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# Datapoint Filters

In this section, the various filters which can be applied to the reading and reference point clouds before performing the ICP process.

As a reminder, *datapoint filters* can have several purposes:

- Removing noisy points which render the alignment of point clouds difficult.
- Removing redundant points so as to speed up alignment
- Adding descriptive information to the points such as a surface normal vector, or the direction from the point to the sensor.

Note that *datapoint filters* differ from *outlier filters* which appear further down the ICP chain and have a different purpose.

Libpointmatcher provides developers with a number of datapoint filters which process an input point cloud into an intermediate point cloud used in the alignment procedure. Filters function as independent modules that can and often are combined into chains. Sequential chains of datapoint filters can thus be adapted to the alignment problem at hand.

## Filter Index

### Down-sampling

### Descriptor Augmenting

## An Example Point Cloud View of an Appartment

The following examples are drawn from the apartment dataset available for download from the ASL at ETH Zurich. A top-down view of the point cloud is depicted below, with the colors showing vertical elevation. The ceiling has been removed from the point cloud such that the floor (in blue) and the walls (in red) are clearly visible. Note that the coordinate origin is placed in the kitchen at the starting point of data capture, which is in the top-left of the top-down view and floor plan.

## Bounding Box Filter

### Description

Points can be excluded from a rectangular bounding region by using this filter. The box dimensions are specified by defining the maximum and minimum coordinate values in the x,y,z directions.

**Required descriptors:** none

**Output descriptor:** none

**Sensor assumed to be at the origin:** no

**Impact on the number of points:** reduces number of points

Parameter | Description | Default value | Allowable range |
---|---|---|---|

xMin | Minimum value on the x-axis defining one side of the box | -1.0 | -inf to inf |

xMax | Maximum value on the x-axis defining one side of the box | 1.0 | -inf to inf |

yMin | Minimum value on the y-axis defining one side of the box | -1.0 | -inf to inf |

yMax | Maximum value on the y-axis defining one side of the box | 1.0 | -inf to inf |

zMin | Minimum value on the z-axis defining one side of the box | -1.0 | -inf to inf |

zMax | Maximum value on the z-axis defining one side of the box | 1.0 | -inf to inf |

removeInside | if set to 1, points contained within the box are removed, else points outside are removed | 1 | 0 or 1 |

### Example

In the following example, a box filter of the following dimensions was applied to the input point cloud.

Note that only points **outside** the bounding box are removed by the filter by setting the property *removeInside* to 0. Because the point cloud center is located in the kitchen in the top-left, a square region of 2m x 2m is selected by this filter. In the following image, the output of the filter is overlaid in white.

Figure: Top down view of the appartment point cloud with a box filter applied. The input is shown in color and the output of the filter is overlaid in white |
Parameters used |
---|---|

xMin : -1.0 xMax : 1.0 yMin : -1.0 yMax : 1.0 zMin : -1.0 zMax : 2.0 removeInside : 0 |

Figure: Top down view of the appartment point cloud with a box filter applied. The input is shown in color and the output of the filter is overlaid in white |
Parameters used |
---|---|

xMin : -1.0 xMax : 1.0 yMin : -1.0 yMax : 1.0 zMin : -1.0 zMax : 2.0 removeInside : 1 |

## Maximum Density Filter

### Description

A number of filters are used to reduce the number of points in a cloud by randomly sub-sampling or randomly rejecting a set of points. Points in regions of high density often contain redundant information, and the ICP algorithm could be performed more efficiently with a smaller number of points. This filter is thus used to homogenize the density of a point cloud by rejecting a sub-sample of points in high-density regions.

Points are only considered for rejection if they exceed a density threshold, otherwise they are preserved. The single parameter of this filter sets the maximum density that should be obtained in the output point cloud. Points are randomly rejected such that this maximum density is obtained as closely as possible.

**Required descriptors:** `densities`

(see SurfaceNormalDataPointsFilter and SamplingSurfaceNormalDataPointsFilter)

**Output descriptor:** none

**Sensor assumed to be at the origin:** no

**Impact on the number of points:** reduces number of points

Parameter | Description | Default value | Allowable range |
---|---|---|---|

maxDensity | The desired maximum density of points in points/m^3 (for 3D), points/m^2 (for 2D) |
10 | min: 0.0000001, max: inf |

### Example

In the following example we observe the effect of the maximum density filter on the apartment point cloud. Sub-sampling occurs mostly in high density regions, which colored in red in the image below. The result is an image with lower density overall with the low density regions in blue being preserved.

