Ludovico Biagi Digital Elevation Models: th march 2015

Ludovico Biagi Digital Elevation Models: generation and applications DICA seminars, 13th march 2015

Outline

Digital Elevation Models: generation and applications Ludovico Biagi 1.  Fields, elevations, models and applications 2.  Elevations in cartography 3.  Digital models (& GRIDS) 4.  Generation techniques 5.  Spatial scale, resolution and accuracy 6.  Examples from local to global scale 7.  Other data models 8.  Morphology extraction 9.  Examples of applications 10. Heli-DEM project

2

Fields: a definition

A physical phenomenon that can be matematically described as a function of independent variables Example: the temperature at the ground level depends on 1 & 2: the geographical position (latitude/North and longitude/East), 4: the time: Our case: the topography elevation!

3

T = f (ϕ ,λ,t)

1 2( ) ( , ,..., )nz f x x x=x

Elevation: definition 4

Topography

Topography is the surface of the Earth, topography can be considered a field

Elevation: definition 5

Elevation of topography

Topography is the bare soil surface, not including vegetation, buildings,...

The Earth surface

Reference surface Geoid: equipotential surface for the Earth gravity field passing for the so-called mean sea level

The Earth surface

Reference surface Geoid: equipotential surface for the Earth gravity field passing for the so-called mean sea level

Topography

P1 = (ϕ1, λ1)

H(P1) = H(ϕ1, λ1)

P2 = (ϕ2, λ2)

H(P2)

P3 = (ϕ3, λ3)

H(P3)

The Earth surface

Elevation model: the Alp example

Surveying of elevations of particular points (summits, passes, ...), graphical interpolation

Topography: historical surveying

Principle of stereo vision for 3D reconstruction

By stereo vision 3D reconstruction of objects is possible Human vision!

The Earth surface: aerial photogrammetry

Analogic images Stereo vision principles are applied... Check points (ground truth) are needed to coregister the images Then georeferenced 3D models can be built by images stereo pairs

13 Stereo analysis

From 3D stereo analysis   Elevations of particular points

  Contour (equal elevation equally spaced) lines

The Earth surface: cartographic description

100

200

300 400

500

600

700 400

300 200

100

+ 739

+ 453 + 611

+ 87

+ points

contour lines

The Earth surface: cartographic description

Digital Models: definitions

A Digital Model is a set of digital data and tools that allows the computation of (orthometric) elevations of terrain points with a given accuracy

Continuous surface

TERRAIN

Discrete points

SAMPLED OBSERVATIONS

Continuous model

TERRAIN MODEL

Numerical models of digitally stored elevations

Example: the GRID model Georeferenced Matrix of equally spaced elevations

The Earth surface: Digital Elevation Models

Generally: a model to describe 2D (z=f(x,y)) fields

GRID DEM model

A georeferenced matrix of nodes, regularly spaced in X and Y

GRID DEM model

The origin is assigned (lower left node X and Y)

GRID DEM model

The total number of nodes in X and Y are assigned

GRID DEM model

The horizontal spatial resolution in X and Y is assigned

GRID DEM model

A numerical matrix of elevations (field values) is stored ...

GRID DEM model

+ the needed metadata to georeference it:

Reference Frame

Origin position (X & Y)

Number of rows (Ny) and columns (Nx)

Horizontal spatial resolution (Dx & Dy)

GRID DEM model

Cartography

Other geographic Informations

Topographic maps

Tematic maps

Contours

From cartography to Digital Models

DEM

Digital Elevation

Model

Geographic Information Systems

DEM

Vegetation

Buildings

Others ...

DEM - Applications

Classical cartography

New digital applications

versus

DEM - Applications

Primary

Ancillary

versus

DEM - Applications

Earth Science River basins: delineation Hydrological run off model Geomorphology Geology

Environmental and urban planning Meteorology, climatology Emergency management Forestry Pollution diffusion Agricultural planning Airborne images georeferencing

DEM - Applications

At the beginning: digitizing and interpolation of elevations from cartographic contour lines

Digital Elevation Models production

100 200

300 400

500

600 700 400

300 200 100

DEM from stereoscopic digital images

Images become digital Stereo vision principles are applied to metric digital images firstly air-borne

DEM from stereoscopic digital images

Images become digital Stereo vision principles are applied to metric digital images firstly air-borne then satellite-borne Digital Models are directly produced without maps as intermediate step

