>>> from skimage.feature import structure_tensor >>> from skimage.feature import structure_tensor_eigenvalues >>> square = np.zeros((5, 5)) >>> square[2, 2] = 1 >>> A_elems = structure_tensor(square, sigma=0.1,
Classification of the structure tensor eigenvalues permits removal of voxels that are part of planar regions (e.g. floors, walls, and ceilings). The remaining voxels trace a wire-frame-like model of the environment, dramatically reducing the number of voxels required to represent the same space....
The parameters for the structure tensor calculations areρ(rho) andσ(sigma), which are scalar values. 2D and 3D using NumPy Thestructure_tensorpackage support doing either 2D or 3D structure tensor analysis. Eigenvalues (val) are sorted acending. ...
However, for the diffusion schemes we use here, we now prove a maximum–minimum principle for the field of eigenvalues associated with a matrix field. Let F=(fi,j):Ω→Rn×n denote the initial field of n×n-matrices, while U(x,t)=(uij(x,t)) stands for the diffused matrix field,...
The molecular eigenfunctions and eigenvalues are generated using the discrete variational method (DVM) with numerical basis functions. The results obtained for SF6 are compared with other ab initio calculations. Information about relativistic level shifts and spin-orbit splitting has been obtained by ...
where the ionization potential, electron affinity and HOMO–LUMO gap are obtained (exactly in exact DFT) as total-energy differences from separate self-consistent field (SCF) calculations performed with N − 1, N and N + 1 electrons, rather than as eigenvalues of a single calculation...
where\({\textbf {U}} = [\mu _1, \mu _2, \ldots , \mu _N]\), is the matrix of eigenvectors\(\mu _i\), and\(\Lambda = \text {diag}(\lambda _1, \lambda _2, \ldots , \lambda _N)\)is the diagonal matrix of eigenvalues\(\lambda _i\). Each eigenvalue\(\lambda _...
To quantify these differences in local orientations of collagen I fibers, we performed tensor analysis of local image structure to calculate the coherency parameter (C), which is the ratio of the difference and sum of the largest (λmax) and smallest (λmin) tensor eigenvalues (averaged for ...
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3.2.3. Tensor orientation For each pixel, the tensor orientation is estimated based on the voting result T′, which is a 2-dimensional, symmetric, nonnegative definite matrix that can be decomposed as follows:(8)T′=λ1v1v1T+λ2v2v2Twhere λi are the eigenvalues in decreasing order and ...