| 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376377378379380381382383384385386387388389390391392393394395396397398399400401402403404405406407 |
- <?xml version="1.0" encoding="UTF-8" standalone="no"?>
- <svg
- xmlns:dc="http://purl.org/dc/elements/1.1/"
- xmlns:cc="http://creativecommons.org/ns#"
- xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
- xmlns:svg="http://www.w3.org/2000/svg"
- xmlns="http://www.w3.org/2000/svg"
- xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
- xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
- width="297mm"
- height="210mm"
- viewBox="0 0 297 210"
- version="1.1"
- id="svg1130"
- inkscape:version="1.0.2 (e86c870879, 2021-01-15)"
- sodipodi:docname="SafeArea.svg">
- <defs
- id="defs1124">
- <marker
- style="overflow:visible"
- id="marker2073"
- refX="0.0"
- refY="0.0"
- orient="auto"
- inkscape:stockid="Arrow1Mstart"
- inkscape:isstock="true">
- <path
- transform="scale(0.4) translate(10,0)"
- style="fill-rule:evenodd;stroke:#000000;stroke-width:1pt;stroke-opacity:1;fill:#000000;fill-opacity:1"
- d="M 0.0,0.0 L 5.0,-5.0 L -12.5,0.0 L 5.0,5.0 L 0.0,0.0 z "
- id="path2071" />
- </marker>
- <marker
- style="overflow:visible"
- id="Arrow1Mstart"
- refX="0.0"
- refY="0.0"
- orient="auto"
- inkscape:stockid="Arrow1Mstart"
- inkscape:isstock="true"
- inkscape:collect="always">
- <path
- transform="scale(0.4) translate(10,0)"
- style="fill-rule:evenodd;stroke:#000000;stroke-width:1pt;stroke-opacity:1;fill:#000000;fill-opacity:1"
- d="M 0.0,0.0 L 5.0,-5.0 L -12.5,0.0 L 5.0,5.0 L 0.0,0.0 z "
- id="path1757" />
- </marker>
- <marker
- style="overflow:visible;"
- id="Arrow1Mend"
- refX="0.0"
- refY="0.0"
- orient="auto"
- inkscape:stockid="Arrow1Mend"
- inkscape:isstock="true">
- <path
- transform="scale(0.4) rotate(180) translate(10,0)"
- style="fill-rule:evenodd;stroke:#000000;stroke-width:1pt;stroke-opacity:1;fill:#000000;fill-opacity:1"
- d="M 0.0,0.0 L 5.0,-5.0 L -12.5,0.0 L 5.0,5.0 L 0.0,0.0 z "
- id="path1760" />
- </marker>
- </defs>
- <sodipodi:namedview
- id="base"
- pagecolor="#ffffff"
- bordercolor="#666666"
- borderopacity="1.0"
- inkscape:pageopacity="0.0"
- inkscape:pageshadow="2"
- inkscape:zoom="3.959798"
- inkscape:cx="615.90513"
- inkscape:cy="244.69408"
- inkscape:document-units="mm"
- inkscape:current-layer="g956"
- inkscape:document-rotation="0"
- showgrid="false"
- inkscape:window-width="2560"
- inkscape:window-height="1381"
- inkscape:window-x="0"
- inkscape:window-y="0"
- inkscape:window-maximized="1" />
- <metadata
- id="metadata1127">
- <rdf:RDF>
- <cc:Work
- rdf:about="">
- <dc:format>image/svg+xml</dc:format>
- <dc:type
- rdf:resource="http://purl.org/dc/dcmitype/StillImage" />
- <dc:title></dc:title>
- </cc:Work>
- </rdf:RDF>
- </metadata>
- <g
- inkscape:label="Ebene 1"
- inkscape:groupmode="layer"
- id="layer1">
- <circle
- style="fill:#ff0000;fill-opacity:0.261664;stroke-width:0.705556"
- id="path1725"
- cx="40.394451"
- cy="45.349041"
- r="12.256145" />
- <circle
- style="fill:#ff0000;fill-opacity:0.261664;stroke-width:0.705556"
- id="circle1727"
- cx="43.639767"
- cy="28.739388"
- r="12.256145" />
- <circle
- style="fill:#e6e6e6;fill-opacity:1;stroke-width:1.54142"
- id="circle1745"
- cx="56.016735"
- cy="38.398243"
- r="5.507617" />
- <circle
- style="fill:#ff0000;fill-opacity:0.261664;stroke-width:0.705556"
- id="circle1733"
- cx="44.016521"
- cy="68.289619"
- r="12.256145" />
- <circle
- style="fill:#e6e6e6;fill-opacity:1;stroke-width:1.54142"
- id="circle1743"
- cx="50.958904"
- cy="55.647419"
- r="5.507617" />
- <circle
- style="fill:#e6e6e6;fill-opacity:1;stroke-width:1.54142"
- id="circle1741"
- cx="56.052494"
- cy="81.273361"
- r="5.507617" />
- <circle
- style="fill:#ff0000;fill-opacity:0.261664;stroke-width:0.705556"
