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0d-defpart1.tex
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% EVAL
\newcommand{\becir}{\mathbf{B}}
\newcommand{\becire}{\mathbf{b}}
\newcommand{\onepoint}{\mathbf{P}}
\newcommand{\onepointset}{\mathcal{P}}
\newcommand{\anotherpoint}{\mathbf{Q}}
\newcommand{\anotherpointset}{\mathcal{Q}}
\newcommand{\vxpatch}{\mathbf{v}}
\newcommand{\pointx}{P_x}
\newcommand{\pointy}{P_y}
\newcommand{\pointz}{P_z}
\newcommand{\pointscale}{P_s}
\newcommand{\volumep}{\mathbf{v}_P}
\newcommand{\volumeq}{\mathbf{v}_Q}
\newcommand{\scalefactor}{f}
\newcommand{\meshset}{\textbf{mesh}\ }
\newcommand{\mriset}{\textbf{MRI}\ }
\newcommand{\stereoset}{\textbf{stereo}\ }
\newcommand{\areascore}{R_\textrm{area}}
\newcommand{\disp}{D}
% 3D REG
\newcommand{\prob}{p}
\newcommand{\quasi}{q}
\newcommand{\comp}{} % Transform composition \otimes
\newcommand{\order}{\mathcal{O}}
\newcommand{\trsp}{\textsf{T}}
\newcommand{\model}{\mathcal{M}}
\newcommand{\shapemodel}{\mathcal{M}_\mathrm{SRT}}
\newcommand{\appmodel}{\mathcal{M}_\mathrm{appearance}}
\newcommand{\setassign}{\mathcal{H}} % Part assignments over all instances
\newcommand{\allassign}{\mathbb{H}} % Set of possible part assignments
\newcommand{\assignval}{{H}} % A value in the part assignment matrix
\newcommand{\setpartapp}{\mathcal{A}} % Set of part appearances
\newcommand{\setfeatapp}{\mathcal{B}} % Set of feature appearances
\newcommand{\setpartshape}{\mathcal{X}} % Set of part shapes
\newcommand{\setfeatshape}{\mathcal{Y}} % Set of feature shapes
\newcommand{\setseen}{\mathcal{D}} % Set of feature shapes
\newcommand{\partapp}{\mathbf{A}} % Part Appearance
\newcommand{\featapp}{\mathbf{B}} % Feature Appearance
\newcommand{\partshape}{\mathbf{X}} % Part Shape
\newcommand{\featshape}{\mathbf{Y}} % Feature Shape
\newcommand{\assign}{\mathbf{H}} % Part Assignment
\newcommand{\pose}{\mathbf{T}} % Pose
\newcommand{\apose}{\mathbf{\hat{T}}} % affine pose
\newcommand{\particle}{{J}} % Particle
\newcommand{\seen}{{D}} % Part seen?
\newcommand{\weight}{{w}} % weight
\newcommand{\dirsim}{S^{+}} % Similarity Group
\newcommand{\dist}{d} % "distance"
\newcommand{\srtdist}{\dist_{\mathrm{SRT}}} % SRT distance
%\newcommand{\fg}{\mathrm{Foreground}}
%\newcommand{\bg}{\mathrm{Background}}
\newcommand{\fg}{\mathrm{Object}}
\newcommand{\bg}{\mathrm{No~object}}
% SRT Components of shapes
% Note that the pair of extra curly bractkets {} is used
% to prevent double underscript error
\newcommand{\poses}{{\pose_{\mathbf{s}}}}
\newcommand{\poser}{{\pose_{\mathbf{r}}}}
\newcommand{\poset}{{\pose_{\mathbf{t}}}}
\newcommand{\posed}{{\pose_{\bm{\Delta}}}}
\newcommand{\poseds}{{\pose_{\bm{\Delta s}}}}
\newcommand{\posedr}{{\pose_{\bm{\Delta r}}}}
\newcommand{\posedt}{{\pose_{\bm{\Delta t}}}}
\newcommand{\featshapesrt}[1][]{{\featshape_{#1}}}
\newcommand{\featshapes}[1][]{{\featshape_{#1\mathbf{s}}}}
\newcommand{\featshaper}[1][]{{\featshape_{#1\mathbf{r}}}}
\newcommand{\featshapet}[1][]{{\featshape_{#1\mathbf{t}}}}
\newcommand{\muapp}{{\mu_{\partapp}}}
\newcommand{\sigmaapp}{{\Sigma_{\partapp}}}
\newcommand{\mushape}{{\mu_{\partshape}}}
\newcommand{\mushapes}{{\mu_{\mathbf{s}}}}
\newcommand{\mushaper}{{\mu_{\mathbf{r}}}}
\newcommand{\mushapet}{{\mu_{\mathbf{t}}}}
\newcommand{\sigmashape}{{\Sigma_{\partshape}}}
