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Gradient vector flow (GVF) is the process that spatially extends the edge map gradient vectors, yielding a new vector field that contains information about the location of object edges throughout the entire image domain. GVF is defined as a diffusion process operating on the components of the input vector field.
The gradient vector flow (GVF) snake model [6] addresses two issues with snakes: poor convergence performance for concave boundaries; poor convergence performance when snake is initialized far from minimum; In 2D, the GVF vector field minimizes the energy functional
The gradient (or gradient vector field) of a scalar function f(x 1, x 2, x 3, …, x n) is denoted ∇f or ∇ → f where ∇ denotes the vector differential operator, del. The notation grad f is also commonly used to represent the gradient.
Vector fields can usefully be thought of as representing the velocity of a moving flow in space, and this physical intuition leads to notions such as the divergence (which represents the rate of change of volume of a flow) and curl (which represents the rotation of a flow). A vector field is a special case of a vector-valued function, whose ...
Here D ⊆ R × M is the flow domain. For each p ∈ M the map D p → M is the unique maximal integral curve of V starting at p. A global flow is one whose flow domain is all of R × M. Global flows define smooth actions of R on M. A vector field is complete if it generates a global flow. Every smooth vector field on a compact manifold without ...
Flow lines on a tilted torus: the height function satisfies the Morse-Smale condition. Any Morse function f on a compact Riemannian manifold M defines a gradient vector field. If one imposes the condition that the unstable and stable manifolds of the critical points intersect transversely, then the gradient vector field and the corresponding ...
A two-dimensional flow that, at the highlighted point, has only a strain rate component, with no mean velocity or rotational component. In continuum mechanics, the strain-rate tensor or rate-of-strain tensor is a physical quantity that describes the rate of change of the strain (i.e., the relative deformation) of a material in the neighborhood of a certain point, at a certain moment of time.
Given a Morse function f on a manifold M, a gradient-like vector field X for the function f is, informally: away from critical points, X points "in the same direction as" the gradient of f, and; near a critical point (in the neighborhood of a critical point), it equals the gradient of f, when f is written in standard form given in the Morse ...