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| A computation graph for a memory efficient guided filter implementation. | ||
| The stored value in each image is shown at each computation step. | ||
| $I(x)$ denotes the integral image of $x$ and $\overline{x}$ denotes a mean value computed from the integral image over a window $w_k$. |
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| \documentclass[border=0pt,multi,tikz]{standalone} | ||
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| \usetikzlibrary{positioning} | ||
| \usetikzlibrary{patterns} | ||
| \usetikzlibrary{hobby} | ||
| \usetikzlibrary{svg.path} | ||
| \usetikzlibrary{calc} | ||
| \usetikzlibrary{decorations} | ||
| \usetikzlibrary{decorations.markings} | ||
| \usetikzlibrary{arrows.meta} | ||
| \usetikzlibrary{arrows} | ||
| \usetikzlibrary{fit} | ||
| \usetikzlibrary{fadings} | ||
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| \pgfdeclarelayer{bg} % declare background layer | ||
| \pgfsetlayers{bg,main} % set the order of the layers (main is the standard layer) | ||
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| \begin{document} | ||
| \begin{tikzpicture}[ | ||
| % xscale=1.0, | ||
| % yscale=-0.5, | ||
| arrow/.style={-{Latex[length=3pt]}, shorten <=-3pt, shorten >=-3pt}, | ||
| stage/.style={dotted}, | ||
| every node/.style={right,font=\small}, | ||
| ] | ||
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| \matrix [] | ||
| { | ||
| \node(c0){}; \node(i0){}; & \node(i1){1-4}; & \node(i2){5}; & \node(i3){6-9}; & \node(i4){10}; & \node(i5){11-14}; & \node(i6){15}; & \node(i7){16-19}; & \node(i8){20}; \\ | ||
| \node(im0){Input}; & \node[](a){}; &&&&& \node(i){$\overline{a_k} v_i$}; && \node(k){$q_i = \overline{a_k} v_i + \overline{b_k}$}; \\ | ||
| \node(im1){Integral}; & \node(b){$I(v_i)$}; && \node(e){$I\left(\left(v_i-\mu_k\right)^2\right)$}; && \node(h){$I(a_k)$}; && \node(j){$I(b_k)$}; \\ | ||
| \node(im2){Transient results}; && \node(c){$\mu_k = \overline{v_i}$}; && \node[right](f){$a_k=\sigma_k^2 / (\sigma_k^2 + \epsilon)$}; && \\ | ||
| \node(im3){Transient results}; &&&& \node[right](g){$b_k = (1 - a_k)\mu_k$}; \\ | ||
| &&&& \node[gray](bot){$\sigma_k^2 = \overline{\left(v_i - \mu_k \right)^2}$}; \\ | ||
| }; | ||
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| \node[anchor=east,xshift=-0.1cm](aa) at (a.west) {$v_i$}; | ||
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| \draw[arrow] (aa.south) |- (b.west); | ||
| %\draw[arrow] (a2.east) -- (b.west); | ||
| % \draw[arrow] (b.west) -- (a2.east); | ||
| \draw[arrow] (b.south) |- (c.west); | ||
| \draw[arrow] (c.east) -- (f.west); | ||
| \draw[arrow] (c.north) |- (e.west); | ||
| % \draw[arrow,ultra thick,white] (d.north) |- (e.west); | ||
| \draw[arrow] (aa.east) -| (c.south|-e.east) -- (e.west); | ||
| %\draw[arrow] (d.east) -- (e.west); | ||
| % \draw[arrow] (e.west) -- (d.east); | ||
| \draw[arrow] (e.south) |- (f.west); | ||
| \draw[arrow] (e.south) |- (g.west); | ||
| \draw[arrow] (f.north) |- (h.west); | ||
| \draw[arrow] (h.north) |- (i.west); | ||
| %\coordinate[] (is) at (g.east -| i.south); | ||
| %\draw[] (g) -- (is); | ||
| %\draw[arrow] (is) |- (j.west); | ||
| \draw[arrow] (g.east) -| (i.south|-j.west) -- (j.west); | ||
| \draw[arrow] (j.north) |- (k.west); | ||
| \draw[arrow] (i.east) -- (k.west); | ||
| \node[circle, fill=black, anchor=center,inner sep=0pt, minimum size=3pt](intersection) at (c.south|-e.east){}; | ||
| \node[circle, fill=black, anchor=center,inner sep=0pt, minimum size=3pt](intersection) at (e.south|-f.west){}; | ||
| \node[circle, fill=black, anchor=center,inner sep=0pt, minimum size=3pt](intersection) at (j.north|-k.west){}; | ||
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| \node[rotate=90,anchor=south,align=center] at ($(im0.west)!0.5!(im3.west)$) {\textbf{Images}}; | ||
| \node[anchor=east,align=right] at (i1.west) {Computation step:}; | ||
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| % Black lines | ||
| \draw[] (i1.west|-k.north east) -- (k.north east); | ||
| % \draw[] (i0.west|-k.north east) -- (i0.south west |- bot.south); | ||
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| % Dashed lines memory | ||
| \draw[stage] (im0.west|-k.south east) -- (k.south-|k.east); | ||
| \draw[stage] (im0.west|-f.north east) -- (f.north-|k.east); | ||
| \draw[stage] (im0.west|-f.south east) -- (f.south-|k.east); | ||
| \draw[stage] (im0.west|-g.south east) -- (g.south-|k.east); | ||
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| % Dashed lines computation steps | ||
| \draw[stage] (i1.north west) -- (i1.west |- g.south); | ||
| \draw[stage] (i2.north west) -- (i2.west |- g.south); | ||
| \draw[stage] (i3.north west) -- (i3.west |- g.south); | ||
| \draw[stage] (i4.north west) -- (i4.west |- g.south); | ||
| \draw[stage] (i5.north west) -- (i5.west |- g.south); | ||
| \draw[stage] (i6.north west) -- (i6.west |- g.south); | ||
| \draw[stage] (i7.north west) -- (i7.west |- g.south); | ||
| \draw[stage] (i8.north west) -- (i8.west |- g.south); | ||
| %\draw[stage] (i9.north west) -- (i9.west |- bot.south); | ||
| %\draw[stage] (i10.north west) -- (i10.west |- bot.south); | ||
| \end{tikzpicture} | ||
| \end{document} |
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