\newcommand{\sigmashapes}{{\sigma^{2}_{\mathbf{s}}}}
\newcommand{\sigmashaper}{{\sigma^{2}_{\mathbf{r}}}}
\newcommand{\sigmashapet}{{\sigma^{2}_{\mathbf{t}}}}
\newcommand{\SRT}{\mathrm{SRT}}
\newcommand{\auxfunct}{\mathcal{L}}
\newcommand{\partprior}{{\alpha}}
\newcommand{\particleprior}{{\beta}}
% \newcommand{\partprior}{\bm{\alpha}}
% \newcommand{\particleprior}{\bm{\beta}}
\newcommand{\numinstance}{M}
\newcommand{\numfeat}{N}
\newcommand{\numparticle}{Q}
\newcommand{\numpart}{K}
\newcommand{\anyinstance}{m}
\newcommand{\anyfeat}{n}
\newcommand{\anyparticle}{q}
\newcommand{\anotherparticle}{q'}
\newcommand{\anypart}{k}
\newcommand{\regdata}{\mathrm{reg}}
\newcommand{\oneassign}{\assign_{\anyinstance\anyfeat\anyparticle\anypart}}
\newcommand{\zeroassign}{\assign_{\anyinstance\anyfeat\anyparticle0}}
\newcommand{\oneparticle}{\particle_{\anyinstance\anyparticle}}
\newcommand{\onefeatapp}{\featapp_{\anyinstance\anyfeat}}
\newcommand{\onefeatshape}{\featshape_{\anyinstance\anyfeat}}
\newcommand{\onefeatshapet}{\featshape_{\mathbf{t}\anyinstance\anyfeat}}
\newcommand{\onepose}{\pose_{\anyinstance\anyparticle}}
\newcommand{\oneposes}{\poses[\anyinstance\anyparticle]}
\newcommand{\oneposer}{\poser[\anyinstance\anyparticle]}
\newcommand{\oneposet}{\poset[\anyinstance\anyparticle]}
\newcommand{\onepartapp}{\partapp_{\anypart}}
\newcommand{\onepartshape}{\partshape_{\anypart}}
\newcommand{\sumparticle}{\displaystyle\sum_{\anyparticle = 1}^{\numparticle}}
\newcommand{\sumparticleinline}{\sum_{\anyparticle = 1}^{\numparticle}}
\newcommand{\sumpart}{\displaystyle\sum_{\anypart = 1}^{\numpart}}
\newcommand{\sumpartbginline}{\sum_{\anypart = 0}^{\numpart}}
\newcommand{\suminstance}{\displaystyle\sum_{\anyinstance = 1}^{\numinstance}}
\newcommand{\sumpartbg}{\displaystyle\sum_{\anypart = 0}^{\numpart}}
\newcommand{\sumfeat}{\displaystyle\sum_{\anyfeat = 1}^{\numfeat}}
\newcommand{\prodparticle}{\displaystyle\prod_{\anyparticle = 1}^{\numparticle}}
\newcommand{\prodinstance}{\displaystyle\prod_{\anyinstance = 1}^{\numinstance}}
\newcommand{\prodpart}{\displaystyle\prod_{\anypart = 1}^{\numpart}}
\newcommand{\prodpartbg}{\displaystyle\prod_{\anypart = 0}^{\numpart}}
\newcommand{\prodfeat}{\displaystyle\prod_{\anyfeat = 1}^{\numfeat}}
\newcommand{\Gauss}{\mathcal{G}}
\newcommand{\NormDist}{\mathcal{N}}
\newcommand{\UniformDist}{\mathcal{U}}
\newcommand{\wavg}{\mathcal{W}}
\newcommand{\parameter}{\theta}
\newcommand{\EMQ}{\mathcal{Q}} %(\parameter^{(t)},\parameter^{(t-1)})
\newcommand{\expect}{\mathcal{L}_{\anyinstance\anyparticle}}
\newcommand{\expectall}{\mathcal{L}}
\newcommand{\tof}{\mathbf{t}}
\newcommand{\sof}{\mathbf{s}}
\newcommand{\rof}{\mathbf{r}}
\newcommand{\transformedpoint}{\pose_{\anyinstance\anyparticle}\onefeatshape}
\newcommand{\dimension}{d}
\newcommand{\deltapose}{\onepose^{\Delta}}
\newcommand{\background}{\gamma}
\newcommand{\backgrounds}{\background_\mathrm{S}}
\newcommand{\backgroundr}{\background_\mathrm{R}}
\newcommand{\backgroundt}{\background_\mathrm{T}}
\newcommand{\backgroundreg}{\background_\mathrm{reg}}
\newcommand{\refptfront}{\mathbf{R}_\mathrm{front}}
\newcommand{\refptrear}{\mathbf{R}_\mathrm{rear}}
\newcommand{\remarka}{\textsuperscript{\textbf{\S}}}
\newcommand{\remarkb}{\textsuperscript{\textbf{\dag}}}
\newcommand{\remarkc}{\textsuperscript{\textbf{*}}}