ANISOTROPIC SURFACES DETECTION USING INTENSITY MAPS ACQUIRED BY AN AIRBORNE LIDAR EMITTING IN NEAR-IR OVER COASTAL ENVIRONMENTS.pdf

Anisotropic surfaces detection using

near-IR LiDAR intensity maps

over coastal environments

Franck Garestier, Patrice Bretel, Olivier Monfort & Franck Levoy

Lab M2C ”Morphodynamique Continentale et Cotiere”UMR CNRS 6143 - University of Caen, France

IGARSS 2011

Vancouver, Canada

Outline

❑ Context

❑ Estimation of the surface spatial anisotropy

• presentation of the estimators

• evaluation of the estimators

❑ Investigation of the LiDAR intensity data

❑ Conclusion & perspectives

Context

The CLAREC project :

Coastal survey using an airborne LiDAR

Studied area : NW coasts of France (from Manche to North Sea)

Characteristics of the system :

✗ sensor : Leica ALS 60

✗ emitting frequency : 1064 nm

✗ maximum scan aperture : 70◦

✗ point density until several points/m2

✗ vertical precision of the order of 10 cm

Context

Example of work achieved in CLAREC :sedimentary budgets between different dates in the bay of Mont Saint Michel

Context


Context


Context

Simultaneously to DEMs → recording of associated intensity maps

Image formation : automatic gain correction and constant pixel size rasterization

→ backscatter principally depends on the soil moisture, roughness and lithology

Two main interests to investigate intensity maps :

✗ the texture is linked to topography (surface-LASER beam angle variations)possibly below the DEM accuracy

✗ intensity contrasts can reveal natural discontinuities without anytopography

Hydrodynamics governs the formation of current ridges and multiplescale/gradient discontinuities⇒ indicators of sedimentary processes signing as spatially anisotropic surfaces

Necessity of developing estimator fast enough to be applied to widecoverage high resolution data (several HR LiDAR acquisitions)

Estimation of the surface spatial anisotropyPresentation of the estimators

Global idea : spatial anisotropy of a surface estimated by correlation of the twoorthonormal spatial dimensions

Two ways to achieve a cross-dimension coherence inside a sliding window :

✗ 1D correlations of columns and lines

✗ 2D correlation of the whole window and its transposed

Fourier space well adapted to the signal properties :

For (asymmetric) current ridges

⇒ periodicity and stationarity at the scale of the windowtrigonometric shape (with sum of harmonics weighted by 1/f 2 in asymmetric case)

For discontinuities of a given width and gradient

⇒ trigonometric decompositionsum of harmonics weighted by 1/f (∞ gradient) or δ/f 2 (δ gradient)


The classical normalyzed correlation can be expressed as

γxy = max

(

|x ⋆ y |√

< |x |2 >< |y |2 >

)

with x ⋆ y = F−1(F(x)F(y)∗)

”<.>”expresses averaging

And becomes under the vectorial formalism

γxy = N‖x ⋆ y‖∞‖x‖2‖y‖2

with x ⋆ y = F−1(F(x) ◦ F(y)∗)

”◦” symbolizes the Hadamard -direct- product

With the natural vectorial norms

‖x‖p =

(

n∑

i=1

|xi |p

)1p

and ‖x‖∞ = limp→+∞

‖(x1, . . . , xn)‖p = max (|x1|, . . . , |xn|)

→ correlation comprised between 0 and 1


1D correlations of columns and lines

Surface included in a N × N sliding window is symbolized by a matrix Z. Thecorrelation matrix of each column and line can be defined as

C = N

‖(z1j )1≤j≤N⋆(zi1)1≤i≤N‖∞

‖(z1j )1≤j≤N‖2‖(zi1)1≤i≤N‖2. . .

‖(z1j )1≤j≤N⋆(ziN )1≤i≤N‖∞

‖(z1j )1≤j≤N‖2‖(ziN )1≤i≤N‖2

.... . .

