Sub-Pixel Affine Registration of Space Debris Images via the Radon Point Spread Function

This paper proposes an algorithm for estimating the similarity transformation, namely translation, scale, and rotation, between two images with subpixel accuracy. Image registration is a fundamental technique for aligning images acquired under different viewpoints and imaging conditions, and a representative approach based on maximizing discrete cross-correlation is the Fourier--Mellin registration. However, the Fourier--Mellin approach often fails to achieve sufficient alignment accuracy when subpixel-level estimation is required. The proposed method integrates (i) scale-and-rotation estimation from the Fourier magnitude spectrum in a log-polar representation and (ii) maximization of phase-only correlation based on the auxiliary function method. This integration enables a two-stage estimation procedure: it first estimates scale and rotation without being affected by translation, and then estimates translation with subpixel precision in the spatial domain using the corrected image pair. A simulation experiment on image pairs subjected to random similarity transformations demonstrates that the proposed method reduces estimation errors in scale, rotation, and translation compared with Fourier--Mellin-based registration methods using discrete cross-correlation.

Long-range vision-based deformation monitoring is highly sensitive to motion of the camera platform. Absolute-pose differencing typically relies on dedicated control data and propagates two independent pose errors into the relative-motion estimate. We develop a control-adaptive differential framework that estimates inter-frame platform motion directly from image displacements and known 3D points. With no dedicated control point, the framework recovers platform rotation from measurement-point observations. One surveyed control point enables prior-constrained translation recovery, while two nonparallel control rays recover full 3D translation. The framework requires neither nonlinear optimization nor an initial pose estimate. Excluding control data from the rotation stage makes the rotation estimate exactly immune to contamination confined to the control field. The inherited differential formulation also cancels translational extrinsic errors exactly. We derive the rotation observability condition, a leakage bound for unmodeled translation and nonrigid point motion, and the single-point axial-prior bias law. Under 0.5-pixel image noise, attitude changes of up to 30arcmin, and 3D point perturbations of up to 2mm, the multi-camera estimator achieves a rotation RMSE of 2.97arcsec and an average runtime of 0.46ms. With one surveyed control point, its prior-constrained translation RMSE is 1.19mm. In a bridge experiment without a stable control field, the median coordinate-wise displacement RMSE relative to total-station measurements is 0.85mm. The estimator also maintains zero divergence under the tested 3D coordinate perturbations on public RGB-D and stereo sequences. These results establish state-of-the-art accuracy, calibration robustness, and computational efficiency among the evaluated methods.

In this work we present Polaffini, a robust and versatile framework for anatomically grounded registration. Medical image registration is dominated by intensity-based registration methods that rely on surrogate measures of alignment quality. In contrast, feature-based approaches that operate by identifying explicit anatomical correspondences, while more desirable in theory, have largely fallen out of favor due to the challenges of reliably extracting features. However, such challenges are now significantly overcome thanks to recent advances in deep learning, which provide pre-trained segmentation models capable of instantly delivering reliable, fine-grained anatomical delineations. We aim to demonstrate that these advances can be leveraged to create new anatomically-grounded image registration algorithms. To this end, we propose Polaffini, which obtains, from these segmented regions, anatomically grounded feature points with 1-to-1 correspondence in a particularly simple way: extracting their centroids. These enable efficient global and local affine matching via closed-form solutions. Those are used to produce an overall transformation ranging from affine to polyaffine with tunable smoothness. Polyaffine transformations can have many more degrees of freedom than affine ones allowing for finer alignment, and their embedding in the log-Euclidean framework ensures diffeomorphic properties. Polaffini has applications both for standalone registration and as pre-alignment for subsequent non-linear registration, and we evaluate it against popular intensity-based registration techniques. Results demonstrate that Polaffini outperforms competing methods in terms of structural alignment and provides improved initialisation for downstream non-linear registration. Polaffini is fast, robust, and accurate, making it particularly well-suited for integration into medical image processing pipelines.