{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T22:42:33Z","timestamp":1775601753643,"version":"3.50.1"},"reference-count":46,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2024,12,1]],"date-time":"2024-12-01T00:00:00Z","timestamp":1733011200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Department of Geodesy, University of Warmia and Mazury","award":["29.610.001-110"],"award-info":[{"award-number":["29.610.001-110"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Light Detection and Ranging (LiDAR) systems become more prevalent in remote sensing for modeling buildings, engineering structures, or their deformations and displacements. Processing data from such systems, usually point clouds, can be performed using different methods, including Msplit estimation. The method in question is relatively novel but it has several variants. From a practical point of view, the variants that are globally or locally robust against outliers seem very promising. The paper addresses robustness and the problem of different types of outliers that might disturb LiDAR point cloud processing by Msplit estimation. The basic variants, the squared and the absolute Msplit estimations, are often sensitive to global outliers and cannot always deal with local outliers. The comparative analyses show that the modifications of the basic Msplit estimation variants complement each other. Hence, one can always find an Msplit estimation variant that is appropriate for processing LiDAR data disturbed by different types or share of outliers. The paper points out such variants and their application range. It also gives clues on using the methods in question in practice.<\/jats:p>","DOI":"10.3390\/rs16234512","type":"journal-article","created":{"date-parts":[[2024,12,3]],"date-time":"2024-12-03T04:04:04Z","timestamp":1733198644000},"page":"4512","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Msplit Estimation with Local or Global Robustness Against Outliers\u2014Applications and Limitations in LiDAR Data Processing"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0080-7897","authenticated-orcid":false,"given":"Patrycja","family":"Wyszkowska","sequence":"first","affiliation":[{"name":"Department of Geodesy, Institute of Geodesy and Civil Engineering, Faculty of Geoengineering, University of Warmia and Mazury in Olsztyn, 1 Oczapowskiego Street, 10-719 Olsztyn, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6331-8345","authenticated-orcid":false,"given":"Robert","family":"Duchnowski","sequence":"additional","affiliation":[{"name":"Department of Geodesy, Institute of Geodesy and Civil Engineering, Faculty of Geoengineering, University of Warmia and Mazury in Olsztyn, 1 Oczapowskiego Street, 10-719 Olsztyn, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1179\/003962613X13726661625708","article-title":"Msplit Transformation of Coordinates","volume":"45","author":"Janicka","year":"2013","journal-title":"Surv. Rev."},{"key":"ref_2","first-page":"57","article-title":"Msplit estimate the relationship between LS and its application in gross error detection","volume":"2","author":"Li","year":"2013","journal-title":"Mine Surv."},{"key":"ref_3","first-page":"249","article-title":"Determination of Vertical Indicators of Ground Deformation in the Old and Main City of Gdansk Area by Applying Unconventional Method of Robust Estimation","volume":"12","author":"Zienkiewicz","year":"2015","journal-title":"Acta Geodyn. Geomater."},{"key":"ref_4","first-page":"195","article-title":"Multi Split Functional Model of Geodetic Observations in Deformation Analyses of the Olsztyn Castle","volume":"14","author":"Zienkiewicz","year":"2017","journal-title":"Acta Geodyn. Geomater."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1007\/s00190-018-1221-4","article-title":"Squared Msplit(q) S-Transformation of Control Network Deformations","volume":"93","author":"Nowel","year":"2019","journal-title":"J. Geod."},{"key":"ref_6","first-page":"1419","article-title":"A Squared Msplit Similarity Transformation Method for Stable Points Selection of Deformation Monitoring Network","volume":"49","author":"Guo","year":"2020","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Janicka, J., Rapi\u0144ski, J., B\u0142aszczak-B\u0105k, W., and Suchocki, C. (2020). Application of the Msplit Estimation Method in the Detection and Dimensioning of the Displacement of Adjacent Planes. Remote Sens., 12.","DOI":"10.3390\/rs12193203"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Wyszkowska, P., Duchnowski, R., and Dumalski, A. (2021). Determination of Terrain Profile from TLS Data by Applying Msplit Estimation. Remote Sens., 13.","DOI":"10.3390\/rs13010031"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1007\/s00190-022-01668-z","article-title":"Total Msplit Estimation","volume":"96","year":"2022","journal-title":"J. Geod."