Multispectral satellite-borne sensors

Remote sensing ≈ 1970 ... Stereo pairs: 1986: SPOT 1, 10 m ... 1999: IKONOS2, 1m ... 2001: Quickbird 2, 0.5 m ... 2014: WorldView 3, 0.31 m

Other techniques: LIDAR

From Baltsavias (http://www.igp.ethz.ch/photogrammetry/education/lehrveranstaltungen/Photo2_FS14/course/ALS-Baltsavias_2014a.pdf)

A Laser Scanner onboard to an aircraft emits laser pulses and records return times from topography The Laser scanner is georeferenced (GPS) and oriented (INS) Reflection time è Distance è (GPS+INS+Distance) è

è Reflecting surface elevation

è From 1990

Other techniques: SAR

Synthetic Aperture Radar Radar images of the same feature taken by two different directions (like stereo-optical images) Radargrammetry Images contain magnitude (intensity) of radar returns; pairs of images are used to extract 3D features airborne radargrammetry: from 1970 satellite radargrammetry: from 1980 Interferometry (InSAR) Images contain phase (timing) of radar returns; pairs of images separated by a known baseline are differenced in one interferogram, that is used to extract 3D features from 1990

DEM spatial scale

Spatial resolution of DEMs High resolution: 1 m or better Medium resolution: tenth of meters Low resolution: up to 1 Km Local models: LIDAR, aerial photogrammetry Regional, national: LIDAR, aerial photogrammetry, satellite remote sensing Global: Past: recompilation of existing cartographic sources ETOPO5 (1988): global grid with 5 arc minute (10 km) resolution Present: Satellite remote sensing by SAR and stereo techniques

Accuracy

Function of   terrain smoothness

  vegetation coverage Biases (RF alignement) and random errors In GRID: also function of the horizontal spatial resolution

Biases: errors in the reference frame of the model

Must be reduced by calibration with GCP’s (Ground Control Points), truth independent points on the terrain (for example RTK-GPS surveys)

DSM

Reference Model

Accuracy

A 2.5D calibration is applied

Fitting is performed by fixing X, Y and adjusting elevations

The mean difference between DTM heights and GCP’s is removed

Reference Model

DSM

Accuracy

Random errors remain and can be assessed by the Root Mean Square Error analysis.

The accuracy can be evaluated on Check Points (CP’s) that represent the truth, and have not been used to calibrate the model.

CP’s accuracy must be at least one order of magnitude better than the nominal one of the model.

Accuracy

The quality index is given by the

LE95 = 1.96 ss (Linear Error at 95 % probability) “ISO/TC 211: TS 19138 - Geographic Information - Data quality

measures - N 2029, 5 June, 2006 “ similar to the tolerance

TH = 2ssH

of Commissione Geodetica Italiana.

Accuracy

The accuracy is expressed as a function of the nominal scale of the relevant cartography.

Tolerances are defined: §  TH(a) in open field §  TH(b) in forest (tree coverage > 70%) §  TH(c) for buildings §  TEN in planimetry

Accuracy

Accuracy levels

Level Type Spacing (m)

TH(a) (m)

TH(b) (DEM)

(m)

TH(c) (DSM)

(m)

TEN (m)

0 DEM, DSM 40-100 30 30 30 20 1 DEM, DSM 20 10 20 10 10

2 DEM, DSM 20 4 ½ mean

trees height

5 4

3 DEM, DSM 10 2 ½ mean

trees height

3 2

4 DEM, DSM 5 0.60 1.20 0.80 0.60 5 DEM, DSM 2 0.40 0.80 0.54 0.40 6 DDEM, DDSM 1 0.60 1.20 0.80 0.60 7 DDEM, DDSM 0.50 0.30 0.60 0.40 0.30

8 DDEM, DDSM 0.10-0.20 0.20 0.30 0.26 0.20

Model generation issues 44

Digital Terrain Model: model of topography elevations


Digital Surface Model: elevation of topography + forestry + buildings + ...

Almost all the observation techniques provide DSMs!


  Extraction of DTMs from DSMs

  Data filtering (blunder identification)

  Reference frame registration

  Accuracy assessment

  Merging of local and partly overlapping DTMs

One LIDAR DTM example

PST-A (Piano Straordinario di Telerilevamento Ambientale) of Italian Ministry of Environment: main valleys of Po basin Gridded in geographic coordinates Spatial resolution: 10-5 degrees (≈1 m) Vertical accuracy ≈1 m

47

!

