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%% ---------------------------------------------------------------- %% Definitions.tex %% ---------------------------------------------------------------- \newcommand{\BibTeX}{{\rm B\kern-.05em{\sc i\kern-.025em b}\kern-.08em T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}} %% People \newcounter{address} \setcounter{address}{1} \renewcommand{\theaddress}{\textsuperscript{\fnsymbol{address}}} \newcommand{\address}[1]{\refstepcounter{address}\theaddress#1\\} \newcommand{\Name}[3]{\texorpdfstring{\href{mailto:#3}{#2}#1}{#2}\xspace} \newcommand{\SteveRGunn}[1]{\Name{#1}{Steve R. Gunn}{S.R.Gunn@ecs.soton.ac.uk}} %% Dingbats \newcommand{\tick}{\ding{51}} \newcommand{\cross}{\ding{55}} %% Calculus \newcommand{\pd}[2]{\ensuremath{\frac{\partial #1}{\partial #2}}\xspace} \newcommand{\fd}[2]{\ensuremath{\frac{d #1}{d #2}}\xspace} \newcommand{\dint}{\ensuremath{\int\!\!\!\int}\xspace} \newcommand{\tint}{\ensuremath{\int\!\!\!\int\!\!\!\int}\xspace} %% Math Sets \newcommand{\Q}[1]{\ensuremath{\mathbb{#1}}\xspace} \newcommand{\R}{\Q{R}} %% Matrix, Vector \newcommand{\V}[1]{\ensuremath{\boldsymbol{#1}}\xspace} \newcommand{\M}[1]{\ensuremath{\boldsymbol{#1}}\xspace} \newcommand{\0}{\V{0}} \newcommand{\1}{\V{1}} \newcommand{\I}{\M{I}} %% Math Functions \newcommand{\F}[1]{\ensuremath{\mathrm{#1}}\xspace} \newcommand{\sgn}{\F{sgn}} \newcommand{\tr}{\F{trace}} \newcommand{\diag}{\F{diag}} %% Math Names \newcommand{\N}[1]{\ensuremath{\mathit{#1}}\xspace} %% Data \newcommand{\mc}[1]{\ensuremath{\mathcal{#1}}\xspace} \newcommand{\Hyp}{\mc{H}} \newcommand{\D}{\mc{D}} %% Kernel \newcommand{\K}{\M{K}} \newcommand{\eins}{\texorpdfstring{\ensuremath{\epsilon}}{\textepsilon}-insensitive\xspace} \newcommand{\e}{\ensuremath{\epsilon}\xspace} \newcommand{\Bxi}{\ensuremath{\boldsymbol{\xi}}\xspace} \newcommand{\Kanova}{\ensuremath{\mathit{K_{ANOVA}}}\xspace} \newcommand{\Kspline}{\ensuremath{\mathit{K_{spline}}}\xspace} %% Bayesian \newcommand{\MP}{\ensuremath{\mathit{{\scriptscriptstyle \hspace{-1.5pt}M\hspace{-1.5pt}P}}}\xspace} \newcommand{\ML}{\ensuremath{\mathit{{\scriptscriptstyle \hspace{-1.5pt}M\hspace{-1.5pt}L}}}\xspace} \newcommand{\Qw}{\ensuremath{Q_{\w}(\w)}\xspace} \newcommand{\Qa}{\ensuremath{Q_{\Ba}(\Ba)}\xspace} \newcommand{\Qb}{\ensuremath{Q_{\beta}(\beta)}\xspace} \newcommand{\wMPab}{\ensuremath{\w_{\MP|\bar {\Ba},\bar \beta}}\xspace} \newcommand{\wMP}{\ensuremath{\w_{\MP}}\xspace} \newcommand{\yMP}{\ensuremath{y_{\MP}}\xspace} \newcommand{\BaMP}{\ensuremath{\Ba_{\hspace{1pt}\MP}}\xspace} \newcommand{\aMP}{\ensuremath{\alpha_{\hspace{1pt}\MP}}\xspace} \newcommand{\bMP}{\ensuremath{\beta_{\hspace{1pt}\MP}}\xspace} \newcommand{\Sab}{\ensuremath{\M{\Sigma}_{\bar \Ba,\bar \beta}}\xspace} \newcommand{\Ba}{\ensuremath{\boldsymbol{\alpha}}\xspace} \newcommand{\Bb}{\ensuremath{\boldsymbol{\beta}}\xspace} \newcommand{\Bm}{\ensuremath{\boldsymbol{\mu}}\xspace} \newcommand{\BL}{\ensuremath{\boldsymbol{\Lambda}}\xspace} \newcommand{\BPhi}{\ensuremath{\boldsymbol{\Phi}}\xspace} \newcommand{\SMP}{\ensuremath{\M{\Sigma}_{\MP}}\xspace} \newcommand{\Pa}{\ensuremath{P(\alpha|\mathcal{H})}\xspace} \newcommand{\Pb}{\ensuremath{P(\beta|\mathcal{H})}\xspace} \newcommand{\Pab}{\ensuremath{P(\alpha,\beta|\mathcal{H})}\xspace} \newcommand{\Pw}{\ensuremath{P(\w|\mathcal{H})}\xspace} \newcommand{\PD}{\ensuremath{P(\D|\mathcal{H})}\xspace} \newcommand{\PwIa}{\ensuremath{P(\w|\alpha,\mathcal{H})}\xspace} \newcommand{\PDIwb}{\ensuremath{P(\D|\w,\beta,\mathcal{H})}\xspace} \newcommand{\PDwab}{\ensuremath{P(\D,\w,\alpha,\beta|\mathcal{H})}\xspace} \newcommand{\PDIw}{\ensuremath{P(\D|\w,\mathcal{H})}\xspace} \newcommand{\PwID}{\ensuremath{P(\w|\D,\mathcal{H})}\xspace} \newcommand{\PwabID}{\ensuremath{P(\w,\alpha,\beta|\D,\mathcal{H})}\xspace} \newcommand{\PanH}{\ensuremath{P(\alpha)}\xspace} \newcommand{\PbnH}{\ensuremath{P(\beta)}\xspace} \newcommand{\PabnH}{\ensuremath{P(\alpha,\beta)}\xspace} \newcommand{\PwnH}{\ensuremath{P(\w)}\xspace} \newcommand{\PDnH}{\ensuremath{P(\D)}\xspace} \newcommand{\PwIanH}{\ensuremath{P(\w|\alpha)}\xspace} \newcommand{\PDIwbnH}{\ensuremath{P(\D|\w,\beta)}\xspace} \newcommand{\PDwabnH}{\ensuremath{P(\D,\w,\Ba,\beta)}\xspace} \newcommand{\PDIwnH}{\ensuremath{P(\D|\w)}\xspace} \newcommand{\PwIDnH}{\ensuremath{P(\w|\D)}\xspace} \newcommand{\PwabIDnH}{\ensuremath{P(\w,\alpha,\beta|\D)}\xspace} \newcommand{\PDwBab}{\ensuremath{P(\D,\w,\Ba,\beta|\mathcal{H})}\xspace} \newcommand{\PwIBa}{\ensuremath{P(\w|\Ba,\mathcal{H})}\xspace} \newcommand{\PBab}{\ensuremath{P(\Ba,\beta|\mathcal{H})}\xspace} \newcommand{\PwBabID}{\ensuremath{P(\w,\Ba,\beta|\D,\mathcal{H})}\xspace} \newcommand{\PBanH}{\ensuremath{P(\Ba)}\xspace} \newcommand{\PwIBanH}{\ensuremath{P(\w|\Ba)}\xspace} %% Snakes \newcommand{\Esnake}{\ensuremath{\mathit{E_{snake}}}\xspace} \newcommand{\Eimage}{\ensuremath{\mathit{E_{image}}}\xspace} \newcommand{\Econt}{\ensuremath{\mathit{E_{cont}}}\xspace} \newcommand{\Ecurv}{\ensuremath{\mathit{E_{curv}}}\xspace} \newcommand{\Eint}{\ensuremath{\mathit{E_{int}}}\xspace} \newcommand{\Eext}{\ensuremath{\mathit{E_{ext}}}\xspace} \newcommand{\Eterm}{\ensuremath{\mathit{E_{term}}}\xspace} \newcommand{\Eline}{\ensuremath{\mathit{E_{line}}}\xspace} \newcommand{\Eedge}{\ensuremath{\mathit{E_{edge}}}\xspace} \newcommand{\Econ}{\ensuremath{\mathit{E_{con}}}\xspace} \newcommand{\Eangle}{\ensuremath{\mathit{E_{angle}}}\xspace} \newcommand{\Elshape}{\ensuremath{\mathit{E_{lshape}}}\xspace} \newcommand{\Eedgedir}{\ensuremath{\mathit{E_{edgedir}}}\xspace} \newcommand{\Emodel}{\ensuremath{\mathit{E_{model}}}\xspace} \newcommand{\wte}{\ensuremath{\mathit{w_{term}}}\xspace} \newcommand{\wli}{\ensuremath{\mathit{w_{line}}}\xspace} \newcommand{\wed}{\ensuremath{\mathit{w_{edge}}}\xspace} \newcommand{\wco}{\ensuremath{\mathit{w_{con}}}\xspace} %% Environments \newcounter{alg} \newenvironment{algorithm}[1] { \stepcounter{alg} \begin{table}[htb] \centering \begin{tabular}[t]{ll} \hline&\\ \multicolumn{2}{l}{\bf Algorithm \arabic{alg}: #1}\\&\\ } { &\\ \hline \end{tabular} \end{table} }