ] (PSNR 27.0, SSIM 0.744).
Figure 9: Visualization of Neuroblastoma dataset and reconstructed translations.
Figure 10: Reconstructed rotations for the Neuroblastoma. The four plots are the components of the quaternions. Blue: Common circle method. Red: Optimization approach [ 27 ] .
Figure 11: Reconstructed rotations for the Neuroblastoma. Left: Rotation angle d(Rt,R0) in degrees. Right: Angle d(RtCC,RtOpt) in degrees between the rotation RtCC reconstructed with the common circle method and RtOpt with the Optimization approach [ 27 ] , the average over all time steps is 7.7 °.
Figure 12: Reconstructed refractive index n(x) for the Neuroblastoma with different methods. Columns are sections through the coordinate planes (left to right: xy-plane, xz-plane, yz-plane).
Event-based motion estimation is central to tasks that demand high temporal resolution and robustness to fast motion. Existing methods typically rely on iterative optimization or repeated hypothesis comparison, offsetting the sensor's low-latency advantage. We propose Oriented Distance Field Motion Estimation (ODF Motion Estimation), which replaces this optimization with a single averaging step over a precomputed field of event distance vectors, combined with an adaptive event-count selection strategy and a parameter-free trail filter. On public and self-collected datasets, ODF motion estimation reaches sub-pixel accuracy at the lowest latency among compared methods. We validate its generality on two downstream applications rather than treating them as separate contributions. First, the estimated trajectory is converted into a blur kernel and paired with a compact iterative-unfolding network, trained on simulated motion-estimation noise, for real-time non-blind image deblurring, attaining competitive or superior PSNR/SSIM with under 1M parameters. Second, the same precomputed field is repurposed for directional event filtering in a low-power asynchronous pupil and glint tracker, sustaining stable tracking for tens of seconds while lowering a near-eye module's power draw.
Lei Sun, Yuqin Ma, Weilun Li +5
INSAIT, Sofia University “St. Kliment Ohridski”, Sofia, Bulgaria · Zhejiang University, Hangzhou, China
Optical coherence tomography is a promising modality for markerless motion tracking due to its high spatial resolution and inherent depth perception. However, existing OCT-based tracking approaches are limited in terms of trackable velocity, particularly when multiple landmarks are tracked sequentially for 6D pose estimation. In this work, we present a predictive tracking approach that propagates positional updates between multiple tracked landmarks to obtain a global pose prediction. This enables more robust tracking under high velocities. Our results demonstrate RMSEs below 1 mm for velocities up to 100 mm/s and up to nine consecutively tracked landmarks, highlighting the potential of global motion propagation and prediction for improving the robustness of OCT-based tracking.
Konrad Reuter, Suresh Guttikonda, Chaitali Uday Karekar +2
Department of Otorhinolaryngology, Head and Neck Surgery and Oncology, University Medical Center Hamburg-Eppendorf, Hamburg, Germany
This work presents GS-DOT, a novel image reconstruction framework based on Gaussian Splatting (GS) for diffuse optical tomography (DOT). Inspired by GS for rendering applications, absorption coefficients are represented as a sparse sum of anisotropic Gaussian primitives optimized to fit measured time-resolved point-spread functions through analytic gradients and Adam optimization. This is the first adaptation of GS algorithms in the photon diffusion regime, where the ray transport function is replaced by the diffusion functions to enable accurate modeling of light transport in highly scattering media. Validation on synthetic tissue models demonstrate high accuracy in localization and quantification of reconstructed absorption maps for both clean and noisy signals. GS-DOT has demonstrated high robustness to noise and showed a huge reduction in memory demand.
Jingjing Jiang
Computational Optical Imaging Group, Biomedical Optics Research Laboratory, Dept. of Neonatology, University Hospital Zurich and University of Zurich, Switzerland