Figure: Max density filter applied to subsection of the apartment dataset. On the original data, low density regions are blue and high density regions are red. The sampled points are overlaid in white. |
Parameters used |
---|---|

maxDensity: 50000 |

## Maximum Distance Filter

### Description

These filters remove points which lie beyond a threshold distance from the coordinate center. Points are kept if their distance from the center **greater than** the threshold. The distance threshold can be defined on the x,y, and z axes or can be a radial distance from the center.

**Required descriptors:** none

**Output descriptor:** none

**Sensor assumed to be at the origin:** no

**Impact on the number of points:** reduces number of points

Parameter | Description | Default value | Allowable range |
---|---|---|---|

dim | Dimension over which the distance is thresholded. If -1, then the threshold is a radial distance from the center | -1 | 0: x, 1: y, 2: z, -1: radial |

maxDist | Distance threshold (in m) beyond which points are rejected | 1.0 | min: -inf, max: inf |

### Example

In the following example, a maximum distance threshold of 1m is applied radially by setting the dimension parameter to -1. As shown on the image below, points which lie within a sphere of radius 1m centered at the origin are selected by the filter and are displayed in white. All other points are rejected by the filter. Were a maximum distance filter to be replaced by an equivalent minimum distance filter, only points outside the sphere would be selected.

Figure: Max density filter applied to subsection of the apartment dataset. On the original data, low density regions are blue and high density regions are red. The sampled points are overlaid in white. |
Parameters used |
---|---|

maxDist : 1.0 dim : -1 |

## Minimum Distance Filter

### Description

These filters remove points which lie beyond a threshold distance from the coordinate center. Points are kept if their distance from the center **smaller than** the threshold. The distance threshold can be defined on the x,y, and z axes or can be a radial distance from the center.

**Required descriptors:** none

**Output descriptor:** none

**Sensor assumed to be at the origin:** no

**Impact on the number of points:** reduces number of points

Parameter | Description | Default value | Allowable range |
---|---|---|---|

dim | Dimension over which the distance is thresholded. If -1, then the threshold is a radial distance from the center | -1 | 0: x, 1: y, 2: z, -1: radial |

minDist | Distance threshold (in m) beyond which points are selected | 1.0 | min: -inf, max: inf |

## Maximum Point Count Filter

### Description

Conditional subsampling. This filter reduces the size of the point cloud by randomly dropping points if their number is above `maxCount`

. The resulting point cloud while have `maxCount`

number of point. the Based on: Registration and integration of multiple range images for 3-D model construction. Masuda, T. and Sakaue, K. and Yokoya, N. In Pattern Recognition, 1996., Proceedings of the 13th International Conference on. 879--883. 1996.

**Required descriptors:** none

**Output descriptor:** none

**Sensor assumed to be at the origin:** no

**Impact on the number of points:** reduces number of points

Parameter | Description | Default value | Allowable range |
---|---|---|---|

seed | srand seed | 0 | min: 0 max: 2147483647 |

maxCount | number of points beyond which subsampling occurs | 1000 | min: 0, max: 2147483647 |

### Example

No example available.

## Maximum Quantile on Axis Filter

### Description

Points are filtered according to where they lie on a distribution of their positions along a given axis. The entire distance range is divided into quantiles which lie between 0 and 1. One can specify the distance quantile above which points are rejected by the filter.

**Required descriptors:** none

**Output descriptor:** none

**Sensor assumed to be at the origin:** no

**Impact on the number of points:** reduces number of points

Parameter | Description | Default value | Allowable range |
---|---|---|---|

dim | Dimension over which the distance (from the center) is thresholded | 0 | x:0 y:1 z:2 |

ratio | Quantile threshold. Points whose distance exceed this threshold are rejected by the filter | 0.5 | min: 0.0000001, max: 0.9999999 |

### Example

In the following example, maximum quantile filtering is performed over the x-axis with a quantile threshold of 0.5. Therefore, points which have an x-value which exceeds the 50% quantile are rejected. The output of the filter is displayed in white and overlaid with the input point cloud in the image below. A sampling region centered at the origin and extending in both directions of the x-axis is clearly visible.

Figure: Maximum quantile on axis filter in the x-direction with a maximum quantile of 0.5. |
Parameters used |
---|---|

dim : 0 ratio : 0.5 |

## Random Sampling Filter

### Description

This filter behaves similarly to the Maximum Point Count Filter but does not enforce a maximum point constraint. Instead points are kept by the filter with a fixed probability.

