DTM

This article presents an airborne Light Detection and Ranging (LiDAR)-based method to extract interesting stand attributes for forest management in high-density Eucalyptus globulus Labill. plantations. An adaptive morphological filter (AMF) for classifying terrain LiDAR points in forested areas is used to classify LiDAR points; canopy cover (CC), number of LiDAR-detected trees per hectare (N LD) and individual tree height (h tree) were calculated using the canopy height model (CHM); and several statistics and metrics extracted from the CHM and the normalized height of the LiDAR data cloud (NHD) were incorporated into the linear and multiplicative models for estimating mean height (H m), dominant height (H d), mean diameter (d m), quadratic mean diameter (d g), number of stems per hectare (N), basal area (G) and volume (V). The height accuracy results of the LiDAR-derived digital terrain model (DTM), root mean square error (RMSE) = 0.303 m, revealed that the developed filter behaved well. The values of the RMSE for CC, N LD and h tree were 13.2%, 733.3 stems ha–1 and 1.91 m, respectively. The regressions explained 78% of the variance in ground-truth values for H m (RMSE = 1.33 m); 92% for H d (RMSE = 1.18 m); 71% for d m (RMSE = 1.68 cm); 73% for d g (RMSE = 1.66 cm); 49% for N (RMSE = 667 stems ha–1); 78% for G (RMSE = 5.30 m2 ha–1); and 81% for V (RMSE = 53.6 m3 ha–1).

The main use of GIS in archaeology is connected to regional research or management of excavation data sets. The use of GIS for urban archaeological research is far less extensive.
The urban GIS about the medieval town of Pisa contains all archaeological data from occasional findings to modern stratigraphic excavations, geographical data, historical cartography data and urban data, each described by the geometrical shape (point, line, polygon) that best represents each feature. The distinguishing environmental context to which the town is connected is characterized by a complex hydrographic system; GIS analysis enabled us to study the relationships between the urban transformations and the surrounding environment. The article explains how geostatistical analysis allowed us to create a model of the ancient landscape and how the use of map algebra was useful in understanding the medieval environment. The difficulty in finding raw archaeological data, that is, all the excavation and fieldwork recording (planning of context, context recording sheet, photographs, findings quantification sheet), suggested the necessity to create an open digital archive and to provide possible standardization of digital formats, metadata records and archaeological data recording, so as to allow a comparison between the data.

Scopo di questo lavoro è individuare, sperimentare e mettere a punto una metodologia per la restituzione e l’analisi degli elementi geografici di interesse geologico presenti nelle foto aeree, utilizzando efficientemente tecnologie dal costo relativamente contenuto.
La mia scelta, verificati gli strumenti disponibili nel laboratorio di cartografia digitale diretto dal Relatore, è stata quella di realizzare delle ortofotocarte digitali dalle foto aeree disponibili utilizzando il programma Erdas Imagine  (Erdas Inc.), di fatto il più diffuso e sicuramente uno dei più completi prodotti per il trattamento delle immagini digitali telerilevate.
L’area proposta su cui sviluppare e testare il metodo, è una delle più studiate all’interno della finestra tettonica ove affiora il complesso metamorfico delle Alpi Apuane. La scelta costituisce una sfida e comunque una giustificazione a tale metodo, come vedremo, date la sua morfologia e la qualità degli aerofotogrammi disponibili. Le condizioni clivometriche, unite alla praticamente inesistente viabilità, impediscono a tutt’oggi l’uso dei normali strumenti per il rilevamento topografico di campagna, e già alla fine del secolo scorso giustificarono l’uso della neonata disciplina della fotogrammetria da parte dell’Ing. Paganini per eseguire sulle Apuane uno dei primi rilievi da piattaforme aerostatiche (MALAGOLI 1999).
Per quanto riguarda il rilevamento geologico di campagna, se da una parte l’assenza di suolo e vegetazione permette l’osservazione della roccia in posto anche a distanza, la natura generalmente molto impervia dei versanti rende spesso difficoltoso se non impossibile raggiungerli per effettuarvi misure puntuali.
Oltre a presentare uno spiccato interesse geologico applicativo dimostrato dalle numerose cave presenti, l’area è interessata da un insieme di fenomeni geodinamici e morfogenetici evidenziati da varie categorie di elementi geografici. Solo a titolo di esempio, sono presenti doline di varie dimensioni e altre tracce di carsismo, aree lisciate  e altre forme di origine glaciale, pattern  angolari di reticolo idrografico che evidenziano un forte controllo strutturale.
La richiesta del relatore è stata di concentrare l’attenzione sulle lineazioni  in particolare quelle dovute ai sistemi di fratture presenti e visibili nelle foto aeree disponibili.
In questo lavoro è stata quindi realizzata una carta delle lineazioni la quale fa comunque parte di una cospicua banca dati digitali georeferenziati che è destinata a crescere e a essere usata per ulteriori analisi.