},{"key":"ref_10","first-page":"175","article-title":"Evaluation of Unstable Points Detection Methods in Geodetic GNSS-Based Networks","volume":"16","author":"Banimostafavi","year":"2023","journal-title":"Iran. J. Geophys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1007\/s00190-008-0241-x","article-title":"Estimation of Parameters in a Split Functional Model of Geodetic Observations (Msplit Estimation)","volume":"83","year":"2009","journal-title":"J. Geod."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1007\/s00190-010-0373-7","article-title":"Msplit(q) Estimation: Estimation of Parameters in a Multi Split Functional Model of Geodetic Observations","volume":"84","year":"2010","journal-title":"J. Geod."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1007\/s11200-018-0548-x","article-title":"Robustness of Msplit(q) Estimation: A Theoretical Approach","volume":"63","author":"Duchnowski","year":"2019","journal-title":"Stud. Geophys. Geod."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1007\/s11200-019-0356-y","article-title":"Robustness of Squared Msplit(q) Estimation: Empirical Analyses","volume":"64","author":"Duchnowski","year":"2020","journal-title":"Stud. Geophys. Geod."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"111298","DOI":"10.1016\/j.measurement.2022.111298","article-title":"Processing TLS Heterogeneous Data by Applying Robust Msplit Estimation","volume":"197","author":"Wyszkowska","year":"2022","journal-title":"Measurement"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1515\/jag-2020-0009","article-title":"Empirical Analyses of Robustness of the Square Msplit Estimation","volume":"15","author":"Zienkiewicz","year":"2021","journal-title":"J. Appl. Geod."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"05023004","DOI":"10.1061\/JSUED2.SUENG-1451","article-title":"Tolerance for Growing Errors of Observations as a Measure Describing Global Robustness of Msplit Estimation and Providing New Information on Other Methods","volume":"149","author":"Duchnowski","year":"2023","journal-title":"J. Surv. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"04019006","DOI":"10.1061\/(ASCE)SU.1943-5428.0000286","article-title":"Msplit Estimation Based on L1 Norm Condition","volume":"145","author":"Wyszkowska","year":"2019","journal-title":"J. Surv. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Wyszkowska, P., and Duchnowski, R. (2024). Locally Robust Msplit Estimation. J. Appl. Geod.","DOI":"10.1515\/jag-2024-0023"},{"key":"ref_20","first-page":"79","article-title":"Segmentation Based Robust Interpolation\u2014A New Approach to Laser Data Filtering","volume":"36","author":"Pfeifer","year":"2005","journal-title":"Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Carrilho, A.C., Galo, M., and Santos, R.C. (2018, January 10\u201312). Statistical Outlier Detection Method for Airborne LiDAR Data. Proceedings of the ISPRS TC I Mid-term Symposium Innovative Sensing\u2014From Sensors to Methods and Applications (The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences), Karlsruhe, Germany.","DOI":"10.5194\/isprs-archives-XLII-1-87-2018"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2421","DOI":"10.1080\/01431161.2015.1041617","article-title":"Application of the Msplit Method for Filtering Airborne Laser Scanning Data-Sets to Estimate Digital Terrain Models","volume":"36","author":"Janowski","year":"2015","journal-title":"Int. J. Remote Sens."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Chen, Z., Gao, B., and Devereux, B. (2017). State-of-the-Art: DTM Generation Using Airborne LIDAR Data. Sensors, 17.","DOI":"10.3390\/s17010150"},{"key":"ref_24","unstructured":"Matkan, A.A., Hajeb, M., Mirbagheri, B., Sadeghian, S., and Ahmadi, M. (2014, January 15\u201317). Spatial Analysis for Outlier Removal from LiDAR Data. Proceedings of the 1st ISPRS International Conference on Geospatial Information Research (The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences), Tehran, Iran."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"052002","DOI":"10.1088\/1361-6501\/ad28ec","article-title":"Robust Procedures in Processing Measurements in Geodesy and Surveying: A Review","volume":"35","author":"Duchnowski","year":"2024","journal-title":"Meas. Sci. Technol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/s11370-024-00515-8","article-title":"LiDAR Odometry Survey: Recent Advancements and Remaining Challenges","volume":"17","author":"Lee","year":"2024","journal-title":"Intell. Serv. Robot."},{"key":"ref_27","unstructured":"Forlani, G., and Nardinocchi, C. (2007, January 12\u201314). Adaptive Filtering of Aerial Laser Scanning Data. Proceedings of the ISPRS Workshop on Laser Scanning 2007 and SilviLaser 2007, Espoo, Finland."