To decrease the chance of overfitting, data augmentation techniques are applied based on image transforms such as rotation, translation, reflection, and scaling.
The Procrustes approach matches one configuration to another and produces a measure of match, while seeking the isotropic dilation and the rigid translation, reflection and rotation needed to best match one configuration to another (Cox and Cox, 1994).
Various different textures will be gained to tessellate figures by mathematical transformations including translation, rotation, reflection and glide reflection on a surface.
Instead of visualization, we find the rotation, translation, and reflection that gives the closest positions to the true locations in the least-squares sense.
The main results thus extend from general fermionic systems to the action of Hamiltonians with and without restrictions like quadratic interactions, translation invariance, reflection symmetry, or particle-number conservation.
Procedures were designed to yield features invariant to translation, scale, reflection, and rotation in the xy-plane.
These Euclidean transformations are sometimes called isometries, and they include translations, rotations, reflections, and their compositions.
These information-theoretic measures of the associated Rakhmanov probability density, which are direct measures of the polynomial spreading in the sense of having the same units as the variable, share interesting properties: invariance under translations and reflections, linear scaling and vanishing in the limit that the variable tends towards a given definite value.
As well as her own, the pop version of Reflection has 2 Spanish translations, because the movie has separate Spanish translations for Spain (performed by Malú) and Latin America (performed by Lucero).
A network is globally rigid if its only continuous and discontinuous motions satisfying measurement constraints are those corresponding to translation, rotation, or reflection of the entire network.
We found in practice that this clearly outperforms the usual PCA alignment (see Figure 10 and Table 2) and makes the retrieval process invariant to several transformations including rotation, reflection, translation, and scaling.
