ANISOTROPIC SURFACES DETECTION USING INTENSITY MAPS ACQUIRED BY AN AIRBORNE LIDAR EMITTING IN...
Transcript of ANISOTROPIC SURFACES DETECTION USING INTENSITY MAPS ACQUIRED BY AN AIRBORNE LIDAR EMITTING IN...
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
Example of work achieved in CLAREC :sedimentary budgets between different dates in the bay of Mont Saint Michel
Context
Example of work achieved in CLAREC :sedimentary budgets between different dates in the bay of Mont Saint Michel
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)
Estimation of the surface spatial anisotropyPresentation of the estimators
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
Estimation of the surface spatial anisotropyPresentation of the estimators
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
Estimation of the surface spatial anisotropyPresentation of the estimators
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)
Estimation of the surface spatial anisotropyPresentation of the estimators
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)
Estimation of the surface spatial anisotropyPresentation of the estimators
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
Estimation of the surface spatial anisotropyPresentation of the estimators
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
Estimation of the surface spatial anisotropyPresentation of the estimators
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
Estimation of the surface spatial anisotropyPresentation of the estimators
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
Estimation of the surface spatial anisotropyPresentation of the estimators
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
Estimation of the surface spatial anisotropyEvaluation of the estimators
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
Estimation of the surface spatial anisotropyEvaluation of the estimators
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
Investigation of the dataIntensity and coherence maps
Intensity map presents contrasted SNR distribution since noise level is constantand backscatter is highly variable
⇒ after SNR correction, coherence appears independent of SNR
Investigation of the dataIntensity and coherence maps
⇒ anisotropic surfaces are discriminated regarding to their textureamplitude independently of SNR and intensity level
Investigation of the dataIntensity and coherence maps
To characterize unambiguously the coastal surfaces, the texture only can also beassessed as follows since coherence is naturally independent of amplitude
→
Investigation of the dataIntensity and coherence maps
texture only approach well adapted to sea surface state characterizationplane : high anisotropy refracted : low anisotropy breaking : isotropic
Investigation of the dataIntensity and coherence maps
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
✗ ...