smooth_object_model_3d🔗
Short description🔗
smooth_object_model_3d — Smooth the 3D points of a 3D object model.
Signature🔗
smooth_object_model_3d( object_model_3d ObjectModel3D, string Method, attribute.name GenParamName, attribute.value GenParamValue, out object_model_3d SmoothObjectModel3D )
Description🔗
The operator smooth_object_model_3d smoothes the 3D points in
ObjectModel3D and returns the smoothed points in
SmoothObjectModel3D.
Currently, the operator offers three methods for smoothing that can be
selected in Method: 'mls', 'xyz_mapping' and
'xyz_mapping_compute_normals'. 'mls' applies a Moving
Least Squares (MLS) algorithm on the 3D points. As a side effect of the
smoothing, the method extends SmoothObjectModel3D by
corresponding normals. 'xyz_mapping' smoothes the coordinates
of the 3D points using a 2D filter and the 2D mapping contained in
ObjectModel3D. 'xyz_mapping_compute_normals' applies
the same smoothing as 'xyz_mapping', but additionally extends
SmoothObjectModel3D by normals.
Additional parameters can be set with GenParamName and
GenParamValue. The parameter names settable for
Method='mls' use the prefix 'mls'.
Analogically, parameter names settable for
Method='xyz_mapping' and
Method='xyz_mapping_compute_normals' use the prefix
'xyz_mapping'.
MLS smoothing🔗
By selecting Method='mls', for each point P, the
MLS smoothing algorithm fits a planar surface or a higher order polynomial
surface to its texttt{k}-neighborhood (the texttt{k}
nearest points).
The surface fitting is essentially a standard weighted least squares
parameter estimation of the plane or polynomial surface parameters,
respectively.
The closest neighbors of P have higher contribution than the other
points, which is controlled by the following weighting function
with a parameter \(\sigma\):
The point is then projected on the surface. This process is repeated for all points resulting in a smoothed point set. The fitted surfaces have well defined normals (i.e., they can easily be computed from the surface parameters). Therefore, the points are augmented by the corresponding normals as side effect of the smoothing.
Additional parameters can be adjusted for the MLS smoothing
specifically using the following parameter names and values for
GenParamName and GenParamValue:
-
'mls_kNN': Specify the number of nearest neighbors texttt{k} that are used to fit the MLS surface to each point.
Suggested values: 40, 60, 80, 100, 400.
Default: 60.
-
'mls_order': Specify the order of the MLS polynomial surface. For 'mls_order'=1 the surface is a plane.
Suggested values: 1, 2,3.
Default: 2.
-
'mls_abs_sigma': Specify the weighting parameter \(\sigma\) as a fixed absolute value in meter. The value to be selected depends on the scale of the point data. As a rule of thumb, \(\sigma\) can be selected to be the typical distance between a point P and its k/2-th neighbor \(P_{k/2}\). Note that setting an absolute weighting parameter for point data with varying density might result in different smoothing results for points that are situated in parts of the point data with different densities. This problem can be avoided by using 'mls_relative_sigma' instead that is scale independent, which makes it also a more convenient way to specify the neighborhood weighting. Note that if 'mls_abs_sigma' is passed, any value set in 'mls_relative_sigma' is ignored.
Suggested values: 0.0001, 0.001, 0.01, 0.1, 1.0.
-
'mls_relative_sigma': Specify a multiplication factor \(\sigma_{rel}\) that is used to compute \(\sigma_{P}\) for a point P by the formula:
\[\begin{eqnarray*} \sigma_{P} = \sigma_{rel}\Vert P_{k/2}-P\Vert, \end{eqnarray*}\]where \(P_{k/2}\) is the k/2-th neighbor of P. Note that, unlike \(\sigma\), which is a global parameter for all points, \(\sigma_{P}\) is computed for each point P and therefore adapts the weighting function to its neighborhood. This avoids problems that might appear while trying to set a global parameter \(\sigma\) ('mls_abs_sigma') to a point data with highly varying point density. Note however that if 'mls_abs_sigma' is set, 'mls_relative_sigma' is ignored.
Suggested values: 0.1, 0.5, 1.0, 1.5, 2.0.
Default: 1.0.
