[PPT] - Segmentation of tomographic images and caracterisation of porous PowerPoint Presentation

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 1 de 1

Segmentation of tomographic images and caracterisation of porous media : Application to tuffeau, historical Loire-Valley building stone.

E. Le Trong, O. Rozenbaum, S. Anne, J.L. Rouet

ISTO September 4, 2008

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 2 de 1

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 2 de 1

Cultural heritage of the Loire Valley

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 3 de 1

Alteration

different origins physical (wind, rain, mecanical constraints,. . .) chemical (pollutant) biological (bacteries, lichens . . .)

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 4 de 1

Tuffeau : the typical Loire Valley limestone

Hight porosity : around 50% Composition (% of total mass) :

Calcite (≃ 50%) sparitic (large grains) or micritic (small grains) Silica (≃ 45%) clays, minerals (few %)

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 5 de 1

SEM image

50 µm Micritic calcite Sparitic calcite Opal spheres etc. Void SEM image of a tuffeau sample, ×1000.

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 6 de 1

Main Goals

1 To Identify, Caracterise, Understand the alteration process

f Tuffeau

2 To find some way to prevent stone alteration

⇒ One way : 3D X-ray micro-tomography, segmentation, then image analysis of weathered and non weathered samples.

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 7 de 1

Principle of X-ray tomography

Scintillator & CCD detector X-ray beam Light source Filtered back-projection algorithm Reconstructed slice Rotating object

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 8 de 1

X-ray microtomography at the ESRF

The European Synchrotron Radiation Facility, Grenoble, France.

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 9 de 1

Example of an image obtained at SLS

Image is 10243 voxels, voxel size is 0.7µm

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 10 de 1

Example of image obtained at ESRF

200 µm

Full 3d image is 20483 voxels Here, one slice (2048×2048 pixels) pixel size is 0.28µm.

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 11 de 1

Example of image obtained at ESRF (zoom)

50 µm Micritic calcite Sparitic calcite Opal spheres

Zoom on the previous image (556×640 voxels).

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 12 de 1

Segmentation :

→ To organize the information given by micro-tomography To get the microstructure : a description of the geometry and topology of each phase (here : calcite, silica and void). Requires the separation of these phases, i.e. a segmentation of the image. Each phase can only be identified by its grey level.

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 13 de 1

Segmentation :

An image is a set of N 3 = 20483 pixels which values go from 0 (black) to 255 (white) defined by : f(x) = vi,j,k where x = i, j, k i, j, k = 0, . . . N − 1 and vi,j,k ∈ [0, 255] The pixel size is around 0.5 µm. The grey level distribution...

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 14 de 1

Histogram of the 3D orignal image

1e+07 2e+07 3e+07 4e+07 5e+07 50 100 150 200 250 Original

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 15 de 1

A Grey Level cut

50 100 150 200 250 500 550 600 650 700 750 800

The images are noisy ! More work is needed...

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 16 de 1

Morphological tools

Let us try morphological tools to our images....

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 17 de 1

Morphological tools : Dilatation operator

Dilation δ operators by a structuring element B(y) centered on y is defined on a grey level image at every point y by δB(f)(y) = ∨{f(x), x − y ∈ B(y)} (1) where ∨ if the supremum (or maximum) operator.

f(x) x

1D dilatation example.

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 18 de 1

Morphological tools : Erosion operator

Erosion ε operator by a structuring element B(y) centered on y is defined on a grey level image at every point y by εB(f)(y) = ∧{f(x), x − y ∈ B(y)} (2) where ∧ the infimum (minimum) operator.

f(x) x

1D erosion example.

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 19 de 1

Morphological tools : Opening and Closing

Opening operator γ : γB = δB ◦ εB

f(x) x

1D opening example.

Closing operator ϕ : ϕB = εB ◦ δB

f(x) x

1D closing example.

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 20 de 1

Application to µ-tomography image of tuffeau : Opening and Closing filtering

riginal image.

After application of ϕB1γB1.

