We show that for every α > 0, there exist n-point metric spaces (X, d) where every “scale” admits a Euclidean embedding with distortion at most α, but the whole space requires distortion at least Ω( √ α log n). This shows that the scale-gluing lemma [Lee, SODA 2005] is tight, and disproves a conjecture stated there. This matching upper bound was known to be tight at both endpoints, i.e. when α ...

We describe a new method for pairwise retinal image registration. The proposed method is unique in that the radial distortion due to image acquisition is corrected prior to the geometric transformation. Since the overlapping region is typically small in a retinal image pair, only a few correspondences are available, thus limiting the applicable model to an affine transform at best. To recover t...

In structure light measurement systems or 3D printing systems, the errors caused by optical distortion of a digital projector always affect the precision performance and cannot be ignored. Existing methods to calibrate the projection distortion rely on calibration plate and photogrammetry, so the calibration performance is largely affected by the quality of the plate and the imaging system. Thi...

This article presents a method for removing geometric distortions in taken images of rectangular planar patterns (such as maps, pictures, or posters) in the absence of any calibration information or explicit knowledge of the imaging device. Our approach removes lens distortion form single-view images. The method is based on Least-Square-Error (LSE) approximations and Hough transforms. We approx...

We present a novel image resizing method which attempts to ensure that important local regions undergo a geometric similarity transformation, and at the same time, to preserve image edge structure. To accomplish this, we define handles to describe both local regions and image edges, and assign a weight for each handle based on an importance map for the source image. Inspired by conformal energy...

INTRODUCTION Diffusion Weighted Imaging (DWI), which is based on Echo Planar Imaging (EPI) protocols, is becoming increasingly important for neurosurgical applications. However, its use in this context is limited in part by significant spatial distortion inherent to EPI. METHOD We evaluated an efficient algorithm for EPI distortion correction (EPIC) across 814 DWI scans from 250 brain tumor p...

Natural images can be viewed as combinations of smooth regions, textures, and geometry. Wavelet-based image coders, such as the space-frequency quantization (SFQ) algorithm, provide reasonably efficient representations for smooth regions (using zerotrees, for example) and textures (using scalar quantization) but do not properly exploit the geometric regularity imposed on wavelet coefficients by...

PURPOSE Accurate geometry is required for radiotherapy treatment planning (RTP). When considering the use of magnetic resonance imaging (MRI) for RTP, geometric distortions observed in the acquired images should be considered. While scanner technology and vendor supplied correction algorithms provide some correction, large distortions are still present in images, even when considering considera...

In this paper, two new quadrilateral elements are formulated to solve plane problems. Low sensitivity to geometric distortion, no parasitic shear error, rotational invariance, and satisfying the Felippa pure bending test are characteristics of these suggested elements. One proposed element is formulated by establishing equilibrium equations for the second-order strain field. The other suggested...