Abstract We prove several sharp distortion and monotonicity theorems for spherically convex functions defined on the unit disk involving geometric quantities such as spherical length, area, total curvature. These results can be viewed variants of classical Schwarz lemma functions.

A special acrylic phantom designed for both magnetic resonance imaging (MRI) and computed tomography (CT) was used to assess the geometric accuracy of MRI-based stereotactic localization with the Leksell stereotactic head frame and localizer system. The acrylic phantom was constructed in the shape of a cube, 164 mm in each dimension, with three perpendicular arrays of solid acrylic rods, 5 mm i...

In diffusion MRI, a tensor field or a spherical function field, e.g., an Orientation Distribution Function (ODF) field, are estimated from measured diffusion weighted images. In this paper, inspired by microscopic theoretical treatment of phases in liquid crystals, we introduce a novel mathematical framework, called Director Field Analysis (DFA), to study local geometric structural information ...

Conventional radiographs used for the management of endodontic problems yield limited information because of the two-dimensional nature of images produced, geometric distortion and anatomical noise. This newer review paper seeks to clarify three-dimensional imaging techniques that have been suggested as adjuncts to conventional radiographs. These include tuned aperture computed tomography, magn...

where ΔB0(r) represents a field inhomogeneity, FOVpe is the phase-encoding FOV, and Tro = Nro * Δtro is the readout time for one k-space line (or echo spacing), and Nro is the number of samples in the readout direction. From Eq. 1, one can reduce geometric distortion by reducing FOVpe and/or by reducing Tro. The former can be achieved by accelerating the traversal of kspace with parallel imagin...

There has been a dramatic increase in the handling of geospatial information, and also in the production of maps. However, because the Earth is three-dimensional, geo-referenced data must be projected on a two-dimensional surface. Depending on the area being mapped, the projection process generates a varying amount of distortion, especially for continental and world maps. Geospatial users have ...

This work investigates the optimization of mesh quality at lossy rates for a lossless scalable wavelet-based irregular mesh codec. Whereas previously proposed wavelet-based irregular mesh codecs offer coarse-grain resolution scalability, in this paper we propose a coding scheme which enables fine-grain quality scalability. This is done by avoiding the use of geometric data in the encoding proce...

We propose a technique, called TextureMontage, to seamlessly map a patchwork of texture images onto an arbitrary 3D model. A texture atlas can be created through the specification of a set of correspondences between the model and any number of texture images. First, our technique automatically partitions the mesh and the images, driven solely by the choice of feature correspondences. Most chart...

We propose a watermarking scheme based on the multi-channel watermarking framework, which is mainly used to resist geometric attacks. This watermarking scheme generates watermarking templates from one image transform domain which is obtained after DWT (Discrete wavelet transform) and DFT (Discrete Fourier transform) transformation to one of image channels and then embeds these watermarking temp...