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 21 de 1

Application to µ-tomography image of tuffeau : Opening and Closing filtering

riginal image.

ϕB2γB2ϕB1γB1.

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 22 de 1

Application to µ-tomography image of tuffeau : Opening and Closing filtering

riginal image.

ϕB3γB3ϕB2γB2ϕB1γB1.

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 23 de 1

Application to µ-tomography image of tuffeau : Opening and Closing filtering

riginal image.

ϕB4γB4ϕB3γB3ϕB2γB2ϕB1γB1.

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 24 de 1

Application to µ-tomography image of tuffeau : Opening and Closing filtering

5e+06 1e+07 1.5e+07 2e+07 2.5e+07 3e+07 3.5e+07 4e+07 50 100 150 200 250

grey-level histogram of a filtered image

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 25 de 1

Morphological tools : Morphological Gradient

g(x) = δBf(x) − εBf(x) (3)

x f(x)

1D gradient example.

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 26 de 1

Morphological tools : Morphological Gradient

g(x) = δBf(x) − εBf(x) (4)

x f(x)

1D gradient example : 1-dilatation.

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 27 de 1

Morphological tools : Morphological Gradient

g(x) = δBf(x) − εBf(x) (5)

x f(x)

1D gradient example : 2-erosion.

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 28 de 1

Morphological tools : Morphological Gradient

g(x) = δBf(x) − εBf(x) (6)

g(x) x f(x) x

1D gradient example

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 29 de 1

Application to µ-tomography image of tuffeau : Morphological gradient

riginal image 1024 pixels.

gradient : structuring element 3 pixels

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 30 de 1

Morphological tools : Watershed

The goal is to identify the influence area of gradient minima. To start the watershed, usually one takes min(g)

g(x) x f(x) x

1D gradient example : gradient.

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 31 de 1

Morphological tools : Watershed

We propose to take : (max(h) ∨ min(h)) ∧ min(g)

g(x) x f(x) x

watershed.

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 32 de 1

Morphological tools : Watershed

We propose to take : (max(h) ∨ min(h)) ∧ min(g)

g(x) x f(x) x

watershed.

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 33 de 1

Morphological tools : Watershed

We propose to take : (max(h) ∨ min(h)) ∧ min(g)

g(x) x f(x) x

watershed.

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 34 de 1

Morphological tools : Watershed

We propose to take : (max(h) ∨ min(h)) ∧ min(g)

g(x) x f(x) x

watershed.

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 35 de 1

Morphological tools : Watershed

We propose to take : (max(h) ∨ min(h)) ∧ min(g)

g(x) x f(x) x

watershed.

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 36 de 1

Application to µ-tomography image of tuffeau : Filtering

riginal image.

filtered image using an ASF.

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 37 de 1

Application to µ-tomography image of tuffeau : Gradient

filtered image. Morphological gradient.

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 38 de 1

Application to µ-tomography image of tuffeau : Watershed

Morphological gradient. Watershed.

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 39 de 1

Application to µ-tomography image of tuffeau : Moza¨ ıc

Original image. Moza¨ ıc : averaging on each zone.

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 40 de 1

Application to µ-tomography image of tuffeau : Result

Moza¨ ıc.

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 41 de 1

Results

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 42 de 1

Results

Detail.

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 43 de 1

Conclusions and Perpectives

Volume composition of the segmented image :

Void : 31% Calcite : 36% Silica : 33%

Efficient tools But it has to be improved especially to determine the micritic calcite phase Comparison of weathered and non weathered samples Modelisation and numerical simulation of water flow in the tuffeau porous network (gravitary flow) using Lattice Boltzmann Method. Other work in progress : Biological, Chemical and Physical caracterisation of a bio-coating obtained by an industrial process.

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Summary: Segmentation of X-ray tuffeau images September 4, 2008 44 de 1

Bio-Remediation

The formation of a coating called “calcin” on the limestone seems to protect them. The main idea of the bio-remediation is to produce a coating using the calcite formation properties of bacteries (here, Bacillus Cereus).