For each point P, the MLS smoothing algorithm fits a planar surface
or a higher order polynomial surface to its k-neighborhood
(the 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 :
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.
Specify the weighting parameter 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,
can be selected to be the typical distance between a point P
and its k/2-th neighbor . 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'"mls_relative_sigma""mls_relative_sigma""mls_relative_sigma""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'"mls_abs_sigma""mls_abs_sigma""mls_abs_sigma""mls_abs_sigma" is passed, any value set in
'mls_relative_sigma'"mls_relative_sigma""mls_relative_sigma""mls_relative_sigma""mls_relative_sigma" is ignored.
Specify a multiplication factor
that is used to compute for a point
P by the formula:
where is the k/2-th neighbor of
P. Note that, unlike , which
is a global parameter for all points,
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
('mls_abs_sigma'"mls_abs_sigma""mls_abs_sigma""mls_abs_sigma""mls_abs_sigma") to a point data
with highly varying point density. Note however that if
'mls_abs_sigma'"mls_abs_sigma""mls_abs_sigma""mls_abs_sigma""mls_abs_sigma" is set, 'mls_relative_sigma'"mls_relative_sigma""mls_relative_sigma""mls_relative_sigma""mls_relative_sigma" is
ignored.
If this parameter is set to 'true'"true""true""true""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 SmoothObjectModel3DSmoothObjectModel3DSmoothObjectModel3DSmoothObjectModel3DsmoothObjectModel3D is used
for surface-based matching, either as model in
create_surface_modelcreate_surface_modelCreateSurfaceModelCreateSurfaceModelCreateSurfaceModel or 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'"mls_force_inwards""mls_force_inwards""mls_force_inwards""mls_force_inwards" is set to 'false'"false""false""false""false", the
normal vectors are oriented arbitrarily.
Possible values:'true'"true""true""true""true", 'false'"false""false""false""false"(default)
List of values: 'mls_abs_sigma'"mls_abs_sigma""mls_abs_sigma""mls_abs_sigma""mls_abs_sigma", 'mls_force_inwards'"mls_force_inwards""mls_force_inwards""mls_force_inwards""mls_force_inwards", 'mls_kNN'"mls_kNN""mls_kNN""mls_kNN""mls_kNN", 'mls_order'"mls_order""mls_order""mls_order""mls_order", 'mls_relative_sigma'"mls_relative_sigma""mls_relative_sigma""mls_relative_sigma""mls_relative_sigma"