In floodplains, anthropogenic features such as levees or road scarps, control and influence flows. An up-to-date and accurate digital data about these features are deeply needed for irrigation and flood mitigation purposes. Nowadays, LiDAR Digital Terrain Models (DTMs) covering large areas are available for public authorities, and there is a widespread interest in the application of such models for the automatic or semiautomatic recognition of features. The automatic recognition of levees and road scarps from these models can offer a quick and accurate method to improve topographic databases for large-scale applications. In mountainous contexts, geomorphometric indicators derived from DTMs have been proven to be reliable for feasible applications, and the use of statistical operators as thresholds showed a high reliability to identify features. The goal of this research is to test if similar approaches can be feasible also in floodplains. Three different parameters are tested at different scales on LiDAR DTM. The boxplot is applied to identify an objective threshold for feature extraction, and a filtering procedure is proposed to improve the quality of the extractions. This analysis, in line with other works for different environments, underlined (1) how statistical parameters can offer an objective threshold to identify features with varying shapes, size and height; (2) that the effectiveness of topographic parameters to identify anthropogenic features is related to the dimension of the investigated areas. The analysis also showed that the shape of the investigated area has not much influence on the quality of the results. While the effectiveness of residual topography had already been proven, the proposed study underlined how the use of entropy can anyway provide good extractions, with an overall quality comparable to the one offered by residual topography, and with the only limitation that the extracted features are slightly wider than the investigated one. Copyright © 2013 John Wiley & Sons, Ltd.

In the estimation of volume of stockpiles of earthworks, the question is no longer whether the data collected is dense and accurate (equipment and techniques capable of accurate data measurement are available), but how to manipulate the data to yield accurate volume estimation. Although surface modeling through TIN yields more accurate volumes than grid modeling, the delineation of footprint of the stockpile remains one of the main sources of errors in volume determination due to spurious surfaces created within the convex hull of the TIN model. In this paper, an approach for automatic delineation of the stockpile footprint based on a concave hull is introduced. A concave hull as a geometry (usually point data) container is realized by minimizing the enclosing planimetric area and it is usually not unique. Several algorithms for creating concave hulls are suggested, in this paper an algorithm based on Delaunay triangulation and linear referencing was used to create the concave hull. A comparison of volume estimations of stockpiles taking into consideration the footprint via convex hull, concave hull and manually delineated outline showed that volumes based on the concave hull are closer in value to volumes based on manually delineated footprint. Therefore in the absence of points manually picked to represent the outline of a footprint, the concave hull can be relied on.

Key words: Volume of Earthworks, TIN, Concave hull, Linear referencing, Footprint delineation.

The work presented was aimed at constructing a semi-automatic work-flow of Digital
Surface Model (DSM) and Digital Terrain Model (DTM) generation based on an ALS point cloud gathered in a very difficult mountain area. The study area located in the Polish part of the Tatras Mountains covered about 60 km2 and included the Kasprowy Wierch, Kuźnice, and downtown Zakopane with the Gubałówka. ALS data, collected in 2007, consisted of 33 scans (minimum density of 20 points/m2). To combine all the scans and match them to the coordinate system, planar surfaces (building roofs) were measured using a tachimeter and a dGPS survey. Position errors of the ALS points in the horizontal plane varied from -0.09m to +0.28m; height errors ranged from -0.12m to 0.14m (HAE). The operator delivered the data separately from 2 Riegl Q- 560 scanners, for every FE and LE. The ALS files, due to their huge size, were divided into smaller ones and generated 353 sheets (500x500 m in size ) for every scanner and number of returns combination. The point cloud was filtered and assigned to the following levels: "low points”, "ground", "low vegetation”, "medium vegetation”, "high vegetation” and "air points”. To generate a DSM, a special class called "ground_inverse" was created; it required an operator control supported by a digital orthophoto (RGB\CIR; Vexcel camera). For every sheet processed, the DTM and DSM were generated. Those verified models served as a basis for developing an nDSM model using the ER Mapper software. The nDSM shows relative heights of objects in the study area (forest stands, dwarf mountain pines, buildings, power lines, ski lifts, etc.). Development of a precise DSM and nDSM as well as analyses of the nDSM open new perspectives for numerous scientific projects.

