Multidirectional Shift Rasterization (MDSR) Algorithm for Effective Identification of Ground in Dense Point Clouds
Abstract
:1. Introduction
Current Ground Filtering Approaches
2. Materials and Methods
2.1. Algorithm Description
 Moving the raster as a whole (i.e., shifting the cells in which the lowest point is identified) in steps much smaller than the cell size in both horizontal axes (X, Y);
 Tilting (or, rather, rotation) of the raster around all 3 axes (X, Y, Z) changes the perspective for the evaluation of the elevations of individual points in the given projection. After such tilting, the raster is again gradually shifted as in the previous step, and points with the lowest elevation in each cell after each displacement are selected.
2.2. Illustration of the Algorithm Principle
2.3. Data for Testing
2.4. Data Processing and Evaluation
2.5. Filters Selected for Comparison
2.6. Visual Evaluation
2.7. Evaluation of the Differences from the MDSRBased Surface
3. Results
3.1. Visual Evaluation
3.2. Comparison of Point Clouds with an MDSRBased Surface
4. Discussion
 No approximations, simplifications, and assumptions of the terrain are made;
 The filtering step also dilutes the point cloud;
 Compared with the common geometric filters, this one can be used for much more complex terrains and, therefore, is much more versatile;
 The computational demands approximately quadratically increase with increasing required detail (due to the number of raster shifts and raster size);
 Similar to all filtering methods, this one also needs verification by an operator; here, typically, a thin layer of filtering artifacts on the edges of the area needs to be removed either manually or simply by cropping by (typically) several decimeters to a few meters;
 Where a dense point cloud is needed, the MDSR method could be also used as the first step of an advanced multistep algorithm for the acquisition of the first terrain approximation, after which the remaining points can be identified based on a threshold as in standard filters.
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A. MDSR Algorithm Code
Points = [ (1) x1 y1 z1 R G B ... (2) x2 y2 z2 R G B ... . . (p) xp yp zp R G B ...]
 0.
 Calculation parameters
Raster cell size:  
RasterSize = R  
Number of shifts:  
NumberofShifts = N  
Shift size  
Shift = R/N 
 1.

Reduction of the coordinates of the entire point cloud in a way ensuring that the minimum X, Y, and Z coordinates are equal to zero
function Result = ReduceCoords(Points) Xm = min(Points(:,1)); Ym = min(Points(:,2)); Zm = min(Points(:,3)); For i = 1:p Result(i, :) = Points(i,:) – [Xm Ym Zm] end; End;
 2.

Rotation of the entire point cloud by defined angles about individual axes
function Result = RotatePoints(alfa, beta, gama, Points) RotX = [1 0 0; 0 cos(alfa) sin(alfa); 0 sin(alfa) cos(alfa)] RotY = [cos(beta) 0 sin(beta); 0 1 0; sin(beta) 0 cos(beta)] RotZ = [cos(gama) sin(gama) 0; sin(gama) cos(gama) 0; 0 0 1] Rot = RotZ*RotX*RotY; For i = 1:p Result(i, :) = (Rot*Points(i,:)’)’ end; End;
 3.

Shift of the X and Y coordinates by a predefined value
function Result = ShiftPoints(Sx, Sy, Points) For i = 1:p Result(i,:) = Points(i,:) + [Sx Sy 0] end; End;
 4.

Search for the point with the lowest elevation in each raster cell
function rastr = Rasterize(RasterSize, Points) max_x = max(Points(:,1)); max_y = max(Points(:,2)); limit_x = ceil(max_x/ RasterSize); limit_y = ceil(max_y/ RasterSize); rastr = zeros((limit_x, limit_y); for i = 1:p do x = floor(Points(i,1)/RasterSize)+1; y = floor(Points(i,2)/RasterSize)+1; if rastr(x,y) == 0 then rastr(x,y) = i else if Points(i,3) < Points(rastr(x,y),3) then rastr(x,y) = i; end; end; end; End;
 5.

Saving the identified data—this is solely a routine programming issue of data management
function result = SaveLowestPoints(LPointsID, Points) //here, the storage pathways and form are to be programmed. End;
 6.

