Why Curves

De Pontão Nós Digitais

Why is a curve-based graphical representation important for 3D computer vision and structure from motion? This is an ongoing (rather informal) list of the reasons we can think of. Add your own!

Main Reasons Why You Should Care About Curves

Curves arising from edge discontinuities are denser and more structured than interest points, while efficiently representing the image or 3D scene. They provide a useful middle ground between a costly and redundant pixel/voxel array representation and a very sparse, unstructured point cloud representation. This allows the fast computation of 3D reconstructions that, although not meshed, are still recognizable, structured and cheap to manipulate and store. This representational efficiency is reflected by a recent trend in computer graphics to use line-based renderings in low-resource internet-based applications. The structural richness of curves can be illustrated by the fact that it is impossible to register a new uncalibrated view to a given 3D point cloud (without its originating images), but given a 3D curve representation of the scene this task becomes plausible due to the added structure (\eg, by reprojecting the 3D curves onto the new view and aligning them to the curves detected in the image). Furthermore, it is well-known that edge-based representations can efficiently represent most of the image content~\cite{Elder:Edges:IJCV99}, and this motivates an efficient 3D curve-based reconstruction for storing the most relevant geometric information of a 3D scene. Curves also have greater invariance than interest points to changes in illumination, and are stable over a greater range of baselines as compared to interest points. Curves have good localization in the orthogonal direction at each point, and their long extent and richer structure allows for more accurate detection, matching, and localization under a wider variety of viewpoint changes than point features. Moreover, edge curve structure is correlated with surface properties: the reflectance or ridge curves provide boundary condition for surface reconstruction, while occluding contour variations across views indicate surface curvature~\cite{Giblin:Motion:Book}.

Other Reasons

  • 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 "initial" form of geometry/shape information. In a curve, all points co-occur, which can potentially be very powerful.




Main author: Ricardo Fabbri, Ph.D. [1]