Open Access
Table A.1.
Symbols in algorithm descriptions.
Symbol | Description |
---|---|
% | The integer modulo operator |
← | The assignment operator |
∥⋯∥ | The Euclidean norm operator |
FFT(⋯) | The Fourier transform operator implemented with FFT algorithm |
IFFT(⋯) | The inverse Fourier transform operator |
The element-wise complex conjugation operator | |
ϵ | A small number specified as an input parameter |
i and j | Array indices |
N and M | Numbers of rows and columns of the original kernel matrix |
k | Cluster index |
K | The number of clusters |
J | The expected number of principal components |
d | Array of N elements represents the observed data |
H | N × M array representing the original kernel matrix |
X | N × M array representing the shifted kernel matrix so that row vectors are aligned |
X_{0} | Array of N elements storing the arithmetic average of the M column vectors of X |
T | N × J array representing the principal component scores of the N row vectors of X, i.e., T[i] is the principal |
component score of X[i] | |
R | N × M array storing residuals in PCA Subroutine ^{2} |
λ and λ_{p} | Estimates of the eigenvalue of the covariance in Subroutine ^{2} |
S | Array of K lists, while the kth list S[k] contains all the row numbers of vectors classified into the kth cluster |
at the current step | |
L | Array of K elements representing the numbers of vectors |
in the K clusters, e.g. L[k] is the number of vectors in the kth cluster | |
C (and C_{p}) | K × J array, the kth row of which stores the central vector of the kth cluster calculated at the current step |
(and the previous step), represented by principal component scores | |
Y | An K × M array storing the central vectors of each cluster in pixel-wise representation |
D | An K × N array representing the Euclidean distance between the N shifted vectors and central vectors of the K |
clusters, e.g. D[k][i] represents the Euclidean distance between the ith shifted vector X[i] and the kth | |
central vector C[k] | |
P | An K × N × M array representing the K circulant kernel matrices in Eq. (3) |
A | An K × N × N array representing the K diagonal coefficient matrices in Eq. (3) |
a | An K × N array representing the vectors of diagonal elements of the K matrices |
w | An array of M elements representing the normalization factor in Eq. (19) |
f (and f_{p}) | Array of M elements representing the object image estimated at the current step (and the previous step) |
r | An array of N elements |
q | An array of M elements |
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.