Sentence examples for mean shape s from inspiring English sources

Firstly, each image I 1, …, I N is warped into a common reference frame - usually the mean shape s ¯.

The result is a linear model which describes an arbitrary shape s based on its shape parameters b s, the shape eigenvectors P s, and the mean shape s ¯ of all samples via s = s ¯ + P s b s. (1).

Alignment s 2 d is aligned with the 2D mean shape produced by rotating the 3D mean shape ( s 0 ) from 0° to θ ^ and projecting it onto the x y plane.

A mesh deformation is thus modeled as a linear combination of a mean shape s 0 and n m basis shapes (deformation modes) (mathbf {S}=left [mathbf {s}_{1},ldots,mathbf {s}_{n_{m}}right ]): mathbf{s}=mathbf{s}_{0}+sumlimits_{k}mathbf{s}}w_{k}=mathbf{s_{k}=mathbf{s}_{0}+mathbf{Sw} (2).

During the alignment step, an accurate alignment result is obtained by aligning the input 2D FFPs with the FFPs of the 2D mean shape, which are obtained by rotating the 3D mean shape (s 0) from 0° to θ ^ and projecting it onto the x – y plane.

The piecewise affine warp function W ( s ; p ~ ) maps pixels inside the source shape s into the mean shape s0 using the barycentric coordinates of Delaunay triangulation.

Layout and cut the leaf shape(s).

As first step, the shape model is built by aligning the given shape samples l 1, …, l N with respect to translation, rotation, and scale via Procrustes analysis [38, 39], resulting in shapes s 1, …, s N. The shape variations are then parameterized by applying principal component analysis (PCA) to the matrix S = ( s 1 − s ¯, …, s N − s ¯ ), where s ¯ = 1 N ∑ n = 1 N s n is the mean shape.

The mean shape s0 and m shape basis vectors s i are obtained by using PCA for training data.

Alignment s 2d is aligned with the 2D mean shape obtained by projecting the frontal 3D mean shape (s0) onto the x – y plane.

The mean shape s0 and m shape variations si are then obtained, and a new shape S can be expressed as a linear combination of the mean shape s0 and the shape variations si as follows: S = s 0 + ∑ i = 1 m β i s i (1).