This paper presents an effective acquisition and data processing method for landscape surveying aimed at producing cartographic data dedicated to archaeological cartography. The case study presented, part of the Banditaccia necropolis and of the "Via degli Inferi”, allows to analyze in detail the acquisition phases and the vegetation filtering procedures to obtain a single DTM by separately processing photogrammetric surveys from UAV and data obtained with TLS (Terrestrial Laser Scanner). The aim for this paper is to underline the importance of producing cartographic bases dedicated to archaeological cartography, rather than using cartography created for other purposes.

Openness is proposed as a visualization technique for the archaeological interpretation of digital terrain models derived from airborne laser scanning. In contrast to various shading techniques, openness is not subject to directional bias and relief features highlighted by openness do not contain any horizontal displacement. Additionally, it offers a clear distinction between relief features and the surrounding topography, while it highlights both the highest and lowest parts of features. This makes openness an ideal tool for mapping and outlining of archaeological features. A comparison with sky-view factor and local relief model visualizations helps to evaluate advantages and limits of the technique.

Resumen La disfunción témporo-mandibular es un trastorno de frecuencia creciente, en cuya etiopatogenia se considera que pueden intervenir factores de tipo psicofisiológico. De manera estandarizada, hemos administrado la versión española del Cuestionario de 90 Síntomas (SCL90R) a 105 pacientes con disfunción témporo-mandibular, 218 pacientes psiquiátricos ambulatorios y 136 personas de la población general. Los pacientes con disfunción témporo-mandibular presentan niveles generales de psicopato-logía significativamente más elevados que los sujetos normales, aunque no tanto como los psiquiátricos, ocupando un lugar intermedio entre estos dos grupos. La correspondencia entre los distintos indices psicopatológicos es análoga a la encontrada en la población general, lo cual apoya la hipótesis de que las alteraciones psíquicas que acompañan la DTM no corresponden a un perfil psicopatológico carac-terístico, sino que son de naturaleza generalizada inespecífica. Abstract We administered the spanish version of SCL90R to 105 patients with TMD, 218 ambulatory psychiatric patients and 136 matching subjects from the general population. All the psychopathological indexes are elevated in TMD patients, although not as much as in the psychiatric population, showing an intermediate profile between these two populations. The internal correspondence among indexes is analogous to that found in the general population, which supports the hypothesis that the noted psychic dysfunctions are of a general unspecific nature.

This paper reports the experiments carried out for extraction of DEMs from Cartosat-1 stereo imagery using stereo correlation technique for Manali region. The focus of this paper was to assess the accuracy of extracted DEM with respect to DGPS observations, DEM generated from digitized contours of Survey of India (SoI), 1:50,000 scale topographic map(converted to ellipsoidal height using egm2008 geoid model) as well as well-known freely available DEMs ASTER GDEM and SRTM. The vertical accuracy of Cartosat-1 DEMs was analysed with DGPS derived ground control points. The relative vertical accuracy (root mean square error; RMSE) of Cartosat-1 DEM with DGPS control points was ±9.6 m. The RMSE with the topographic DEM was found to be ±10.6 for 22 spot heights and ±10.8 m for 6,458,800 checkpoints. The relative vertical accuracy assessment is more important than the absolute vertical accuracy assessment. The result of relative accuracy assessment of DEMs with respect to field measurement of DGPS points and reference DEMs shows Cartosat-1 DEM is more accurate when compared to ASTER DEM, SoI Topographic DEM, and SRTM DEM for Manali region.

