Related papers: Rotational smoothing
The usual approach to developing and analyzing first-order methods for smooth convex optimization assumes that the gradient of the objective function is uniformly smooth with some Lipschitz constant $L$. However, in many settings the…
Inverse problems in physical or biological sciences often involve recovering an unknown parameter that is random. The sought-after quantity is a probability distribution of the unknown parameter, that produces data that aligns with…
We study linear operators on a finite-dimensional space whose Kippenhahn curves consist of concentric circles centered at the origin. We say that such operators have Circularity property. One class of examples is rotationally invariant…
Rotation averaging is a synchronization process on single or multiple rotation groups, and is a fundamental problem in many computer vision tasks such as multi-view structure from motion (SfM). Specifically, rotation averaging involves the…
We study the appearance of large scale mean motion sustained by stochastic forcing on a rotating fluid (in the quasigeostrophic approximation) flowing over topography. As in other noise rectification phenomena, the effect requires…
The Boltzmann equation without Grad's angular cutoff assumption is believed to have regularizing effect on the solution because of the non-integrable angular singularity of the cross-section. However, even though so far this has been…
In this paper we explore the role of duality principles within the problem of rotation averaging, a fundamental task in a wide range of computer vision applications. In its conventional form, rotation averaging is stated as a minimization…
This paper studies Schauder theory to transmission problems modelled by fully nonlinear uniformly elliptic equations of second order. We focus on operators F that fails to be concave or convex in the space of symmetric matrices. In a first…
We study Tikhonov regularization for solving ill--posed operator equations where the solutions are functions defined on surfaces. One contribution of this paper is an error analysis of Tikhonov regularization which takes into account…
We find that circular kinks form on the surface of granular material when the axis of rotation is tilted more than the angle of internal friction of the material. Radius of the kinks is measured as a function of the spinning speed and the…
Bilevel programming has recently received a great deal of attention due to its abundant applications in many areas. The optimal value function approach provides a useful reformulation of the bilevel problem, but its utility is often limited…
Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…
To minimize or upper-bound the value of a function "robustly", we might instead minimize or upper-bound the "epsilon-robust regularization", defined as the map from a point to the maximum value of the function within an epsilon-radius. This…
Let $V$ be a potential on $\RR^3$ that is smooth everywhere except at a discrete set $\maS$ of points, where it has singularities of the form $Z/\rho^2$, with $\rho(x) = |x - p|$ for $x$ close to $p$ and $Z$ continuous on $\RR^3$ with $Z(p)…
The synchronization problem over the special orthogonal group $SO(d)$ consists of estimating a set of unknown rotations $R_1,R_2,...,R_n$ from noisy measurements of a subset of their pairwise ratios $R_{i}^{-1}R_{j}$. The problem has found…
In the framework of real Hilbert spaces, we investigate first-order dynamical systems governed by monotone and continuous operators. We demonstrate that when the monotone operator flow is augmented with a Tikhonov regularization term, the…
The Gauss map of non-degenerate surfaces in the three-dimensional Minkowski space are viewed as dynamical fields of the two-dimensional O(2,1) Nonlinear Sigma Model. In this setting, the moduli space of solutions with rotational symmetry is…
Regularizing neural networks is important for anticipating model behavior in regions of the data space that are not well represented. In this work, we propose a regularization technique for enforcing a level of smoothness in the mapping…
We investigate the action of Alesker's Lefschetz operators on translation invariant valuations on convex bodies. For scalar valued valuations, we describe this action on the level of Klain-Schneider functions by a Radon type transform,…
Road corrugation refers to the formation of periodic, transverse ripples on unpaved road surfaces. It forms spontaneously on an initially flat surface under heavy traffic and can be considered to be a type of unstable growth phenomenon,…