One photogrammetric DTM example

Regione Piemonte DTM Gridded in UTM coordinates Spatial resolution 50 m Vertical accuracy ≈2.5 m

48

!

Satellite global DSMs: SRTM

2000: Shuttle Radar Topography mission (SRTM) Based on 2 SIR-C/X-SAR (8.8 & 3.1 cm wl) radar systems (flew 60 mt apart) to produce interferometric images. Almost global coverage: 80% of Earth land surface (60°S – 60°N) Spatial resolution: 1 arcsec in USA, 3 arcsec Vertical accuracy: 15 m, presence of voids (no data) and artifacts New release @ 1 arcsec announced in 2014

Satellite global DSMs: GDEM (from ASTER)

Advanced Spaceborne Thermal Emission and Reflection Radiometer From 2000, NASA and Japan Remote sensing mission: multispectral sensor for several purposes GDEM1 (2009) and GDEM2 (2011): almost global coverage: 83°S – 83°N; spatial resolution: 1 arcsec Vertical accuracy: 10 m; presence of voids (no data) and artifacts

GMTED2010

By merging 11 data sources Global coverage, spatial resolution of 7.5, 15, 30 arc seconds Vertical accuracy: 30 m

Recomputation (interpolation) inside nodes

Other data models: TINs

Triangular Irregular Networks


Irregularly spaced horinzontal nodes are connected by Delaunay trangulation

Y

X


Y

X

Given one triangle, for each node (vertex)


Y

X

Z

elevations are stored and define a 3D plane that can be used to compute elevations in other points


For each node: identifier, X and Y coordinates, elevation

For each triangle: identifiers of the three vertices

Y

X

Z

58 TINs VS GRIDS

TIN is more complex but can be multiresolution: better for heterogeneous orography


Himachal Pradesh region, centred in

31° 5' 22'' N, 76° 47' 51'' E

Count: 1052 x 1052 cells

Resolution: 30 m x 30 m

Area: 31 Km x 31 Km

Minimum h: 275 m

Maximum h: 2080 m

Mean h: 770 m

RMS h: 355 m

TIN / GRID storage size: 0.3


Italian pre-alpine area (Como lake)

Statistics:

Count: 422’610 cells

Resolution: 2 m x 2 m

Area: 2 Km x 2 Km

Minimum h: 197.4 m

Maximum h: 332.3 m

Mean h: 225.3 m

RMS h: 27.8 m

TIN / GRID storage size: 0.5

Slope computation in a GRID node

The slope between the node and the 8 adjacent nodes can be numerically computed

Δ ij =

Hi − H j

dhorizontal ij

Slope in a GRID DEM node


...

The slope is the maximum


The aspect is the direction angle of the slope

Normal to topography

Sun direction θ

DEM Representation: shaded relief

θ

θ

θ

θ = 0°

θ = 90°



Contours

Shaded relief Color map

3D patches

Composed representations

composed

Composed representations

Shaded relief

Shaded relief + color classes

DEM, applications: Hydrography

aspects: water directions





Po basin


Europe basins


DEM, applications:visibility

Interest point

Profile

profile

visible part

profile not visible part

Planning of communications nodes

DICA, Geomatics Laboratory at Como Campus

THE HELI-DEM model estimation

L. Biagi, S. Caldera, L. Carcano, A. Lucchese, M. Negretti, F. Sansò, D. Triglione, M.G. Visconti

ISPRS 2014, Suzhou

DIIAR, Laboratorio di Geomatica del Polo Territoriale di Como

General framework: European and alpine context

In Europe typically na�onal / regional (local) DTMs are available that are cut

accordingly to administra�ve borders

In some areas a unified DTM could be useful for cross border analyses

(for example in the Alps for the hydrogeological risks)


Techniques to cross check, re-‐grid and merge different DTMs (with different resolu�ons, reference frames and accuracies)

have to be tested and adopted


The HELI-DEM project (Interreg funding)


Involved partners Regione Lombardia, Regione Piemonte, Politecnico di Milano, Fondazione Politecnico, Politecnico di Torino, SUPSI di Lugano

Computa�on of a unified DTM for a specific alpine area btw Italy (Piedmont and Lombardy) and Switzerland