The program itself
PointsC = ReduceCoords(Points) For alfa = [alfa1, alfa2, …, alfam] For beta = [beta1, beta2, …, betan] For gama = [gama1, gama2, …, gamao] PointsR = RotatePoints(alfa, beta, gama, PointsC) PointsR = ReduceCoords(PointsR) For SX = 0:N For SY = 0:N PointsS = ShiftPoints(SX*Shift, SY*Shift) LowestPointsID = Rasterize(RasterSize, PointsS) SaveLowestPoints(LowestPointsID, Points) end; end; end; end; end;
PointsC = ReduceCoords(Points) For alfa = [alfa1, alfa2, …, alfam] For beta = [beta1, beta2, …, betan] For gama = [gama1, gama2, …, gamao] PointsR = RotatePoints(alfa, beta, gama, PointsC) PointsR = ReduceCoords(PointsR) For SX = 0:N For SY = 0:N PointsS = ShiftPoints(SX*Shift, SY*Shift) LowestPointsID = Rasterize(RasterSize, PointsS) SaveLowestPoints(LowestPointsID, Points) end; end; end; end; end; 
Appendix B. MDSR Algorithm Flowchart
Appendix C. Scanning Systems Used for Data Acquisition
 DJI Zenmuse L1 UAV Scanner
Dimensions  152 × 110 × 169 mm 
Weight  930 ± 10 g 
Maximum measurement distance  450 m at 80% reflectivity 
Recording speed  190 m at 10% reflectivity 
System accuracy (1σ)  Single return: max. 240,000 points/s 
Distance measurement accuracy (1σ)  Multiple return: max. 480,000 points/s 
Beam divergence  Horizontal: 10 cm per 50 m 
Maximum registered reflections  Vertical: 5 cm per 50 m 
RGB camera sensor size  3 cm per 100 m 
RGB camera effective pixels  0.28° (vertical) × 0.03° (horizontal) 
Weight  Approx. 6.3 kg (with one gimbal) 
Max. transmitting distance (Europe)  8 km 
Max. flight time  55 min 
Dimensions  810 × 670 × 430 mm 
Max. payload  2.7 kg 
Max. speed  82 km/h 
 Leica Pegasus Mobile Scanner
Weight  51 kg 
Dimensions  60 × 76 × 68 cm 
Typical horizontal accuracy (RMS)  0.020 m 
Typical horizontal accuracy (RMS)  0.015 m 
Laser scanner  ZF 9012 
Scanner frequency  1 mil points per second 
Other accessories and features  Cameras IMU Wheel sensor GNSS—GPS and GLONASS 
 Trimble X7 Terrestrial Scanner
Weight  5.8 kg 
Dimensions  178 mm × 353 mm × 170 mm 
Laser wavelength  1550 nm 
Field of view  360° × 282° 
Scan speed  Up to 500 kHz 
Range measurement principle  Timeofflight 
Range noise  <2.5 mm/30 m 
Range accuracy (1 sigma)  2 mm 
Angular accuracy (1 sigma)  21″ 
Other important features  Sensors’ autocalibration 3 coaxial calibrated 10 MPix cameras Automatic level compensation (in range ±10°) Inertial navigation system for autoregistration 
 Leica P40 Terrestrial Scanner
Weight  12.25 kg 
Dimensions  238 mm × 358 mm × 395 mm 
Laser wavelength  1550 nm/658 nm 
Field of view  360° × 290° 
Scan speed  Up to 1 mil point/s 
Range measurement principle  Timeofflight 
Range accuracy (1 sigma)  1.2 mm + 10 ppm 
Angular accuracy (1 sigma)  8″ 
Other important features  Dualaxis compensator (accuracy 1.5″) Internal camera 4 MP per each 17° × 17°, color image; 700 MP for panoramic image 
 DJI Phantom 4 RTK
Weight  1.391 g 
Max. transmitting distance (Europe)  5 km 
Max. flight time  30 min 
Dimensions  250 × 250 × 200 mm (approx.) 
Max. speed  58 km/h 
Camera resolution  4864 × 3648 
Appendix D. Filtering Results for All Sites and Filters
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Data  Raster Size (m)  Number of Shifts  Shift Size (m)  Rotations  

