This paper presents a novel methodology for approximate motion synthesis using a PD based distance metric. Finite planar locations are represented using homogenous transformations, which can then be approximated by rotations using the polar decomposition based distance metric. A bi-invariant metric calculates the distance between two locations of a rigid body. A multidimensional nested optimiza...

Sheffield (2016) proposed an inventory accumulation model with two types of products which encodes the critical Fortuin-Kasteleyn model on a random planar map, and showed that a two-dimensional inventory accumulation trajectory in the discrete model scales to a correlated planar Brownian motion. In this work, we generalize the inventory model to k types of products for any integer k ≥ 2, and pr...

Due to previous publications of the author, it is already known that one-parametric self-motions of general planar Stewart Gough platforms can be classified into two so-called Darboux Mannheim (DM) types (I and II). Moreover, the author also proved the necessity of three conditions for obtaining a type II DM self-motion. Based on this result we determine in the article at hand, all general plan...

Although mosaics are well established as a compact and nonredundant representation of image sequences, their application still suffers from restrictions of the camera motion or has to deal with parallax errors. We present an approach that allows construction of mosaics from arbitrary motion of a head-mounted camera pair. As there are no parallax errors when creating mosaics from planar objects,...

Representing videos with layers has important applications such as video compression, motion analysis, 3D modeling and rendering. This thesis proposes a subspace approach to extracting layers from video by taking advantages of the fact that homographies induced by planar patches in the scene form a low dimensional linear subspace. In the subspace, layers in the input images are mapped onto well...

Follow-the-leader propagation allows for the insertion of flexible surgical instruments along curved paths, reducing the access required for natural orifice transluminal endoscopic surgery. Currently, the most promising follow-the-leader instruments use the alternating memory method containing two mechanical memory-banks for controlling the motion of the flexible shaft, which reduces the number...

In this paper, we proposed a randomised algorithm to estimate the motion parameters of a planar shape without knowing a priori point-to-point correspondences. By randomly searching points on two shapes measured at different times, we determine the centroids, after which the algorithm proceeds to determine the rotation by searching points on each shape that form congruent polygons. Key-Words: Mo...

This paper describes a hierarchical estimation framework for the computation of diverse representations of motion information. The key features of the resulting framework (or family of algorithms) a,re a global model that constrains the overall structure of the motion estimated, a local rnodel that is used in the estimation process, and a coa,rse-fine refinement strategy. Four specific motion m...

One-degree-of-freedom mechanisms induced by minimum pseudotriangulations with one convex hull edge removed have been recently introduced by the author to solve a family of non-colliding motion planning problems for planar robot arms (open or closed polygonal chains). They induce canonical roadmaps in configuration spaces of simple planar polygons with

We consider matrices whose elements enumerate weights of walks in planar directed weighted graphs (not necessarily acyclic). These matrices are totally nonnegative; more precisely, all their minors are formal power series in edge weights with nonnegative coefficients. A combinatorial explanation of this phenomenon involves loop-erased walks. Applications include total positivity of hitting matr...