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...

Direct metal SLS processes use a high power laser beam to selectively fuse fully metallic powder to directly produce functional metal components or tooling. As a thermal dynamic process, it inevitably causes thermal stresses, stress-induced deformations and cracking. Understanding these is very important in controlling residual stresses and stress-induced deformations. In this research, the res...

Non-linear geometric deformation (or warping) is a useful tool for working with volumes. Unfortunately, the computational expense of performing the resampling needed to implement volume deformation has precluded its use in interactive applications. In this paper, we show how non-linear deformations can be integrated into interactive volume visualization allowing for dynamic deformations to be u...

Deep tissue injury (DTI) is a severe type of pressure ulcer, in which damage initiates under intact skin, in soft tissues that are mechanically deformed by load-bearing bony prominences. Sitting-acquired DTI typically occurs in the gluteus muscles that could sustain deformations by the weight-bearing ischial tuberosities (ITs). No clinical method currently exists for measuring internal tissue d...

The onset of ventilator-induced lung injury (VILI) is linked to a number of possible mechanisms. To isolate the possible role of alveolar epithelial deformation in the development of VILI, we have developed an in vitro system in which changes in alveolar epithelial cell viability can be measured after exposure to tightly controlled and physiologically relevant deformations. We report here a stu...

A new energy for the description of large deformations of lipid bilayers is formulated with mathematical rigor. This energy is derived by considering the smectic A liquid crystalline nature of lipid bilayers and the coupling between the deformations of the layers and their constituent lipid molecules. Analogies between smectic A liquid crystals, with an infinite number of layers, and lipid bila...

We study a specific class of deformations of curve singularities: the case when the singular point splits to several ones, such that the total δ invariant is preserved (aka equi-generic deformations). We restrict primarily to the deformations of singularities with smooth branches. A new invariant of the singular type is introduced: the dual graph. It imposes severe restrictions on the possible ...

This paper discusses a novel framework to analyze rotational deformations of real 3D objects. The rotational deformations such as twisting or bending have been observed as the major variation in some medical applications, where the features of the deformed 3D objects are directional data. We propose modeling and estimation of the global deformations in terms of generalized rotations of directio...

Additive deformations of bialgebras in the sense of Wirth are deformations of the multiplication map of the bialgebra fulfilling a compatibility condition with the coalgebra structure and a continuity condition. Two problems concerning additive deformations are considered. With a deformation theory a cohomology theory should be developed. Here a variant of the Hochschild cohomology is used. The...

We consider deformations of 2×2 and 3×3 matrix linear ODEs with rational coefficients with respect to singular points of Fuchsian type which don’t satisfy the wellknown system of Schlesinger equations (or its natural generalization). Some general statements concerning reducibility of such deformations for 2× 2 ODEs are proved. An explicit example of the general non-Schlesinger deformation of 2×...