Large deformation diffeomorphic metric mapping of vector fields

Yan Cao1, Michael I Miller, Raimond L Winslow

  • 1Center for Imaging Science, Johns Hopkins University, Baltimore, MD 21218, USA. yan@cis.jhu.edu

Related Concept Videos

Transformation of Plane Strain01:12

Transformation of Plane Strain

When analyzing elongated structures like bars subjected to uniformly distributed loads, it is essential to understand the transformation of plane strain when coordinate axes are rotated. This transformation helps to assess how material deformation characteristics vary with orientation, which is crucial in materials science and structural engineering.
Under plane strain conditions, typical for members where one dimension significantly exceeds the others, deformations and resultant strains are...
Conservative Vector Fields01:29

Conservative Vector Fields

A conservative vector field describes a force or field in which the work done between two points depends only on the initial and final positions. For a ball moving in Earth’s gravitational field, gravity performs work determined by the difference in height, regardless of whether the ball moves vertically or follows a curved trajectory.A vector field is conservative if it can be expressed as the gradient of a scalar potential function, f. In two dimensions, this is written...
Vector Transformation in Rotating Coordinate Systems01:16

Vector Transformation in Rotating Coordinate Systems

Consider a vector rotating about an axis with an angular velocity, such that its tip sweeps a circular path.
Deformation of Member under Multiple Loadings01:11

Deformation of Member under Multiple Loadings

When a rod is made of different materials or has various cross-sections, it must be divided into parts that meet the necessary conditions for determining the deformation. These parts are each characterized by their internal force, cross-sectional area, length, and modulus of elasticity. These parameters are then used to compute the deformation of the entire rod.
In the case of a member with a variable cross-section, the strain is not constant but depends on the position. The deformation of an...
Vectors in Engineering Applications01:30

Vectors in Engineering Applications

A steel beam supported by two identical cables provides a practical example of static equilibrium. The beam has a downward weight of 5000 N, while the two cables support it from opposite sides. Because the arrangement is symmetric, each cable makes the same angle of 60° with the horizontal beam and carries the same tension.In equilibrium, the beam remains completely at rest. This means that the total horizontal and vertical forces must both be zero. Each cable pulls along its own direction, so...
Derivatives of Vector Functions01:17

Derivatives of Vector Functions

A vector-valued function describes position as a function of time. For example, in Cartesian coordinates, the position of a car moving along a curved road can be written as\begin{equation*}\textbf{r}(t)=\langle x(t),y(t),z(t)\rangle\end{equation*}Secant Vector and Average Velocity:This secant vector captures the overall change in position during the interval and provides a crude estimate of the direction of motion.At time t, the car is at point P, with position r(t). After a short interval h,...