Geographic Information Systems allow geographical attributes and historical data to be linked in databases, facilitating spatial analysis. It makes them a significant tool for gathering, arranging and sharing geographical and historical information. The main sources in historical studies concerning floods in Silesia up until the end of 18th century are descriptive. They include rather general information; the reach of floods is described imprecisely and dating is frequently insufficiently detailed. An initial analysis of collected special data indicated that
data obtained from the descriptions is characterized by a high level of uncertainty and diversity. Due to this characteristic of written sources an attempt was undertaken to complete the source knowledge about natural disasters which took place in the past. Modern information tools, such as Geographic Information Systems and the results of analyses of cartographic sources and archaeological, geological and hydrological studies. Spatial presentations of geographical data (mainly detailed numeric land models) and historical data in combination with diachronic simulation of the course of floods can be used as a model for similar studies involving other regions.
For the analysis of the flood range in Silesia, processed satellite images purchased from the Institute of Geodesy and Cartography were used. The data was obtainedusing the MODIS scanner which was designed to observe lands, oceans and atmosphere of the Earth as well as from a numeric land model obtained during the SRTM mission. Images from the scanner allowed visualization which provided a very realistic image, facilitating perception of the entire presentation.
In the case of the output data about floods in Silesia, information about the reach of floods reflected the degree of detail of the description of the phenomenon registered in the source. This resulted in the necessity to unify and specify the information with data obtained from satellite images and results of studies in the field of geology and archaeology.
Historical data about the location of floods in Silesia was specified with the use of a modern database of towns. It has the form of a Digital Map of Poland (DMP) in a scale of 1:200,000 and was developed by the Institute of Geodesy and Cartography based on official topographic maps in a scale of 1:200,000. Moreover, data of the Central Statistical Office was used. In order to develop the method of completing source information about floods in Silesia, three research areas were selected which varied in their landform – surroundings of Kłodzko – Nysa Kłodzka, surroundings of Brzeg Opolski – Odra river, surroundings of Legnica and Zlotoryja – Kaczawa.
The geoinformation system developed within the project consists of two independent modules: a database module and a visualization module. The ArcGIS software was assumed as the basis of the database module. A multimedia application dedicated to presentation of historical data about floods in Silesia and developed especially for the needs of the project constitutes the visualization module.
Final results were presented in the form of interactive digital maps and in a diachronic approach. As assumed in the introduction to the project, basing on the modern numeric land model to determine the maximum hypothetical reach of floods is only a starting point to precise recreation of floods. Depending on its location, additional detailed interdisciplinary analyses are necessary, resulting from the specificity of a given area, in particular archaeological, dendrological, geological, hydrological ones, etc. Simulation of potential flooding areas conducted with the use of a digital terrain model developed based on satellite data showed the possibility to determine the reach of the maximum probable area of flooding. Simultaneously, it indicated one of the methods to specify information obtained from sources written about spatial phenomenon for which only fragmentary, rather general and diversely detailed source information was preserved and for which cartographic documentation is unknown. Opening of the system to integrate such data with the results of studies from other scientific disciplines allow for a further specification of the initial source information.
An additional result of the project is visualization of the information contained in the database about floods in Silesia with the possibility to follow their chronological occurrence in geographic space (arrow of time, map), to observe dynamics of the phenomenon only over time (markings on the arrow of time) and the possibility to simultaneously present all locations of floods in the past (map). There is no doubt that integration of historical data about floods with spatial data gave new quality to this original, diverse and uncertain source information.

This paper describes a method, which uses full-waveform terrestrial laser scanning to survey the surface of the slope below the Temple of Juno, located in the Valley of the Temples in Agrigento (Sicily, Southern Italy). The surface is characterized by the presence of large rock blocks, which have fallen down from the upper side; possible further detachments of rock blocks would cause a situation of general instability, with a very high risk to the archaeological structures in the near future. The methodology was designed to evaluate the potential of full-waveform laser scanning technology for the production of a very high resolution 3D topographic model of the slope, to be used as a support for the interpretation of geomorphological processes and for geotechnical analysis.

