We study the stability of a classical family of metrics defined over functions' Gaussian scale-space representations, focusing on the comparison of images (functions of two variables). These metrics have precedents both in harmonic analysis, specifically the theory of Besov spaces, and in classical methods of image processing; special cases are also known to be metrically equivalent to certain Wasserstein distances. We quantify these metrics' robustness to geometric deformations, and introduce rotationally-invariant versions that are stable to changes in angle when comparing tomographic projections. We also describe computationally efficient algorithms for evaluating the metrics from finite samples, and prove their robustness to additive noise. The results are illustrated through numerical experiments.
We investigate volumetric reconstruction for compressive sensing light-sheet microscopy (CS-LSM), where fast volumetric imaging is achieved by encoding multiple axial planes into each camera exposure. To recover the underlying volume from highly multiplexed measurements, we propo…
Tensor Train (TT) decomposition is a powerful technique for analyzing high-dimensional data. Existing algorithms for computing TT decompositions can be categorized into two main types: conventional batch-based approaches and recursive online methods. In the context of streaming d…
Neural surrogate models offer fast approximate mappings from PDE parameters to solutions, but they typically treat solving as a purely statistical task: once trained, they struggle to correct their own constraint violations and extrapolate beyond the training distribution. Recent…
Accurate geometric calibration is essential for fluoroscopy-guided spinal imaging, digitally reconstructed radiograph (DRR) generation, and 2D--3D vertebral registration. Although calibration quality is typically evaluated using reconstruction-based metrics such as reprojection e…
Dermatological practice routinely involves measuring and tracking lesion size, morphology and texture, as critical components of wound or skin cancer screening, monitoring and diagnosis. To accomplish this task, practitioners often image the skin surface with commonly available o…
A central challenge in image-goal UAV navigation under Global Navigation Satellite System (GNSS) denial is estimating metric distance and heading between current and goal views. Dense pairwise geometry models capture relative scene structure, but without a calibrated metric scale…