- id="circle1735"
- cx="30.641436"
- cy="76.737602"
- r="12.256145" />
- <circle
- style="fill:#e6e6e6;fill-opacity:1;stroke-width:1.54142"
- id="circle1739"
- cx="33.219952"
- cy="61.010719"
- r="5.507617" />
- <circle
- style="fill:#e6e6e6;fill-opacity:1;stroke-width:1.54142"
- id="circle1737"
- cx="38.313541"
- cy="86.636665"
- r="5.507617" />
- <circle
- style="fill:#ff0000;stroke-width:0.705556"
- id="path1693"
- cx="40.394451"
- cy="45.349041"
- r="2.521014" />
- <circle
- style="fill:#000000;stroke-width:0.705556"
- id="circle1695"
- cx="33.219952"
- cy="61.010719"
- r="2.521014" />
- <circle
- style="fill:#000000;stroke-width:0.705556"
- id="circle1697"
- cx="56.016735"
- cy="38.398243"
- r="2.521014" />
- <circle
- style="fill:#000000;stroke-width:0.705556"
- id="circle1699"
- cx="50.958904"
- cy="55.647419"
- r="2.521014" />
- <circle
- style="fill:#ff0000;stroke-width:0.705556"
- id="circle1701"
- cx="44.016521"
- cy="68.289619"
- r="2.521014" />
- <circle
- style="fill:#000000;stroke-width:0.705556"
- id="circle1703"
- cx="38.313541"
- cy="86.636665"
- r="2.521014" />
- <circle
- style="fill:#000000;stroke-width:0.705556"
- id="circle1705"
- cx="61.110325"
- cy="64.024193"
- r="2.521014" />
- <circle
- style="fill:#000000;stroke-width:0.705556"
- id="circle1707"
- cx="56.052494"
- cy="81.273361"
- r="2.521014" />
- <circle
- style="fill:#000000;stroke-width:0.705556"
- id="circle1709"
- cx="70.177757"
- cy="35.867088"
- r="2.521014" />
- <circle
- style="fill:#000000;stroke-width:0.705556"
- id="circle1711"
- cx="65.119926"
- cy="53.116272"
- r="2.521014" />
- <circle
- style="fill:#000000;stroke-width:0.705556"
- id="circle1713"
- cx="87.91671"
- cy="30.50379"
- r="2.521014" />
- <circle
- style="fill:#000000;stroke-width:0.705556"
- id="circle1715"
- cx="82.858879"
- cy="47.752964"
- r="2.521014" />
- <circle
- style="fill:#ff0000;stroke-width:0.705556"
- id="circle1717"
- cx="30.641436"
- cy="76.737602"
- r="2.521014" />
- <circle
- style="fill:#000000;stroke-width:0.705556"
- id="circle1719"
- cx="75.038666"
- cy="67.554436"
- r="2.521014" />
- <circle
- style="fill:#ff0000;stroke-width:0.705556"
- id="circle1721"
- cx="43.639767"
- cy="28.739388"
- r="2.521014" />
- <circle
- style="fill:#ff0000;stroke-width:0.705556"
- id="circle1723"
- cx="21.343784"
- cy="46.201748"
- r="2.521014" />
- <circle
- style="fill:#ff0000;fill-opacity:0.261664;stroke-width:0.705556"
- id="circle1729"
- cx="21.343784"
- cy="46.201748"
- r="12.256145" />
- <path
- style="fill:none;stroke:#000000;stroke-width:0.265;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1;marker-start:url(#Arrow1Mstart)"
- d="M 52.575949,25.264042 69.655293,20.090939"
- id="path1749"
- sodipodi:nodetypes="cc" />
- <text
- xml:space="preserve"
- style="font-style:normal;font-weight:normal;font-size:4.23333px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
- x="70.870911"
- y="21.379452"
- id="text2061"><tspan
- sodipodi:role="line"
- id="tspan2059"
- x="70.870911"
- y="21.379452"
- style="font-size:4.23333px;stroke-width:0.264583">Safe area for synthetic points. Let us call it S(x) = { x + ζ : ∥ζ∥ ≤ ε } / {y + ζ : y ∈ D<tspan
- style="font-size:65%;baseline-shift:sub"
- id="tspan2127">maj</tspan> , ∥ζ∥ ≤ δ}</tspan></text>
- <path
- style="fill:none;stroke:#000000;stroke-width:0.265;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1;marker-start:url(#marker2073)"
- d="m 57.669453,85.167006 17.079344,5.173103"
- id="path2069"
- sodipodi:nodetypes="cc" />
- <text
- xml:space="preserve"
- style="font-style:normal;font-weight:normal;font-size:4.23333px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
- x="77.230827"
- y="91.632088"
- id="text2125"><tspan
- sodipodi:role="line"
- id="tspan2123"
- x="77.230827"
- y="91.632088"
