The sum of all local deformations yield the final spatial alignment of both images.

The author is now a Research Scientist at Google Brain team. The above scaling shows that error correction depends on two factors. Group representation is a central theme in modern mathematics and physics. Thus the above orthogonal relations hold. The average absolute value of correlation is 0.09, and the We project v to v ( ˆ x), which is an re-encoding of v .

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We would like to thank all reviewers for their time and effort writing these valuable reviews. Reviewer 3 mentioned that a performance measure with other recent methods would be beneficial. The code for this paper will be released with the camera-ready version. In the following, we focus on the questions given by Reviewer 2. The presented network does not contain fewer parameters compared to the classical B-spline method for optimization. Furthermore, it is straightforward to extend for the 3D case.

Regression problems with bounded continuous outcomes frequently arise in real-world statistical and machine learning applications, such as the analysis of rates and proportions. A central challenge in this setting is predicting a response associated with a new covariate value. Most of the existing statistical and machine learning literature has focused either on point prediction of bounded outcomes or on interval prediction based on asymptotic approximations. We develop conformal prediction intervals for bounded outcomes based on transformation models and beta regression. We introduce tailored non-conformity measures based on residuals that are aligned with the underlying models, and account for the inherent heteroscedasticity in regression settings with bounded outcomes. We present a theoretical result on asymptotic marginal and conditional validity in the context of full conformal prediction, which remains valid under model misspecification. For split conformal prediction, we provide an empirical coverage analysis based on a comprehensive simulation study. The simulation study demonstrates that both methods provide valid finite-sample predictive coverage, including settings with model misspecification. Finally, we demonstrate the practical performance of the proposed conformal prediction intervals on real data and compare them with bootstrap-based alternatives.

Coordinate transformation models often fail to account for nonlinear and spatially dependent distortions, leading to significant residual errors in geospatial applications. Here we propose a residual-based neural correction strategy, in which a neural network learns to model only the systematic distortions left by an initial geometric transformation. By focusing solely on residual patterns, the proposed method reduces model complexity and improves performance, particularly in scenarios with sparse or structured control point configurations. We evaluate the method using both simulated datasets with varying distortion intensities and sampling strategies, as well as under the real-world image georeferencing tasks. Compared with direct neural network coordinate converter and classical transformation models, the residual-based neural correction delivers more accurate and stable results under challenging conditions, while maintaining comparable performance in ideal cases. These findings demonstrate the effectiveness of residual modelling as a lightweight and robust alternative for improving coordinate transformation accuracy.