acronyms.tex

\Acronym{BA}{Bundle adjustment}
\newacronym{C}{$\mathbb{C}$}{Set of complex numbers}
\Acronym{cl$(S)$}{Closure of the set $S$}
\Acronym{deg$(p)$}{Total degree of the polynomial $p$}
\Acronym{diag$(x)$}{Diagonal matrix with components of the vector $x$ on the diagonal}
\Acronym{dom $f$}{Domain of the function $f$}
\Acronym{Dom $f$}{cl(dom $f$)}
\newacronym{first derivative of f}{$f'(x)$}{First derivative of the function $f(x)$}
\newacronym{second derivative of f}{$f''(x)$}{Second derivative of the function $f(x)$}
\Acronym{G-J elimination}{Gauss-Jordan elimination}
\newacronym{vanishing ideal}{$\mathcal{I}(V)$}{Vanishing ideal of the variety $V$}
\newacronym{identity matrix}{$\mathcal{I}^n$}{Identity matrix of size $n\times n$}
\newacronym{radical ideal}{$\sqrt{I}$}{Radical ideal of the ideal $I$}
\newacronym{real radical ideal}{$\sqrt[\mathbb{R}]{I}$}{Real radical ideal of the ideal $I$}
\newacronym{ideal}{$\langle f_1, f_2, \ldots, f_n\rangle$}{Ideal generated by the polynomials $f_1, f_2, \ldots, f_n$}
\Acronym{int $S$}{Interior of the set $S$}
\newacronym{kernel of quadratic form}{ker$(Q_\Lambda)$}{Kernel of the quadratic form $Q_\Lambda$}
\newacronym{kernel of matrix}{ker$(M)$}{Kernel of the matrix $M$}
\newacronym{eigenvalues of M}{$\big\{\lambda_i(A)\big\}_{i=1}^n$}{Set of all eigenvalues of the matrix $A\in\mathbb{R}^{n\times n}$}
\Acronym{LMI}{Linear matrix inequality}
\Acronym{LP}{Linear program}
\newacronym{N}{$\mathbb{N}$}{Set of natural numbers (including zero)}
\newacronym{normal form}{$\mathcal{N}_\mathcal{B}(f)$}{Normal form of the polynomial $f$ modulo ideal $I$ with respect to the basis $\mathcal{B}$}
\newacronym{P}{$\mathcal{P}^n$}{Cone of positive semidefinite $n\times n$ matrices}
\Acronym{PnP problem}{The perspective-n-point problem}
\Acronym{P3P problem}{The perspective-three-point problem}
\Acronym{P3.5Pf problem}{The perspective-three-and-half-point problem with unknown focal length}
\Acronym{POP}{Polynomial optimization}
\Acronym{QCQP}{Quadratically constrained quadratic program}
\newacronym{R}{$\mathbb{R}$}{Set of real numbers}
\newacronym{Rx}{$\mathbb{R}[x]$}{Ring of polynomials with coefficients in $\mathbb{R}$ in $n$ variables $x\in\mathbb{R}^n$}
\newacronym{Rx*}{$\mathbb{R}[x]^*$}{Dual vector space to the ring of polynomials $\mathbb{R}[x]$}
\Acronym{RANSAC}{Random Sample Consensus}
\newacronym{S}{$\mathcal{S}^n$}{Space of $n\times n$ real symmetric matrices}
\Acronym{SDP}{Semidefinite programming}
\Acronym{SfM}{Structure from motion}
\Acronym{SGM method}{Semi-global matching method}
\newacronym{SO(3)}{$SO(3)$}{Group of all rotations about the origin of three-dimensional space}
\Acronym{SVD}{Singular value decomposition}
\Acronym{tr$(A)$}{Trace of the matrix $A$}
\Acronym{vec$(p)$}{Vector of the coefficients of the polynomial $p$ with respect to some monomial basis}
\newacronym{VC}{$V_\mathbb{C}(I)$}{Algebraic variety of the ideal $I$}
\newacronym{VR}{$V_\mathbb{R}(I)$}{Real algebraic variety of the ideal $I$}
\newacronym{i-th element of x}{$x^{(i)}$}{$i$-th element of the vector $x$}
\newacronym{x transposed}{$x^\top$}{Transpose of the vector $x$}
\newacronym{ceiling of x}{$\lceil x \rceil$}{$\min\{m \in \mathbb{Z}\ |\ m \geq x\}$; ceiling function}
\newacronym{floor of x}{$\lfloor x \rfloor$}{$\max\{m \in \mathbb{Z}\ |\ m \leq x\}$; floor function}
\newacronym{multiplication matrix}{$\mathcal{X}_f$}{Multiplication matrix by the polynomial $f$}
\newacronym{Z}{$\mathbb{Z}$}{Set of integers}