Alfa (gon)  Beta (gon)  Gamma (gon)  
Site 1  1  10  0.1  −25; 0; 25  −25; 0; 25  −25; 0; 25 
Site 2  5  10  0.5  −25; 0; 25  −25; 0; 25  0; 50 
Site 3  1  10  0.1  0; 25; 50; 75; 90; 120  −50; 0; 50  −50; 0; 50 
Site 4  7.5  25  0.3  −25; 0; 25  −25; 0; 25  −25; 0; 25 
Data  PMF  SMRF  CSF  ATIN 

Site 1  Cell size 1.0 Initial distance 0.5 Max distance 0.5 Max window size 1 Slope 1  Cell 0.5 Scalar 1 Slope 3 Threshold 0.1 Window 1  Cloth resolution 0.2 m Classif. threshold 0.1 m Scene slope Slope processing Yes Number of iterations 500 

Site 2  Cell size 0.5 Initial distance 1.0 Max distance 1.0 Max window size 1.0 Slope 3  Cell 0.4 Scalar 0.2 Slope 3 Threshold 0.05 Window 10  Cloth resolution 0.1 m Classif. threshold 0.1 m Scene slope Slope processing Yes Number of iterations 500 

Site 3  Cell size 0.3 Initial distance 0.8 Max distance 1.0 Max window size 0.5 Slope 3  Cell 0.1 Scalar 0.1 Slope 3 Threshold 0.1 Window 1  Cloth resolution 0.1 m Classif. threshold 0.3 m Scene slope Slope Processing Yes Number of iterations 500 

Site 4  Cell size 0.3 Initial distance 0.5 Max distance 1.0 Max window size 12 Slope 2  Cell 0.4 Scalar 0.3 Slope 0.7 Threshold 0.2 Window 10  Cloth resolution 0.1 m Classif. threshold 0.1 m Scene slope Slope processing No Number of iterations 500 

Data  Original  PMF  SMRF  CSF  ATIN  MDSR 

Site 1  1,408,072  1,244,526  1,126,268  1,128,881  959,390  1,028,481 
Site 2  10,016,451  2,009,885  1,407,364  1,251,470  701,946  280,087 
Site 3  2,785,912  592,083  439,181  502,067  420,902  316,611 
Site 4  830,836  190,795  173,228  153,196  166,794  66,791 
Data  Unfiltered (m)  PMF (m)  SMRF (m)  CSF (m)  ATIN (m)  

Above  Below  Above  Below  Above  Below  Above  Below  Above  Below  
Site 1  2.434  0.007  0.072  0.015  0.043  0.014  0.099  0.007  0.048  0.060 
Site 2  10.339  0.025  0.631  0.026  0.950  0.028  0.395  0.025  0.045  0.027 
Site 3  7.764  0.006  0.270  0.003  0.211  0.003  0.316  0.006  0.074  0.002 
Site 4  20.238  0.017  0.145  0.010  0.098  0.010  0.099  0.017  0.080  0.017 
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Štroner, M.; Urban, R.; Línková, L. Multidirectional Shift Rasterization (MDSR) Algorithm for Effective Identification of Ground in Dense Point Clouds. Remote Sens. 2022, 14, 4916. https://doi.org/10.3390/rs14194916
Štroner M, Urban R, Línková L. Multidirectional Shift Rasterization (MDSR) Algorithm for Effective Identification of Ground in Dense Point Clouds. Remote Sensing. 2022; 14(19):4916. https://doi.org/10.3390/rs14194916
Chicago/Turabian StyleŠtroner, Martin, Rudolf Urban, and Lenka Línková. 2022. "Multidirectional Shift Rasterization (MDSR) Algorithm for Effective Identification of Ground in Dense Point Clouds" Remote Sensing 14, no. 19: 4916. https://doi.org/10.3390/rs14194916