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Zhao, R., Pang, M., Liu, C., and Zhang, Y. (2019). Robust Normal Estimation for 3D LiDAR Point Clouds in Urban Environments. Sensors, 19.","DOI":"10.3390\/s19051248"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1111\/j.1467-8659.2007.01016.x","article-title":"Efficient RANSAC for Point-Cloud Shape Detection","volume":"26","author":"Schnabel","year":"2007","journal-title":"Comput. Graph. Forum"},{"key":"ref_30","first-page":"610","article-title":"Outliers Detection by RANSAC Algorithm in the Transformation of 2D Coordinate Frames","volume":"20","author":"Janicka","year":"2014","journal-title":"Biol. Cienc. Geod."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/j.measurement.2015.08.023","article-title":"Algorithm for Beam Deformation Modeling from LiDAR Data","volume":"76","author":"Cabaleiro","year":"2015","journal-title":"Measurement"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Rodr\u00edguez-Gonz\u00e1lvez, P., Jim\u00e9nez Fern\u00e1ndez-Palacios, B., Mu\u00f1oz-Nieto, \u00c1.L., Arias-Sanchez, P., and Gonzalez-Aguilera, D. (2017). Mobile LiDAR System: New Possibilities for the Documentation and Dissemination of Large Cultural Heritage Sites. Remote Sens., 9.","DOI":"10.3390\/rs9030189"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Ding, Z., Sun, Y., Xu, S., Pan, Y., Peng, Y., and Mao, Z. (2023). Recent Advances and Perspectives in Deep Learning Techniques for 3D Point Cloud Data Processing. Robotics, 12.","DOI":"10.3390\/robotics12040100"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"105472","DOI":"10.1016\/j.autcon.2024.105472","article-title":"Stereoscopic Monitoring of Transportation Infrastructure","volume":"164","author":"Wang","year":"2024","journal-title":"Automat. Constr."},{"key":"ref_35","first-page":"3","article-title":"Msplit Estimation. Part I. Theoretical Foundation","volume":"58","year":"2009","journal-title":"Geod. Cartogr."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"04016015","DOI":"10.1061\/(ASCE)SU.1943-5428.0000183","article-title":"Shift-Msplit* Estimation in Deformation Analyses","volume":"142","author":"Zienkiewicz","year":"2016","journal-title":"J. Surv. Eng."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1007\/s00190-002-0256-7","article-title":"Robust Estimator for Correlated Observations Based on Bifactor Equivalent Weights","volume":"76","author":"Yang","year":"2002","journal-title":"J. Geod."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"430","DOI":"10.1007\/s001900050182","article-title":"Robust Biased Estimation and Its Applications in Geodetic Adjustments","volume":"72","author":"Gui","year":"1998","journal-title":"J. Geod."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Huber, P.J., and Ronchetti, E.M. (2009). Robust Statistics, John Wiley & Sons, Ltd.. [2nd ed.].","DOI":"10.1002\/9780470434697"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Duchnowski, R., and Wyszkowska, P. (2022). Msplit Estimation Approach to Modeling Vertical Terrain Displacement from TLS Data Disturbed by Outliers. Remote Sens., 14.","DOI":"10.3390\/rs14215620"},{"key":"ref_41","first-page":"e17","article-title":"Absolute Msplit Estimation as an Alternative for Robust M-Estimation","volume":"71","author":"Duchnowski","year":"2022","journal-title":"Adv. Geod. Geoinf."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1007\/s00190-005-0454-1","article-title":"Sign-Constrained Robust Least Squares, Subjective Breakdown Point and the Effect of Weights of Observations on Robustness","volume":"79","author":"Xu","year":"2005","journal-title":"J. Geod."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"741","DOI":"10.1016\/S0167-9473(02)00078-6","article-title":"Robust Estimation in Very Small Samples","volume":"40","author":"Rousseeuw","year":"2002","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1515\/jag-2021-0012","article-title":"Empirical Influence Functions and Their Non-Standard Applications","volume":"16","author":"Duchnowski","year":"2022","journal-title":"J. Appl. Geod."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"06020002","DOI":"10.1061\/(ASCE)SU.1943-5428.0000318","article-title":"Iterative Process of Msplit(q) Estimation","volume":"146","author":"Wyszkowska","year":"2020","journal-title":"J. Surv. Eng."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1061\/(ASCE)SU.1943-5428.0000112","article-title":"3\u03c3-Rule for Outlier Detection from the Viewpoint of Geodetic Adjustment","volume":"139","author":"Lehmann","year":"2013","journal-title":"J. Surv. Eng."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/23\/4512\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:44:25Z","timestamp":1760114665000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/23\/4512"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,1]]},"references-count":46,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["rs16234512"],"URL":"https:\/\/doi.org\/10.3390\/rs16234512","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,12,1]]}}}