DTM of Piedmont

DTM of Lombardy

Resolution: 50 meters Extension: Piedmont region Year of creation: ’90s (re-organised in 2003) Reference system: WGS84 - IGM95 (ETRF89) Coordinate system: UTM fuse 32, orthometric heights Accuracy: 2.5 m (in height), 4 m (in planimetry)

SwissTopo DTM Resolution: 25 meters (1” sexagesimal) Extension: Switzerland Year of creation: 2001 Reference System: ETRS89 Coordinate system: geographic, orthometric heights LN02

Accuracy: 1.5 - 3 m (in height)

DTM PST-‐A LiDAR Resolution: 1 meter (10-5 sexadecimal degrees) Extension: Piedmont and Lombardy – main idrographic basins Year of creation: currently in realization Reference system: WGS84-IGM95 (ETRF89) Coordinate system: geographic, orthometric heights Accuracy: ~ 1 m (in height)

Steps of HD: 1. census of the available DTMs


Resolution: 20 meters Extension: Lombardy region Year of creation: 2002 Reference system: Roma40 Coordinate system: Gauss-Boaga fuse Ovest, orthometric heights

Accuracy: 5-10 m (in height), 2 m (in planimetry)


Available data

LR resolu�on regional DTMs for Piedmont, Lombardy and Switzerland

+ HR DTM (PST-‐A) for Italian main valleys

DTMs in different Reference Frames and projec�ons

Needed ac�ons

1.a Cross-‐valida�ons between cross-‐border LR regional DTMs

1.b LR DTMs valida�on by HR PST-‐A DTM

2.a Individual LR DTMs re-‐gridding to a common grid

2.b Merging of the individual results to produce a LR unified DTM

3. Correc�on of the LR DTM with PST-‐A data

Following steps of HELI-DEM


DIIAR, Laboratorio di Geomatica del Polo Territoriale di Como DICA, Geomatics Laboratory at Como Campus

1.a Cross-validations between overlapping LR DTMs

Interpola�on of the DTMs in test points Comparison between the interpolated eleva�ons Corrected specific blunders In general, no biases but worse sta�s�cs than nominal accuracies

SWITZERLAND – LOMBARDY

mean = -0.1 m std = ±19 m

Example: comparison between Lombardy and Switzerland The discrepancies follow digi�zing patches are not orographic features


1.b LR DTMs validation by HR PST-A DTMs

Predic�on of PST-‐A (HR LiDAR DTM) on the LR DTMs nodes and their comparison Sa�sfactory sta�s�cs with localized anomalies

n° points: 4048660, m: 0.5 m, std: 6.6 m, max: 204 m (recent landslide in rough orography) Ad hoc GNSS RTK surveys in anomalous areas confirm the sub meter accuracy of PST-‐A


PST-‐A data should be used to correct the LR DTM obtained by merging the input LR DTMs


2.a Individual re-gridding of input DTMs to a common grid

Required individual opera�ons for each input DTM 1. Reference Frame / coordinates transforma�on 2. Re-‐gridding of all input DTMs to a common RF and grid


Output RF: ETRF2000, Output Grid: geographic Extents: φ: [45.10° -‐ 46.70° N], λ: [7.80° -‐ 10.70° E] HR: φ = 2 x 10-‐4 °, ̴22 m, λ = 2 x 10-‐4 °, ̴15 m #nodes: 116M

Note on DTM reference frames and coordinates transforma�ons Input: horizontally gridded 3D points Output: a list of 3D points, no more on a regular grid


Bilinear

A input DTM is a models To re-‐grid it: no smoothing,

isodetermined interpola�on by local polynomial surfaces

Bicubic

2.a Individual re-gridding


00 10 01 11z a a x a y a xy= + + +

z = a00 + a10x + a01y + a20x2 + a11xy + a02 y2

+a30x3 + a21x2 y + a12xy2 + a03 y3 + a31x

3 y

+a22x2 y2 + a13xy3 + a32x3 y2 + a23x2 y3 + a33x

3 y3

4 observa�ons needed Faster

16 observa�ons needed & slower

Several tests on our data: more accurate


Each input DTM is transformed to ETRF2000

Each output node is computed by interpola�ng the nearest 16 RF-‐transformed nodes

A system solu�on (matrix inversion) is needed

The spa�al distribu�on of the input points can cause ill condi�oning problems that should be regularized, for example by:

1.  annihila�on of eigenvalues (by Singular Value Decomposi�on)

2.  introduc�on of redundant observa�ons (by Least Squares es�ma�on)

3.  Tychonoff regulariza�on

2.a RF transformation and re-gridding: the direct approach


Interpola�on with regulariza�on (SVD/LS) has been implemented and tested on HELI-‐DEM dataset

Regulariza�on

1.  required in many points,

2.  introduces (not significant but undesired) smoothing,

3.  slowers (significantly) the re-‐gridding.