**Required descriptors:** none

**Output descriptor:** none

**Sensor assumed to be at the origin:** no

**Impact on the number of points:** reduces number of points

Parameter | Description | Default value | Allowable range |
---|---|---|---|

prob | Probability that a point is kept (1/decimation factor) | 0.75 | min: 0, max: 1 |

### Example

In the following sample, points are kept with a probability of 0.1. Therefore the total number of points in the output point cloud is approximately 10 times less than the number of points in the input point cloud and the density is decreased overall.

Figure: After applying the random sampling filter with a probability of 0.1. The original data is shown in black and the sampled points in white. |
Parameters used |
---|---|

prob : 0.1 |

## Remove NaN Filter

### Description

Due to errors in the capture process point clouds may contain points with invalid coordinates. This filter can be applied to remove points which contain a NaN coordinate, thus producing a "clean" dataset.

**Required descriptors:** none

**Output descriptor:** none

**Sensor assumed to be at the origin:** no

**Impact on the number of points:** reduces number of points

## Shadow Point Filter

### Description

Shadow points are noisy points usually located at point cloud edge discontinuities.

**Required descriptors:** `normals`

(see SurfaceNormalDataPointsFilter)
**Output descriptor:** none

**Sensor assumed to be at the origin:** no

**Impact on the number of points:** reduces number of points

*IMPORTANT:* The surface normal descriptors are required in the input point cloud.

## Voxel Grid Filter

### Description

While, the previous filters were sub-sampling filters in that they returned a sub-set of points from the original point cloud, the voxel grid filter instead returns a point cloud with a smaller number of points which should best represent the input point cloud as a whole.

The voxel grid filter down-samples the data by taking a spatial average of the points in the cloud. In the 2D case, one can simply imagine dividing the plane into a regular grid of rectangles. While the term is more suited to 3D spaces, these rectangular areas are known as *voxels*. The sub-sampling rate is adjusted by setting the voxel size along each dimension. The set of points which lie within the bounds of a voxel are assigned to that voxel and will be combined into one output point.

There are two options as to how to represent the distribution of points in a voxel by a single point. In the first, we take the centroid or spatial average of the point distribution. In the second, we simply take the geometrical center of the voxel. Clearly, the first option is more accurate since it takes into account the point distribution inside the voxels. However it is more computationally intensive since the centroid must be computed for each voxel. The computational cost increases linearly with the number of points in the cloud and the number of voxels.

This filter also provides two methods for sub-sampling descriptors. In the first, all descriptors within a voxel are averaged while in the second, only the first descriptor from a voxel is kept.

**Required descriptors:** none

**Output descriptor:** outputs average or single descriptor per voxel if the input cloud contains descriptors

**Sensor assumed to be at the origin:** no

**Impact on the number of points:** reduces number of points

Parameter | Description | Default value | Allowable range |
---|---|---|---|

vSizeX | Size of the voxel along the x-axis | 1.0 | -inf to inf |

vSizeY | Size of the voxel along the y-axis | 1.0 | -inf to inf |

vSizeZ | Size of the voxel along the z-axis | 1.0 | -inf to inf |

useCentroid | If 1, down-sample by using the centroid of each voxel. If 0, use the voxel center | 1 | 1 or 0 |

averageExistingDescriptors | If 1, descriptors are down-sampled by taking their average in the voxel. If 0, we use the descriptors from the first point found in the voxel | 1 | 1 or 0 |

For more information on the implementation of this filter, refer to this tutorial.

### Example

In this example, we apply the voxel grid filter using centroid down-sampling to the appartment point cloud. The output points are shown in yellow. You can observe a regular grid distribution of points corresponding to each voxel. A finer degree of sub-sampling can be obtained by using smaller voxels. This comes naturally with an increased computational cost and a larger output point cloud.

Figure: Applying the voxel grid filter filter to the appartment point cloud. | Parameters used |
---|---|

vSizeX : 0.2 vSizeY : 0.2 vSizeZ : 0,2 useCentroid : 1 |

## Observation Direction Filter

### Description

As opposed to the previous filters, the following does not yield a sub-sample of points but rather augments the input point cloud with additional information. In particular, this filter adds a descriptor vector to each point representing its direction to the sensor used for capturing the point cloud. Remark that adding a direction vector is useful for locally captured point clouds in which the position of the sensor is fixed. In contrast global point clouds which are formed from several local point clouds do not have a fixed sensor position.

The returned direction vector is a vector connecting the point and the sensor, whose positions can be specified in the filter parameters.

