System and method for extracting dominant orientations from a scene
In one embodiment, a method of identifying the dominant orientations of a scene comprises representing a scene as a plurality of directional vectors. The scene may comprise a three-dimensional representation of a scene, and the plurality of directional vectors may comprise a plurality of surface normals. The method further comprises determining, based on the plurality of directional vectors, a plurality of orientations describing the scene. The determined plurality of orientations explains the directionality of the plurality of directional vectors. In certain embodiments, the plurality of orientations may have independent axes of rotation. The plurality of orientations may be determined by representing the plurality of directional vectors as lying on a mathematical representation of a sphere, and inferring the parameters of a statistical model to adapt the plurality of orientations to explain the positioning of the plurality of directional vectors lying on the mathematical representation of the sphere.
1. A method of identifying dominant orientations from a scene, comprising:
representing, by an orientation agent executing on a processor, a scene as a plurality of directional vectors, wherein the plurality of directional vectors comprise a plurality of surface normals;
determining, based on the plurality of surface normals, a plurality of orientations describing the scene;
wherein the determined plurality of orientations explains the directionality of the plurality of surface normals;
representing the plurality of surface normals as points lying on a mathematical representation of a sphere; and
adapting the plurality of orientations to explain the positioning of the surface normals lying on the mathematical representation of the sphere,
wherein adapting the plurality of orientations comprises initializing a statistical model describing the positioning of the surface normals lying on the mathematical representation of the sphere, and describing the plurality of orientations; and
wherein determining the plurality of orientations comprises inferring the parameters of the statistical model, wherein inferring the parameters of the statistical model comprises:
determining the rotation of each orientation within the mathematical representation of the sphere; and
assigning the plurality of surface normals to an axis of an orientation.
2. The method of claim 1 , wherein the plurality of orientations have independent axes of rotation relative to one another.
3. The method of claim 1 , wherein the scene comprises a three-dimensional representation of a scene.
4. The method of claim 1 , wherein the plurality of orientations comprise a set of orthogonally coupled axes which explain the directionality of the plurality of directional vectors.
5. The method of claim 1 , further comprising:
receiving a representation of a scene; and
extracting the plurality of surface normals from the representation of the scene.
6. The method of claim 1 , wherein the sphere is a unit sphere.
7. The method of claim 1 , wherein determining a plurality of orientations comprises determining a plurality of orientations that explains the positioning of the plurality of surface normals lying on the mathematical representation of the sphere.
8. The method of claim 1 , wherein the statistical model is a Bayesian model.
9. The method of claim 1 , wherein the statistical model is a deterministic model.
10. The method of claim 1 , wherein inferring the parameters of the statistical model further comprises mapping each normal of the plurality of normals to a plane tangent to an associated axis of an associated orientation to the normal.
11. The method of claim 10 , further comprising determining whether the normal belongs to the associated axis of the associated orientation based on its position on the tangent plane.
12. The method of claim 10 , wherein each surface normal is modeled on the tangent space as a Gaussian distribution.
13. The method of claim 12 , further comprising optimizing the rotation of an orientation based on the position of a plurality of associated normals on the tangent plane.
14. The method of claim 5 , wherein the scene is selected from the group consisting of a depth image, stereo vision, a virtual scene, and LiDAR measurements.
15. A system for identifying a dominant set of orientations for a scene, comprising:
a representation of a three-dimensional scene;
a mathematical representation of a sphere;
a statistical model comprising parameters for a plurality of surface normals and a plurality of orientations; and
an orientation agent executing on a processor and configured to:
receive the representation of the scene;
extract a plurality of surface normals from the representation of the scene;
represent the plurality of surface normals as points lying on the mathematical representation of a sphere; and
determine a plurality of orientations that explain the positioning of surface normals on the mathematical representation of a sphere by inferring the parameters of the statistical model, wherein inferring the parameters of the statistical model comprises:
determining the rotation of each orientation within the mathematical representation of the sphere; and
assigning the plurality of surface normals to an axis of an orientation.
16. The system of claim 15 , wherein inferring the parameters of the statistical model further comprises mapping each normal of the plurality of normals to a plane tangent to an associated axis of an associated orientation to the normal.
17. The system of claim 16 , wherein the orientation agent is further configured to determine whether the normal belongs to the associated axis of the associated orientation based on its position on the tangent plane.
18. The system of claim 16 , wherein each surface normal is modeled on the tangent space as a Gaussian distribution.
19. The system of claim 16 , wherein the orientation agent is further configured to optimize the rotation of an orientation based on the position of a plurality of associated normals on the tangent plane.