this article concerned on the study of signature submanifolds for curves under lie group actions se(2), sa(2) and for surfaces under se(3). signature submanifold is a regular submanifold which its coordinate components are dierential invariants of an associated manifold under lie group action, and therefore signature submanifold is a key for solving equivalence problems.

2 Preliminaries in Mathematics and Physics 47 2.1 Surface Theory Based on Moving Frame . . . . . . . . . . . . . . 47 2.1.1. Moving Frame Method . . . . . . . . . . . . . . . . . . . 47 2.1.2. Stokes’ Theorem and Related Identities . . . . . . . . . . 49 2.2 Helfrich’s Model . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.3 Variational Method Based on Moving Frame . . . . . . . . . . ....

Four experiments are reported that investigated the role of the perceived coplanarity of a moving target with respect to a frame of reference in the third dimension on the perceived path of that target. When a target dot and small moving frame appeared coplanar, the dot's perceived trajectory was governed entirely by its changing position relative to the moving frame. However, when the target a...

In today’s world ensuring security for important location is a burning issue. Surveillance system is playing an important role in the field of security. Moving object detection has been widely used in video surveillance system. This paper proposes a simple and efficient approach for real time moving object extraction in video sequences where moving object region is extracted from the moving edg...

Moving Object Detection is one of the key research areas of Image processing. In this regard many researches are underway to provide a novel approach to detect moving object with less space and time complexity. This paper, outlines the novel approach to detect high speed moving object with frame interleaving in frame differencing operation and clustering based compression for frame and backgrou...

Analysis of electromagnetic planewave propagation in a medium which is a spatiotemporally homogeneous, temporally nonlocal, isotropic, chiral medium in a co–moving frame of reference shows that the medium is both spatially and temporally nonlocal with respect to all non–co–moving inertial frames of reference. Using the Lorentz transformations of electric and magnetic fields, we show that plane ...

Generally moving object extraction schemes rely on either optical flow or frame difference. Though optical flow based methods can deal with moving camera situation with ease, the inconsistency at object boundaries causes extraction with inaccurate object boundaries. While frame difference approach, such as three frame difference, yields accurate object boundaries, it usually cannot deal with mo...