Resolution adaptive mesh for performing 3-D metrology of an object

1. A method for generating a resolution adaptive mesh for 3-D metrology of an object, comprising:

receiving, by a processor, point cloud data from a plurality of sensors, the point cloud data from each sensor defining a point cloud that represents the object, wherein each point cloud comprises a multiplicity of points and each point comprises at least location information for the point on the object;

determining, by the processor, a resolution of each sensor in each of three orthogonal dimensions based on a position of each sensor relative to the object and physical properties of each sensor; and

generating, by the processor, a surface representation of the object from the point clouds using the resolutions of each sensor, the surface representation of the object comprising a resolution adaptive mesh corresponding to the object for 3-D metrology of the object.

2. The method of claim 1 , wherein generating the surface representation comprises fitting a triangular mesh to the point clouds, wherein a contribution of each point in the point clouds in generating the surface representation is based on an accuracy or resolution of each point.

3. The method of claim 1 , wherein generating the surface representation comprises fitting a triangular mesh to the point clouds by weighting a distance of each point from the triangular mesh by an inverse of an expected error standard deviation in a direction from each point to the triangular mesh.

4. The method of claim 3 , further comprising estimating the expected standard deviation in a direction from each point to the triangular mesh using a plurality of models of resolution for each sensor for different viewing directions and distances, the models of resolution are determined analytically from sensor physical models or empirically from measurement of resolution targets at several different positions that are interpolated to cover an entire measurement volume.

5. The method of claim 1 , wherein receiving the point cloud data comprises receiving the point cloud from each sensor and an uncertainty ellipsoid for each point, wherein the uncertainty ellipsoids are used to determine the resolutions of each sensor based on the position of the sensor relative to the object.

6. The method of claim 5 , further comprising initializing a triangular mesh using a surface interpolation method to provide an initialized triangular mesh that represents a surface of the object.

7. The method of claim 5 , further comprising assigning each point to a closest mesh triangle of a triangular mesh, the triangular mesh comprising a multiplicity of mesh triangles that collectively represent a surface of the object.

8. The method of claim 7 , further comprising:

measuring a distance from each point to a closest point on an assigned mesh triangle; and

determining a radius of the uncertainty ellipsoid associated with the point in a direction toward the closest point on the assigned mesh triangle for each point.

9. The method of claim 8 , further comprising forming an objective function for fitting the triangular mesh to the point clouds that automatically selects and uses best point cloud data from the point clouds, the objective function comprising a weighted fitting error term and a surface area of a triangular mesh term.

10. The method of claim 9 , further comprising fitting the triangular mesh to the point clouds by finding positions of vertices of each mesh triangle that minimize the objective function.

11. The method of claim 10 , further comprising:

performing rotation and translation operations to register the point clouds to form a composite point cloud;

adding rotation and translation parameters to the objective function and

simultaneously registering the point clouds in the composite point cloud and fitting the triangular mesh to the composite point cloud by finding positions of vertices of each mesh triangle that minimize the objective function.

12. The method of claim 10 , further comprising using particle swarm optimization to minimize the objective function.

13. The method of claim 10 , wherein the vertices of each mesh triangle are unconstrained.

14. The method of claim 10 , wherein the vertices of each mesh triangle are constrained with only one direction being variable and another two directions being fixed on a grid.

15. The method of claim 7 , further comprising fitting the triangular mesh to the point clouds by using multi-resolution mesh fitting, wherein an output triangular mesh of a current level of resolution is subdivided and used as an initial triangular mesh for optimization of a next level of resolution.

16. The method of claim 15 , further comprising upsampling the point cloud for each level of resolution for use with a subdivided triangular mesh.

17. A system for generating a resolution adaptive mesh for 3-D metrology of an object, comprising:

a plurality of sensors for collecting electronic images of an object, the electronic images comprising 3-D point cloud data of the object;

a processor; and

a resolution adaptive mesh module operating on the processor, the resolution adaptive mesh module being configured to perform a set of functions comprising:

receiving the point cloud data from the plurality of sensors, the point cloud data from each sensor defining a point cloud that represents the object, wherein each point cloud comprises a multiplicity of points and each point comprises at least location information for the point on the object;

determining a resolution of each sensor in each of three orthogonal dimensions based on a position of each sensor relative to the object and physical properties of each sensor; and

generating a surface representation of the object from the point clouds using the resolutions of each sensor, the surface representation of the object comprising a resolution adaptive mesh corresponding to the object for 3-D metrology of the object.

18. The system of claim 17 , wherein the set of functions further comprises generating the surface representation comprises fitting a triangular mesh to the point clouds, wherein a contribution of each point in the point clouds in generating the surface representation is based on an accuracy or resolution of each point.

19. A computer program product for generating a resolution adaptive mesh for 3-D metrology of an object, the computer program product comprising a computer readable storage medium having program instructions embodied therewith, wherein the computer readable storage medium is not a transitory medium per se, the program instructions being executable by a device to cause the device to perform a method comprising:

receiving point cloud data from a plurality of sensors, the point cloud data from each sensor defining a point cloud that represents the object, wherein each point cloud comprises a multiplicity of points and each point comprises at least location information for the point on the object;

determining a resolution of each sensor in each of three orthogonal dimensions based on a position of each sensor relative to the object and physical properties of each sensor; and

generating a surface representation of the object from the point clouds using the resolutions of each sensor, the surface representation of the object comprising a resolution adaptive mesh corresponding to the object for 3-D metrology of the object.

20. The computer program product of claim 19 , wherein the method further comprises generating the surface representation comprises fitting a triangular mesh to the point clouds, wherein a contribution of each point in the point clouds in generating the surface representation is based on an accuracy or resolution of each point.