**Required descriptors:** none

**Output descriptor:** `observationDirections`

**Sensor assumed to be at the origin:** yes

**Impact on the number of points:** none

Parameter | Description | Default value | Allowable range |
---|---|---|---|

x | x-coordinate of the sensor position | 0.0 | min: -inf, max: inf |

y | y-coordinate of the sensor position | 0.0 | min: -inf, max: inf |

z | z-coordinate of the sensor position | 0.0 | min: -inf, max: inf |

### Example

**Remark:** The following example uses a local point cloud 10 from the apartment dataset. The filter is used to extract direction informations and a small subset of these directions is shown in the following image. The arrows point towards the position of the sensor. The input point cloud is color coded according to the z-elevation of the points (red represents the ceiling and blue the floor).

Figure: Applying the observation direction filter to a local point cloud. A small subset of point observation directions are displayed |
Parameters used |
---|---|

x : 0 y : 0 z : 0 |

## Surface Normal Filter

### Description

The surface normal to each point is estimated by finding a number of neighboring points and taking the eigen-vector corresponding to the smallest eigen-value of all neighboring points. For more theoretical background on the estimation of normal vectors for a point cloud the reader is invited to visit the following.

Remark that that given a surface, the normal vector can point in two possible directions. Following the apartment example used herein throughout, the normal vector of a wall can point inside towards the room, or outside the apartment. To align all normal vectors in the same direction, the orient normals filter can be used.

**Required descriptors:** none

**Output descriptor:**

`normals`

`densities`

`eigValues`

`eigVectors`

**Sensor assumed to be at the origin:** no

**Impact on the number of points:** none

Parameter | Description | Default value | Allowable range |
---|---|---|---|

knn | Number of neighboring points (including the point itself) to consider when extracting surface normal | 5 | min: 3, max: 2147483647 |

epsilon | Approximation used in nearest neighbor search | 0.0 | min: 0.0, max: inf |

keepNormals | Add the normal vector to descriptors | 1 | 1: true, 0: false |

keepDensities | Add point cloud density to descriptors | 0 | 1: true, 0: false |

keepEigenValues | Add eigen values to descriptors | 0 | 1: true, 0: false |

keepEigenVectors | Add eigen vectors to descriptors | 0 | 1: true, 0: false |

keepMatchedIds | Add identifiers of matched points to descriptors (see) | 0 | 1: true, 0:false |

### Example

In this example, we again use a local point cloud of the apartment. You may recognize the input point cloud as a small portion of the local cloud used in the observation direction filter. The surface normals are extracted using 20 neighboring points and epsilon=0. In this example, for clarity, we only view a wall section of one of the apartment dataset. A random set of normal vectors is shown in the figure with arrows. When looking at the arrow directions on the wall, one may see normal vectors either pointing downwards into the apartment or outside the apartment.

Figure: Applying the observation direction filter to a local point cloud. A small subset of point observation directions are displayed |
Parameters used |
---|---|

knn : 20 epsilon : 0 keepNormals : 1 keepDensities : 1 |

## Orient Normals Filter

### Description

As explained previously, neighboring surface normal vectors obtained from the surface normals filter, do not have the same orientation. This filter enforces this constraint and reorients vectors from the same surface in a consistent direction. Vectors are reoriented to either point towards the center (inwards), or away from the center (outwards).

**Required descriptors:**

`observationDirections`

(see ObservationDirectionDataPointsFilter)

`normals`

(see SurfaceNormalDataPointsFilter, SamplingSurfaceNormalDataPointsFilter)

**Output descriptor:** none

**Sensor assumed to be at the origin:** yes

**Impact on the number of points:** none

Parameter | Description | Default value | Allowable range |
---|---|---|---|

towardCenter | Orient vectors to point towards the center | 1 | 1: true, 0: false |

*IMPORTANT:* Both the normal vector descriptor and observation direction descriptors must be present in the input point cloud. Consequently, both the surface normal and observation filters should be applied prior to using this filter.

### Example

The same input section is used as for extracting the surface normals in the previous section. The vectors are reoriented to point towards the center which lies in the bottom left corner of the image below. We now observe that adjacent surface normal vectors point in a consistent direction.

Figure: Normal vectors reoriented to point towards the center | Parameters used |
---|---|

towardCenter: 1 |

## Sampling Surface Normal Filter

### Description

The above filters extract surface normals at every point in the point cloud. In point clouds representing planar surfaces however, a significant redundant information is contained in adjacent normal vectors. This filter attempts to both reduce the number of points within a point cloud and the number of different normal vectors. The first is achieved by performing either random sub-sampling as seen previously, or by using one point per box (bin sub-sampling). The latter is achieved by recursively decomposing the point-cloud space into boxes until each box contains at most knn points. A single normal vector is computed from the knn points in each box.

