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	<id>http://wiki.nosdigitais.teia.org.br/index.php?action=history&amp;feed=atom&amp;title=Why_Curves</id>
	<title>Why Curves - Histórico de revisão</title>
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	<updated>2026-04-21T13:33:43Z</updated>
	<subtitle>Histórico de revisões para esta página neste wiki</subtitle>
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	<entry>
		<id>http://wiki.nosdigitais.teia.org.br/index.php?title=Why_Curves&amp;diff=7019&amp;oldid=prev</id>
		<title>V1z em 02h28min de 10 de outubro de 2012</title>
		<link rel="alternate" type="text/html" href="http://wiki.nosdigitais.teia.org.br/index.php?title=Why_Curves&amp;diff=7019&amp;oldid=prev"/>
		<updated>2012-10-10T02:28:26Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;col class=&quot;diff-content&quot; /&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Edição anterior&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Edição das 23h28min de 9 de outubro de 2012&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Linha 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linha 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Why is a curve-based graphical representation important for 3D computer vision and structure from motion? This is an ongoing list of the reasons we can think of. Add your own!&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Why is a curve-based graphical representation important for 3D computer vision and structure from motion? This is an ongoing &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;(rather informal) &lt;/ins&gt;list of the reasons we can think of. Add your own!&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Main Reasons Why You Should Care About Curves ==&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Main Reasons Why You Should Care About Curves ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l33&quot;&gt;Linha 33:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linha 33:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;variations across views indicate surface curvature~\cite{Giblin:Motion:Book}.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;variations across views indicate surface curvature~\cite{Giblin:Motion:Book}.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Weaker &lt;/del&gt;Reasons ==&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Other &lt;/ins&gt;Reasons ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;* Powerful correlated statistics for matching etc: Points within curves co-occur. Co-occurrence of point features have been successfully explored by recent work by Noah Snavely et, al. very successfully to get good matches in very large scale models. This is sort of an &amp;quot;initial&amp;quot; form of geometry/shape information. In a curve, all points co-occur, which can potentially be very powerful.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Link ==&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Link ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>V1z</name></author>
	</entry>
	<entry>
		<id>http://wiki.nosdigitais.teia.org.br/index.php?title=Why_Curves&amp;diff=7018&amp;oldid=prev</id>
		<title>V1z: Nova página: Why is a curve-based graphical representation important for 3D computer vision and structure from motion? This is an ongoing list of the reasons we can think of. Add your own!  == Main...</title>
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		<updated>2012-10-10T02:23:40Z</updated>

		<summary type="html">&lt;p&gt;Nova página: Why is a curve-based graphical representation important for 3D computer vision and structure from motion? This is an ongoing list of the reasons we can think of. Add your own!  == Main...&lt;/p&gt;
&lt;p&gt;&lt;b&gt;Página nova&lt;/b&gt;&lt;/p&gt;&lt;div&gt;Why is a curve-based graphical representation important for 3D computer vision and structure from motion? This is an ongoing list of the reasons we can think of. Add your own!&lt;br /&gt;
&lt;br /&gt;
== Main Reasons Why You Should Care About Curves ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Curves arising from edge&lt;br /&gt;
discontinuities are denser and more structured than interest points, while&lt;br /&gt;
efficiently representing the image or 3D scene. They&lt;br /&gt;
provide a useful middle ground between a costly and redundant pixel/voxel&lt;br /&gt;
array representation and a very sparse, unstructured point cloud representation. This&lt;br /&gt;
allows the fast computation of 3D reconstructions that, although not&lt;br /&gt;
meshed, are still recognizable, structured and cheap to manipulate and store.&lt;br /&gt;
This representational efficiency is reflected by a recent trend in computer&lt;br /&gt;
graphics to use line-based renderings in low-resource internet-based&lt;br /&gt;
applications.  The structural richness of curves can be illustrated by the fact&lt;br /&gt;
that it is impossible to register a new uncalibrated view to a given 3D point cloud (without&lt;br /&gt;
its originating images), but&lt;br /&gt;
given a 3D curve representation of the scene this task becomes plausible due to&lt;br /&gt;
the added structure (\eg, by reprojecting the 3D curves onto the new view&lt;br /&gt;
and aligning them to the curves detected in the image). &lt;br /&gt;
Furthermore, it is well-known&lt;br /&gt;
that edge-based representations can efficiently represent most of the image&lt;br /&gt;
content~\cite{Elder:Edges:IJCV99}, and this motivates an efficient 3D&lt;br /&gt;
curve-based reconstruction for storing the most relevant geometric information&lt;br /&gt;
of a 3D scene.  Curves also have greater invariance than interest points to&lt;br /&gt;
changes in illumination, and are stable over a greater range of&lt;br /&gt;
baselines as compared to interest points. Curves have good localization in the&lt;br /&gt;
orthogonal direction at each point, and their long extent and richer structure&lt;br /&gt;
allows for more accurate detection, matching, and localization under a wider variety of&lt;br /&gt;
viewpoint changes than point features.  Moreover, edge curve structure is&lt;br /&gt;
correlated with surface properties: the reflectance or ridge curves provide&lt;br /&gt;
boundary condition for surface reconstruction, while occluding contour&lt;br /&gt;
variations across views indicate surface curvature~\cite{Giblin:Motion:Book}.&lt;br /&gt;
&lt;br /&gt;
== Weaker Reasons ==&lt;br /&gt;
&lt;br /&gt;
== Link ==&lt;br /&gt;
&lt;br /&gt;
http://www.lems.brown.edu/~rfabbri&lt;br /&gt;
&lt;br /&gt;
== Author ==&lt;br /&gt;
Main author: Ricardo Fabbri, Ph.D. [http://www.lems.brown.edu/~rfabbri]&lt;br /&gt;
&lt;br /&gt;
[[Category:Lab Macambira]]&lt;br /&gt;
[[Category:IPRJ]]&lt;/div&gt;</summary>
		<author><name>V1z</name></author>
	</entry>
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