Drainage networks in agrarian landscape within floodplains constitute surface's discontinuities that are expected to affect hydrological response during floods. Drainage network recognition and quantification of water storage capacity within channels are, therefore, crucial for watershed planning and management. These evaluations require accurate spatial information for the area of interest and in most cases, when studying large catchments, broad datasets of ditches locations and descriptions are not available. In order to characterize drainage networks for large areas, the availability of high resolution topography derived by airborne laser scanner (LiDAR) represents a new and effective tool. Nowadays LiDAR DTMs covering large areas are readily available for public authorities, and there is a greater and more widespread interest in the application of such information for the development of automated methods aimed at solving geomorphological and hydrological problems. While LiDAR DTMs reliability in steep landscape has been proven by several recent studies, only few researches have been conducted to take into account the effectiveness of these data in agrarian low relief landscapes. The goal of this research is to propose a semi-automatic approach based on a LiDAR DTM to (1) detect drainage networks in agrarian/floodplain contexts, and (2) to estimate some of the network summary statistics (network length, width, drainage density and storage capacity). The procedure is applied in two typical alluvial-plain areas in the North East of Italy, and tested comparing automatically derived network with surveyed ones. The results underline the capability of high resolution DTMs for drainage network detection and characterization in the context of agrarian landscapes within floodplains, opening at the same time new challenges to evaluate some hydrological processes in these areas.

This paper illustrates a 3D survey performed at the well-known "Villa di Domiziano" site in the Circeo National Park using the new Leica Mobile Mapping System (MMS) BLK2GO. The project's aim is to identify and document earthwork anomalies, a type of evidence extremely frequent in the Villa, but difficultly traceable both for site's extension and for the presence of mixed vegetation, composed of dense foliage of maritime pines and brushwood. This research, realized within the project "The Domitian Villa: An Imperial Residence in Sabaudia, Italy", winner of the 2019 Grant for the "Shelby White and Leon Levy" program, aims to create a multidisciplinary documentation of the entire Villa of Domitian, starting from the extraction of Digital Terrain Model (DTM). The Test-case was an opportunity to test both practicality and accuracy of new Leica BLK2GO with the ultimate aim of identifying and documenting earthwork anomalies and comparing obtained data with those coming from a previous UAV-LiDAR survey.

The development of high resolution LiDAR digital terrain models (DTMs) has enabled the exploration of the statistical signature of morphology on curvature distributions. This work analyzes Minimum Curvature distributions to identify the statistical signature of two types of LiDAR-DTM errors (outliers and striping artifacts) in the derived estimates, rather than morphology itself. The analysis shows the importance of modeling these errors correctly, in relation to the scale of analysis and DTM resolution, in order to have reliable curvature estimates. Nine DTMs of different morphological areas are considered, and grouped into a training dataset (without errors) and a test dataset (with errors). In the training dataset, the original DTMs are considered as true values; errors are then applied to these data. Minimum Curvature is computed at multiple scales from each DTM: changes in curvature distributions due only to morphology and scale are characterized from the original data; error effects are then identified from the datasets with simulated errors, and validated against the test dataset. The analysis shows that outliers and striping artifacts can be realistically simulated by heavily left tailed distributions. For DTMs without errors, the scale-dependent change in curvature distribution is primarily controlled by real morphology. When DTMs include errors, curvature distributions become controlled by these errors, whose propagation depends on error distribution, error spatial correlation, and the scale of analysis. This study shows that the curvature distributions are impacted upon differently by striping artifacts and outliers, and that these are clearly distinguishable from the signal of morphological features: a scale-dependent change in curvature distribution can therefore be interpreted as the signature of these specific errors, rather than morphology. Copyright © 2012 John Wiley & Sons, Ltd.

Low Altitude Aerial Photography (LAAP) is based on the use of small flying platforms to take photographs from very low altitudes. The acquisition of series of Digital Surface Models (DSMs) and orthoimages through photogrammetric and orthorectification processes is one of the main applications. The use of this technique in archaeological sites provides very precise and valuable data, but knowing the reliability of the method is a key to ensuring that the results are valid, since the repeatability of the method is fundamental to multitemporal studies. The present work shows an analysis of the similarity of DSMs obtained from different stereoscopic pairs from the same area. The reliability of the models has been assessed by calculating the Standard Deviation (STD) of the altitude values from the models, to obtain maps displaying the differences among them. Finally, the STD values' spatial distribution has been studied to assess if spatial autocorrelation exists by means of the Moran's Index and Anselin's Local Moran's Index. Results showed good similarity among the models and revealed clearly those areas where the model must be edited.