- style="font-size:4.23333px;stroke-width:0.264583">unsafe area for synthetic points</tspan></text>
- <g
- id="g956"
- transform="translate(112.02089,32.787653)">
- <text
- xml:space="preserve"
- style="font-style:normal;font-weight:normal;font-size:4.23333px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.258878"
- x="13.083162"
- y="16.410084"
- id="text835"><tspan
- sodipodi:role="line"
- id="tspan833"
- x="13.083162"
- y="16.410084"
- style="font-size:4.23333px;stroke-width:0.258878">D = D<tspan
- style="font-size:65%;baseline-shift:sub"
- id="tspan958">maj</tspan> ∪ D<tspan
- style="font-size:65%;baseline-shift:sub"
- id="tspan960">min</tspan> with D<tspan
- style="font-size:65%;baseline-shift:sub"
- id="tspan962">min</tspan> = {x1, x2, …}</tspan></text>
- <ellipse
- style="fill:#000000;stroke:none;stroke-width:0.151522;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0"
- id="path951"
- cx="33.906567"
- cy="13.087456"
- rx="0.32406601"
- ry="0.32406366" />
- </g>
- <text
- xml:space="preserve"
- style="font-style:normal;font-weight:normal;font-size:4.23333px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
- x="22.09767"
- y="118.65482"
- id="text2175"><tspan
- sodipodi:role="line"
- x="22.09767"
- y="118.65482"
- style="font-size:4.23333px;stroke-width:0.264583"
- id="tspan2179">Questions: Can we train a generator so that it produces points respecting S(x) for a given x?</tspan><tspan
- sodipodi:role="line"
- x="22.09767"
- y="123.94649"
- style="font-size:4.23333px;stroke-width:0.264583"
- id="tspan2300"> The generator learns the shape of the safe area.</tspan></text>
- <g
- id="g2256"
- transform="translate(40.94608,22.214649)">
- <g
- id="g2241"
- transform="translate(0,1.1750498)">
- <text
- xml:space="preserve"
- style="font-style:normal;font-weight:normal;font-size:4.23333px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
- x="57.412422"
- y="130.90579"
- id="text2187"><tspan
- sodipodi:role="line"
- id="tspan2185"
- x="57.412422"
- y="130.90579"
- style="font-size:4.23333px;stroke-width:0.264583">noise →</tspan></text>
- <text
- xml:space="preserve"
- style="font-style:normal;font-weight:normal;font-size:4.23333px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
- x="66.166405"
- y="140.29108"
- id="text2191"><tspan
- sodipodi:role="line"
- id="tspan2189"
- x="66.166405"
- y="140.29108"
- style="font-size:4.23333px;stroke-width:0.264583">x →</tspan></text>
- </g>
- <text
- xml:space="preserve"
- style="font-style:normal;font-weight:normal;font-size:4.23333px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
- x="98.556824"
- y="136.32286"
- id="text2199"><tspan
- sodipodi:role="line"
- id="tspan2197"
- x="98.556824"
- y="136.32286"
- style="font-size:4.23333px;stroke-width:0.264583">→v</tspan></text>
- <text
- xml:space="preserve"
- style="font-style:normal;font-weight:normal;font-size:4.23333px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
- x="121.22429"
- y="136.49443"
- id="text2203"><tspan
- sodipodi:role="line"
- id="tspan2201"
- x="121.22429"
- y="136.49443"
- style="font-size:4.23333px;stroke-width:0.264583">with x + v ∈ S(x)</tspan></text>
- <g
- id="g930"
- transform="translate(-15.714536,76.52675)">
- <text
- xml:space="preserve"
- style="font-style:normal;font-weight:normal;font-size:10.5833px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
- x="97.267754"
- y="62.758614"
- id="text851"><tspan
- sodipodi:role="line"
- id="tspan849"
- x="97.267754"
- y="62.758614"
- style="stroke-width:0.264583">G</tspan></text>
- <rect
- style="fill:none;stroke:#000000;stroke-width:0.352778;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0"
- id="rect907"
- width="20.097038"
- height="20.097038"
- x="91.715813"
- y="48.590046" />
- </g>
- </g>
- </g>
- </svg>
|