-
'mls_force_inwards': If this parameter is set to 'true', all surface normals are oriented such that they point ``in the direction of the origin’‘. Expressed mathematically, it is ensured that the scalar product between the normal vector and the vector from the respective surface point to the origin is positive. This may be necessary if the resulting
SmoothObjectModel3Dis used for surface-based matching, either as model increate_surface_modelor as 3D scene in find_surface_model, because here, the consistent orientation of the normals is important for the matching process. If 'mls_force_inwards' is set to 'false', the normal vectors are oriented arbitrarily.List of values: 'true', 'false'.
Default: 'true'.
2D mapping smoothing🔗
By selecting Method='xyz_mapping' or
Method='xyz_mapping_compute_normals', the coordinates
of the 3D points are smoothed using a 2D filter and the 2D mapping
contained in ObjectModel3D.
Additionally, for Method='xyz_mapping_compute_normals',
SmoothObjectModel3D is extended by normals computed from the
XYZ-mapping. If no 2D mapping is available, an exception is raised.
As the filter operates on the 2D depth image, using
Method='xyz_mapping' or
Method='xyz_mapping_compute_normals' is usually faster than
using Method='mls'.
Invalid points (e.g., duplicated points with coordinates [0,0,0]) should be
removed from the 3D object model before applying the operator, e.g., by using
select_points_object_model_3d with attribute 'point_coord_z'
or 'num_neighbors_fast X'.
Additional parameters can be adjusted for the 2D mapping smoothing
specifically using the following parameter names and values for
GenParamName and GenParamValue:
-
'xyz_mapping_filter': Specify the filter used for smoothing the 2D mapping. The sizes of the corresponding filter mask are set with 'xyz_mapping_mask_width' and 'xyz_mapping_mask_height'.
In the default filter mode 'median_separate', the filter method used on the 2D image is comparable to
median_separate. This mode is usually faster than 'median', but can also lead to less accurate results or artifacts at surface discontinuities.Using filter mode 'median', the used filter method is comparable to
median_image.List of values: 'median_separate', 'median'.
Default: 'median_separate'.
-
'xyz_mapping_mask_width','xyz_mapping_mask_height': Specify the width and height of the used filter mask.
For 'xyz_mapping_filter'='median_separate' or 'xyz_mapping_filter'='median', even values for 'xyz_mapping_mask_width' or 'xyz_mapping_mask_height' are increased to the next odd value automatically.
For 'xyz_mapping_filter'='median', the used filter mask must be quadratic ('xyz_mapping_mask_width' = 'xyz_mapping_mask_height'). Thus, when setting only 'xyz_mapping_mask_width' or 'xyz_mapping_mask_height', the other parameter is set to the same value automatically. If two different values are set, an error is raised.
Suggested values: 3, 5, 7, 9.
Default: 3.
Execution information🔗
Execution information
-
Multithreading type: reentrant (runs in parallel with non-exclusive operators).
-
Multithreading scope: global (may be called from any thread).
-
Automatically parallelized on internal data level.
This operator supports canceling timeouts and interrupts.
Parameters🔗
ObjectModel3D (input_control) object_model_3d(-array) → (handle)
Handle of the 3D object model containing 3D point data.
Method (input_control) string → (string)
Smoothing method.
Default: 'mls'
List of values: 'mls', 'xyz_mapping', 'xyz_mapping_compute_normals'
GenParamName (input_control) attribute.name-array → (string)
Names of generic smoothing parameters.
Default: []
List of values: 'mls_abs_sigma', 'mls_force_inwards', 'mls_kNN', 'mls_order', 'mls_relative_sigma', 'xyz_mapping_filter', 'xyz_mapping_mask_height', 'xyz_mapping_mask_width'
GenParamValue (input_control) attribute.value-array → (real / integer / string)
Values of generic smoothing parameters.
Default: []
Suggested values: 10, 20, 40, 60, 0.1, 0.5, 1.0, 2.0, 0, 1, 2, 3, 5, 7, 9
SmoothObjectModel3D (output_control) object_model_3d(-array) → (handle)
Handle of the 3D object model with the smoothed 3D point data.
Combinations with other operators🔗
Combinations
Alternatives
surface_normals_object_model_3d, sample_object_model_3d, simplify_object_model_3d
Module🔗
3D Metrology