**Required descriptors:** none

**Output descriptor:**
`normals`

`densities`

`eigValues`

`eigVectors`

**Sensor assumed to be at the origin:** yes

**Impact on the number of points:** reduces number of points

Parameter | Description | Default value | Allowable range |
---|---|---|---|

ratio | Ratio of points (sampled randomly) that are preserved within a box | 0.5 | min: 0.0000001, max: 0.9999999 |

knn | Number of points contained within a box and number of neighboring points (including the point itself) to consider when extracting surface normal | 7 | min: 3, max: 2147483647 |

samplingMethod | 0: random sub-sampling 1:bin sub-sampling with resulting number of points 1/knn |
0 | 0 or 1 |

maxBoxDim | Maximum allowed length of a box above with boxes are discarded | inf | min: 0.0000001, max: inf |

averageExistingDescriptors | Average existing descriptors within a box or keep existing values | 1 | 0: keep existing 1: average existing |

keepNormals | Add the normal vector to descriptors | 1 | 1: true, 0: false |

keepDensities | Add point cloud density to descriptors | 0 | 1: true, 0: false |

keepEigenValues | Add eigen values to descriptors | 0 | 1: true, 0: false |

keepEigenVectors | Add eigen vectors to descriptors | 0 | 1: true, 0: false |

keepMatchedIds | Add identifiers of matched points to descriptors (see) | 0 | 1: true, 0: false |

### Example

We reuse the same apartment section to illustrate the sampling of normal vectors. The decimation rate used is 0.5 such that half of the points from the original point cloud are discarded randomly. We use a knn value of 100 such that each box contains at most 100 points. In the following two figures, we extract sample points based on the normals and display the normal vectors at these sample points. We first do so for a ceiling section, followed by a ground section. Because the ceiling is essentially a large plane, the sampling is low and the normal vector arrows are dispersed relatively equally as shown in the first figure. On the other hand, the ground section has a higher density of points. This results in a denser sampling of points which is seen in the second figure.

The box centers are shown in red on the following picture. It is clear that as opposed to previous filters, adjacent points within a box have the same normal vector.

Figure: Sampled normal vectors of ceiling section | Parameters used |
---|---|

knn : 100 ratio : 0.5 samplingMethod : 1 |

Figure: Sampled normal vectors ground section | Parameters used |
---|---|

knn : 100 ratio : 0.5 samplingMethod : 1 |

## Simple Sensor Noise Filter

### Description

This filter is used to augment points with an estimation of position uncertainty based on sensor specifications. So far the SICK LMS, Hokuyo URG-04LX and UTM-30LX, as well as the Microsoft Kinect and Asus Xtion sensors are supported. The uncertainty or noise radius is represented in meters, and can be adjusted by varying a gain parameter which amplifies predefined uncertainty levels.

**Required descriptors:** none

**Output descriptor:** `simpleSensorNoise`

**Sensor assumed to be at the origin:** yes

**Impact on the number of points:** none

Parameter | Description | Default value | Allowable range |
---|---|---|---|

sensorType | The type of sensor that was used in the capture. 0: Sick LMS-1xx 1: Hokuyo URG-04LX 2 : Hokuyo UTM-30LX 3 : Kinect/Xtion |
0 | 0, 1, 2, or 3 |

gain | Used to augment uncertainty | 1 | min: 1, max: inf |

### Example

For this example we use another point cloud dataset from the ASL collection called ETH Hauptgebaude. This dataset represents the main gallery of the main building at ETHZ and presents long straight corridors. We therefore use to display the uncertainty estimation of point clouds.

In the following image we show a side view of local point cloud 3 in the dataset. The laser is located at the bottom left corner and one can see the long arched corridor structures. As we move right in the image point are located further away from the sensor, are therefore less numerous and more uncertain. The points are colored by the estimation uncertainty obtained with this filter. More certain points are black, medium certain points are red and less curtain points are white. Naturally the colour shifts from black to white as we move further away from the laser down the corridor.

Figure: Side view of a view 3 from the HG dataset augmented with sensor noise estimations |
Parameters used |
---|---|

sensorType : 1 |

## Fixed Step Sampling Filter (To be completed)

The number of points in a point cloud can be reduced by taking random point subsamples. The filter is parametrized so that a fixed number of points - selected uniformly at random - are 'rejected' in the filtering process.

## Where To Go From Here

This concludes the overview of data point filters. For a tutorial on writing a simple application for applying data point filters to an input point cloud, go here. To learn more about the general configuration of the ICP chain go here.