Sentence examples for transformation rotation from inspiring English sources

The electrode positions were transformed by a rigid body transformation (rotation matrix and displacement vector) minimizing the root-mean-square (RMS) distance of the seven Polhemus marker positions to the MRI marker positions.

Experimental results show that the proposed scheme has a large capacity, good imperceptibility, and is robust against operations such as transformation, rotation, and equal scaling.

For instance, when a sphere rotates around its central vertical axis, that motion preserves the sphere's symmetries about the x and y axes, and thus these symmetries are invariant under that particular transformation (rotation).

Typically, blocks should be much wider than high, since the transformation rotation angle is usually small, after manual coarse rectification; cThe number of necessary memory words is proportional to 2 N s.

The original version of the ICP algorithm relies on the L 2 error to derive the transformation (rotation R∈S O 3 and translation t∈R 3), which minimizes the L 2 type error: mathbf{E}(mathbf{R},mathbf{t})= sumlimits_{mathbf{i}=mathbf{1}}^{mathbf{n}} mathbf{e}_{mathbf{i}}(mathbf{R},mathbf{t})=sumlimits_{mathbf{i}=mathbf{1}}^{mathbf{n}}|mathbf{Rx}_{mathbf{i}}+mathbf{t}-mathbf{y}_{mathbf{j}^| (1).

For this, intra-subject registration was first performed using Automated Image Registration (AIR) [50] to remove linear transformation (rotation and translation) between the 35 diffusion weighted images and T2 weighted image.

The mean image produced from the realignment stage was then spatially normalized to an MNI template image, using a 12-parameter linear affine transformation (translation, rotation, zoom, and shear in x, y, and z directions) and a linear combination of three dimensional discrete cosine transform basis functions.

After identifying pairs of junctions conserved in both meshes using the lineage information, we project for each cell the junctions on the average cell plane and compute a best fit of the 2D transformation (translation, rotation, anisotropic scaling) that will minimize the squared distance between pairs of junctions (Goodall and Green, 1986; Routier-Kierzkowska and Kwiatkowska, 2008).

Each observed joint is then tested to see if it is far enough from the landmark at 6 to potentially be either point 1 or 2. If it is, then the direction from the joint to landmark is used to define an affine transformation (translation, rotation, x and y scaling and shear) of all the observed joints.

Unlike simple affine transformations (translation, rotation, dilation, shearing etc)., non-rigid transformations do not necessarily preserve straight lines as different sub-regions of images may move by differing vectors.

The robustness is tested on various attack, some being a median filter, geometrical transformations (translation, rotation and cropping simultaneously applied), a high-pass filter, local notch filter, and Gaussian noise.