...‖(zNj )1≤j≤N⋆(zi1)1≤i≤N‖∞

‖(zNj )1≤j≤N‖2‖(zi1)1≤i≤N‖2. . .

‖(zNj )1≤j≤N⋆(ziN )1≤i≤N‖∞

‖(zNj )1≤j≤N‖2‖(ziN )1≤i≤N‖2

The C matrix has the same size of Z. Correlation of columns and lines arepositioned at their intersection

The mean correlation is obtained by averaging the real C matrix

γ1D =1

N2

N∑

i,j=1

cij

⇒ 0 anisotropic surfaces and 1 for isotropic ones


2D correlation of the whole window and its transposed

Correlation matrix can be achieved in another way by performing a 2D correlationof the window Z and its transposed, using the F2D transformation :

C = N

√

ℜ{Z ⋆ ZT}2 + ℑ{Z ⋆ ZT}2∑N

i,j=1 |zij |2

The overall correlation is obtained like

γ2D = max(C)


2D correlation of the whole window and its transposed

Correlation matrix can be achieved in another way by performing a 2D correlationof the window Z and its transposed, using the F2D transformation :

C = N

√

ℜ{Z ⋆ ZT}2 + ℑ{Z ⋆ ZT}2∑N

i,j=1 |zij |2

The overall correlation is obtained like

γ2D = max(C)

To reduce time computing over wide and high resolution LiDAR dataEstimators based on cross-spectral densities are developed since they provideadvantage of

✗ avoiding inverse FFT and MAX operationreducing also windowing effect of DFT applied to few samples

✗ full matricial formalism for computing efficiency (IDL/Matlab like softs)


As for the classical approaches, the two column/line and overall windowformalisms will be evaluated. These estimators are inspired from the coherencefunction (related to the cross-correlation).

1D correlations of columns and lines

W and W⊥ matrices containing F transform of respectively each line and eachcolumn of the Z image sample are defined as

W =

F{(z1j)1≤j≤N}...

F{(zNj)1≤j≤N}

W⊥ =

F{(zi1)1≤i≤N}...

F{(ziN)1≤i≤N}

In both cases, F transforms are arranged in lines.

A cross-spectral density-type matrix is formed with the matricial product

WW⊥† =

∑Nk=1 w1kw⊥

∗1k . . .

∑Nk=1 w1kw⊥

∗Nk

.... . .

...∑N

k=1 wNkw⊥∗1k . . .

∑Nk=1 wNkw⊥

∗Nk


For normalization, signal energies are stored in the following vectors

WΣ =

‖(w1k)1≤k≤N‖2...

‖(wNk)1≤k≤N‖2

=

√

∑Nk=1 |w1k |2

...√

∑Nk=1 |wNk |2

W⊥Σ =

‖(w⊥1k)1≤k≤N‖2...

‖(w⊥Nk)1≤k≤N‖2

=

√

∑Nk=1 |w⊥1k |2

...√

∑Nk=1 |w⊥Nk |2

A normalized real coherency matrix is obtained (using Hadamard division ⊘)

C =

√

(ℜ{WW⊥†}2 + ℑ{WW⊥

†}2)⊘WΣW⊥TΣ

As for the classical approach, the matrix C has a N × N size and normalizedcoherences of columns and lines are positioned at their intersection


The mean coherence is computed after averaging the C matrix

ρ1D =1

N2

N∑

i,j=1

cij

2D coherence of the whole window and its transposed

Analogously to the classical correlation approaches, F2D of the sample image andits transposed are performed

W2D = F2D{Z} W⊥2D= F2D{Z

T} = F2D{Z}T

Considering this equality

W2D ◦W⊥2D

∗ = W2D ◦W2D†

Sum of cross-spectral densities can be calculated like

A =

√

ℜ{W2D ◦W2D†}2 + ℑ{W2D ◦W2D

†}2


And the normalization ca be simplified as

B = ℜ{W2D}2 + ℑ{W2D}

2

Then, the quotient of element sum of A and B allows to estimate the meancoherence