Resumo Os perfis batimétricos são atualmente ferramentas importantes para conhecer melhor as carac-terísticas morfométricas de corpos-d'água e suas possíveis alterações. Foram realizados amostragens e levantamentos batimétricos trimestralmente (setembro e dezembro de 2010, março e junho de 2011). Os dados coletados nas batimetrias foram interpolados utilizando o software Surfer® 8.0 para confecção dos MDT (modelos digitais do terreno) e cálculos de volume reais e estimados. Eviden-ciou-se com base nos perfis batimétricos que o açude possui ao longo de seu curso ampla variação de profundidade. O volume aproximado variou bastante, indo de 19.738.857 m 3 no terceiro levan-tamento até 35.319.065 m 3 no quarto, quando atingiu o maior volume observado. Nesse período não ocorreu assoreamento significativo no açude. Toda a variação encontrada no açude mostra que a principal fonte de abastecimento de água são as chuvas. Apesar do variado volume encontrado, o açude apresentou condições para o desenvolvimento de atividades como pesca e aquicultura.
Palavras-chave: Perfis batimétricos. Açude. MDT.

Whilst the availability and affordability of satellite imagery is progressively increasing, the spatial resolution which these afford with which to create digital terrain models (DTMs) is coarse in comparison with active, ground-based techniques.  Presently, the majority of methods capable of surveying complex topography, at high resolution, are accompanied by high costs and difficult portability (e.g. Total Station, TLS). Furthermore, the remoteness and inaccessibility of many field sites renders these approaches impractical.

The research presented herein outlines a novel low-cost, close-range terrestrial photogrammetric approach to obtaining data with which to construct 3D models of breached moraine dams in the Nepal Himalaya.

The size and great dynamism of coastal systems require faster and more automated mapping methods like the use of a remotely piloted aircraft system (RPAS) or unmanned aerial vehicle (UAV). This method allows for shorter intervals between surveys. The main problem for surveying using low-altitude digital photogrammetry in beach areas is their visual homogeneity. Obviously, the fewer the homologous points defined by the program, the lower the accuracy. Moreover, some factors influence the error performed in photogrammetric techniques, such as flight height, flight time, percentage of frame overlap (side and forward), and the number of ground control points (GCPs). A total of 72 different cases were conducted varying these factors, and the results were analyzed. Among the conclusions, it should be highlighted that the error for noon flights is almost double that for the early morning flights. Secondly, there is no appreciable difference regarding the side overlap. But, on the other sid...

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In the estimation of volume of stockpiles of earthworks, the question is no longer whether the data collected is dense and accurate (equipment and techniques capable of accurate data measurement are available), but how to manipulate the data to yield accurate volume estimation. Although surface modeling through TIN yields more accurate volumes than grid modeling, the delineation of footprint of the stockpile remains one of the main sources of errors in volume determination due to spurious surfaces created within the convex hull of the TIN model. In this paper, an approach for automatic delineation of the stockpile footprint based on a concave hull is introduced. A concave hull as a geometry (usually point data) container is realized by minimizing the enclosing planimetric area and it is usually not unique. Several algorithms for creating concave hulls are suggested, in this paper an algorithm based on Delaunay triangulation and linear referencing was used to create the concave hull....

In the estimation of volume of stockpiles of earthworks, the question is no longer whether the data collected is dense and accurate (equipment and techniques capable of accurate data measurement are available), but how to manipulate the data to yield accurate volume estimation. Although surface modeling through TIN yields more accurate volumes than grid modeling, the delineation of footprint of the stockpile remains one of the main sources of errors in volume determination due to spurious surfaces created within the convex hull of the TIN model. In this paper, an approach for automatic delineation of the stockpile footprint based on a concave hull is introduced. A concave hull as a geometry (usually point data) container is realized by minimizing the enclosing planimetric area and it is usually not unique. Several algorithms for creating concave hulls are suggested, in this paper an algorithm based on Delaunay triangulation and linear referencing was used to create the concave hull....

A new robust way for ground surface extraction from mobile laser scanning 3D point cloud data is proposed in this paper. Fitting polynomials along 2D/3D points is one of the well-known methods for filtering ground points, but it is evident that unorganized point clouds consist of multiple complex structures by nature so it is not suitable for fitting a parametric global model. The aim of this research is to develop and implement an algorithm to classify ground and non-ground points based on statistically robust locally weighted regression which fits a regression surface (line in 2D) by fitting without any predefined global functional relation among the variables of interest. Afterwards, the z (elevation)-values are robustly down weighted based on the residuals for the fitted points. The new set of down weighted z-values along with x (or y) values are used to get a new fit of the (lower) surface (line). The process of fitting and down-weighting continues until the difference between ...