Parseval frames can be thought of as redundant or linearly dependent coordinate systems for Hilbert spaces, and have important applications in such areas as signal processing, data compression, and sampling theory. We extend the notion of a Parseval frame for a fixed Hilbert space to that of a moving Parseval frame for a vector bundle over a manifold. Many vector bundles do not have a moving ba...

In this paper, we develop the theory of the discrete moving frame in two different ways. In the first half of the paper, we consider a discrete moving frame defined on a lattice variety, and the equivalence classes of global syzygies that result from the first fundamental group of the variety. In the second half, we consider the continuum limit of discrete moving frames as a local lattice coale...

Given a Lie pseudo-group action, an equivariant moving frame exists in the neighborhood of a submanifold jet provided the action is free and regular. For local equivalence problems the freeness requirement cannot always be satisfied and in this paper we show that, with the appropriate modifications and assumptions, the equivariant moving frame constructions extend to submanifold jets where the ...

It is the purpose of the present paper to outline an introduction in theory of embeddings in the 2-osculator bundle. First, we recall the notion of 2-osculator bundle ([9], [2], [4]) and the notion of submani-folds in the 2-osculator bundle ([9]). A moving frame is constructed. The induced connections and the relative covariant derivation are discussed in the fourth and fifth section ([15], [16...

A combined 2D, 3D approach is presented that allows for robust tracking of moving bodies in a given environment as observed via a single, uncalibrated video camera. Lowlevel features are often insufficient for detection, segmentation, and tracking of non-rigid moving objects. Therefore, an improved mechanism is proposed that combines lowlevel (image processing) and mid-level (recursive trajecto...

This paper introduces a new, fully recursive algorithm for computing moving frames and differential invariants of Lie pseudo-group actions. The recursive method avoids unwieldy symbolic expressions that complicate the treatment of large scale applications of the equivariant moving frame method. The development leads to novel results on partial moving frames, structure equations, and new differe...

The purpose of this note is to explain how to use the equivariant method of moving frames, [1, 10], to derive the differential invariants, invariant differential operators and invariant differential forms for surfaces in three-dimensional Euclidean space. This is, of course, a very classical problem and the results are not new; for the classical moving frame derivation, see, for instance, [2, 3...

This paper is the second in a series that develops a theory of moving frames for pseudogroup actions. In this paper, we define a moving frame for free pseudo-group action on the submanifolds, illustrated by explicit examples. Our methods, based on the consequential moving frame connection, provides an effective means for explicitly determining complete systems of differential invariants and inv...

object detection plays an important role in successfulness of a wide range ofapplications that involve images as input data. in this paper we have presented anew approach for background modeling by nonconsecutive frames differencing.direction and velocity of moving objects have been extracted in order to get anappropriate sequence of frames to perform frame subtraction. stationary parts ofbackg...