ρ2D =

∑Ni,j=1 aij

∑Ni,j=1 bij


And the normalization ca be simplified as

B = ℜ{W2D}2 + ℑ{W2D}

2

Then, the quotient of element sum of A and B allows to estimate the meancoherence

ρ2D =

∑Ni,j=1 aij

∑Ni,j=1 bij

These estimators are only sensitive to the image frequential heterogeneity inits both orthonormal dimensions

⇒ they are independent of the image texture amplitude due to theirnormalization

All the estimators will now be evaluated over synthetic data regarding to

✗ degree of anisotropy

✗ relative anisotropy

✗ Signal to Noise Ratio

Estimation of the surface spatial anisotropyEvaluation of the estimators

Images are synthetized with different degrees of anisotropy α

Z = kxTky with kx = k0 sin(ωu)

ky = k0

[

(1− α) sin(ωu) + α]

α=1

α=0.5

α=0


Images are synthetized with different relative anisotropies β

Z = kxTky with kx = k0[1 . . . 1]

ky = k0

[

1 + β(

sin(ωu)− 1)

]

β=0.1

β=0.5

β=1


Every electronic systems are affected by thermal noise, which follows a Gaussiandistribution according to the central limit theorem.Images are then synthetized with different Signal to Noise Ratios

SNR effect on estimatorscan be modeled with

ρSNR =1

1 + 1SNR

γ2D , ρ1D , ρ2D estimatorscan be corrected for SNR

In coastal environment since tides govern the global moisture distribution, whichhas a strong influence on near-IR LiDAR backscatter

⇒ great importance of remaining independent of SNR

Investigation of the dataIntensity and coherence maps

A way to take into account the degree of anisotropy and its amplitudeindependently of the intensity level is to transform the signal as follows

→

Relative amplitudes impact on coherence → intuitive anisotropy representation


Intensity map presents contrasted SNR distribution since noise level is constantand backscatter is highly variable

⇒ after SNR correction, coherence appears independent of SNR


⇒ anisotropic surfaces are discriminated regarding to their textureamplitude independently of SNR and intensity level


To characterize unambiguously the coastal surfaces, the texture only can also beassessed as follows since coherence is naturally independent of amplitude

→


texture only approach well adapted to sea surface state characterizationplane : high anisotropy refracted : low anisotropy breaking : isotropic


texture only

texture + amplitude

texture only texture + amplitude

Conclusion & perspectives

Over coastal environments, surface spatial anisotropy (current ridge fields, terraindiscontinuities) is related to hydrodynamics governing the major part of thesedimentary processes

LiDAR intensity maps texture is linked to topography possibly below the DEMaccuracy and can reveal ground physical discontinuities (moisture, roughness,lithology...)

An estimator, fast enough to be applied over large LiDAR data, has beendeveloped to estimate unambiguously the degree of spatial anisotropy of coastalsurfaces and its amplitude independently of SNR

Using different date acquisitions :⇒ change detection of anisotropic properties independently of intensitycomplementary to sedimentary budgets

Work in progress :

✗ complementary multi-resolution wavelet approach✗ comparison of intensity and DEM information with estimators✗ intensity Vs incidence angle behavior (PhD E. Poullain)✗ comparison with Dual Pol-InSAR at X-band (TerraSAR-X)

Conclusion & perspectives

TerraSAR-X

✗ frequency : X-band

✗ repetitivity : 11 days

✗ ground resolution : 6 m

✗ polarizations : HH & HV

Complementarity with LiDAR

✗ low sensitivity to atmospheric conditions→ continuous survey (with regularity)

✗ high accuracy in surface movements (sub-cm)(but coarser spatial resolution)

✗ change detection of reflectivity at adifferent/complementary frequency

✗ ...

ANISOTROPIC SURFACES DETECTION USING INTENSITY MAPS ACQUIRED BY AN AIRBORNE LIDAR EMITTING IN NEAR-IR OVER COASTAL ENVIRONMENTS.pdf

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