Warping is one of the key areas of image analysis but there has been no understanding of the effects of different non-linear deformations in literature. This paper addresses the problem of the distortion effect produced by different types of non-linear deformation strategies on textured images. The images are modelled by a Gaussian random field. We first give various examples to illustrate that...

We study a vectorial approximation problem based on thin plate splines with tension involving two positive parameters: one for the control of the oscillations and the other for the control of the divergence and rotational components of the field. The existence and uniqueness of the solution are proved and the solution is explicitly given. As special cases, we study the limit problems as the par...

Vector field approximation is a problem involving the reconstruction of physical fields from a set of scattered observed data. In this paper, we address the problem of interpolation of divergence-free vector fields in three dimensional space by thin plate spline under tension. The problem is formulated as a minimization problem where the cost is related to the equilibrium energy of thin plate w...

We prove some inequalities of Payne-P\'olya-Weinberger-Yang type for eigenvalues fourth-order elliptic operators in weighted divergence form on complete Riemannian manifolds which generalizes the corresponding result clamped plate problem. also estimates lower order that contain from literature. As an application our results, we obtain bi-drifted Cheng-Yau operator.

We study a vectorial approximation problem based on thin plate spline with tension involving two positive parameters one for a control of the oscillations and the other one allows a control on the divergence and rotational components of the field. The existence and uniqueness of the solution is proved and the solution is explicitly given. We study the limit problems and the convergence problem ...