A different approach is possible in DTM re-‐gridding, that is the praxis in image / digital maps registra�on

Eleva�ons of DEMs are a�ributes of the horizontal (2D) coordinates of the nodes and not part of 3D coordinates

2.a RF transformation and re-gridding: the direct approach


For each input DTM

1. RF back transforma�on of the horizontal coordinates of the output nodes to its reference frame

2. Interpola�on of the input DTM on the back transformed horizontal coordinates of the output nodes

3. A�ribu�on by indexing of the interpolated eleva�ons to the output grid

2.a RF transformation and re-gridding: the inverse approach

Local bicubic interpola�on on a regular 4 x 4 grid: no matrix inversion is required Nowhere ill condi�oning problems: everywhere isodetermined interpola�on


Individual interpola�ons of input DTMs on output nodes and back-‐interpola�on of the output on the input nodes

Lombardy (30M points): no bias, Std = 0.8 m 99.1 % of the the differences smaller than 3 meters Five outliers

Switzerland (11M points): no bias, Std = 0.3 m 99.9 % of the the differences smaller than 3 meters No outliers

Piedmont (3M points): no bias, Std = 0.2 m 99.9 % of the the differences smaller than 3 meters No outliers

2.a RF transformation and re-gridding: the inverse approach


Needed in overlap areas of two or three cross-‐border DTMs: in their nodes more (2-‐3) interpolated eleva�ons are available Their simple average could cause sharp discon�nui�es at the borders of overlap areas

2.b Merging of individual interpolations in overlaps

In each node a weighted average of DTMs is adopted

H (x, y) = wDTMi(x, y)HDTM i (x, y)

i∑ ,

wDTMi(x, y) = Kd(x, y, DTMi ), K = 1/ d(x, y, DTMi )

i∑

is the horizontal distance btw the node to average and the border of DTM i

d(x, y, DTMi )


Example of border discon�nuity (jump: 8 m)

Needed to correct LR anomalies Undersampling of PST-‐A on LR grid

Computa�on of the differences between undersampled PST-‐A and LR DTM

Filtering of the differences to avoid discon�nui�es at the borders btw zero and not zero values

(Bu�erworth filter implemented by FFT) Applica�on of the filtered differences to LR DTM

3. Correction of the LR DTM with HR PST-A data


One example of the correc�on effects on a RTK GNSS sec�on blue: LR DTM differences wrt GNSS-‐RTK green: PST-‐A DTM differences wrt GNSS-‐RTK red: corrected DTM differences wrt GNSS-‐RTK



External valida�on by all the RTK GNSS results Interpola�on of original & PST-‐A-‐corrected DTMs on the GNSS RTK points Computa�on of the differences between interpolated and RTK eleva�ons

All the sta�s�cs are sa�sfactory The correc�ons improve the results


DTM bias [m] std [m] max [m] LR 3.4 5.5 24.2 UndSamp PST-‐A -‐0.3 1.0 7.2 Corrected LR -‐0.4 1.7 8.8


The final DTM

Note: strange Southern and Eastern borders due the projects boundaries

HD DTM


Web publication of the products by a geoservice

A geoservice that applies OGC (WMF & WCS) standards has been implemented to freely publish the DTMs WMS h�p://www.helidemdataserver.como.polimi.it:8080/geoserver/Helidem2013/wms?service=wms&request=getcapabili�es WCS h�p://www.helidemdataserver.como.polimi.it:8080/geoserver/Helidem2013/wcs?service=wcs&request=getcapabili�es


Conclusions and outlooks


A unified DTM has been computed for HELI-‐DEM project area To re-‐grid input DTMs on the output grid, an inverse approach, similar to the registra�on of RS images has been applied To merge overlapping interpola�ons, a weighted average has been implemented To correct the LR DTM with HR DTM, a filtered (FFT) approach has been adopted The experience and the implemented procedures will be applied to compute a more complete Western Alpine DTM

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Ludovico Biagi Digital Elevation Models: th march 2015