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

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

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

Segmentation of X-ray tuffeau images September 4, 2008 2 de 1 Summary: Cultural heritage of the Loire Valley

Segmentation of X-ray tuffeau images September 4, 2008 3 de 1 Summary: Alteration different origins physical (wind, rain, mecanical constraints,. . .) chemical (pollutant) biological (bacteries, lichens . . .)

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

Segmentation of X-ray tuffeau images September 4, 2008 5 de 1 Summary: SEM image 50 µ m Void Micritic calcite Sparitic calcite Opal spheres etc. SEM image of a tuffeau sample, × 1000.

Segmentation of X-ray tuffeau images September 4, 2008 6 de 1 Summary: Main Goals 1 To Identify, Caracterise, Understand the alteration process of 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.

Segmentation of X-ray tuffeau images September 4, 2008 7 de 1 Summary: Principle of X-ray tomography Scintillator & Rotating object CCD detector X-ray beam Filtered back-projection algorithm Light source Reconstructed slice

Segmentation of X-ray tuffeau images September 4, 2008 8 de 1 Summary: X-ray microtomography at the ESRF The European Synchrotron Radiation Facility, Grenoble, France.

Segmentation of X-ray tuffeau images September 4, 2008 9 de 1 Summary: Example of an image obtained at SLS Image is 1024 3 voxels, voxel size is 0.7 µ m

Segmentation of X-ray tuffeau images September 4, 2008 10 de 1 Summary: Example of image obtained at ESRF 200 µm Full 3d image is 2048 3 voxels Here, one slice (2048 × 2048 pixels) pixel size is 0.28 µ m.

Segmentation of X-ray tuffeau images September 4, 2008 11 de 1 Summary: Example of image obtained at ESRF (zoom) 50 µ m Sparitic calcite Micritic calcite Opal spheres Zoom on the previous image (556 × 640 voxels).

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

Segmentation of X-ray tuffeau images September 4, 2008 13 de 1 Summary: Segmentation : An image is a set of N 3 = 2048 3 pixels which values go from 0 (black) to 255 (white) defined by : f ( x ) = v i,j,k where x = i, j, k i, j, k = 0 , . . . N − 1 and v i,j,k ∈ [0 , 255] The pixel size is around 0.5 µ m. The grey level distribution...

Segmentation of X-ray tuffeau images September 4, 2008 14 de 1 Summary: Histogram of the 3D orignal image 5e+07 Original 4e+07 3e+07 2e+07 1e+07 0 0 50 100 150 200 250

Segmentation of X-ray tuffeau images September 4, 2008 15 de 1 Summary: A Grey Level cut 250 200 150 100 50 0 500 550 600 650 700 750 800 The images are noisy ! More work is needed...

Segmentation of X-ray tuffeau images September 4, 2008 16 de 1 Summary: Morphological tools Let us try morphological tools to our images....

Segmentation of X-ray tuffeau images September 4, 2008 17 de 1 Summary: 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 δ B ( f )( y ) = ∨{ f ( x ) , x − y ∈ B ( y ) } (1) where ∨ if the supremum (or maximum) operator. f(x) x 1D dilatation example.

Segmentation of X-ray tuffeau images September 4, 2008 18 de 1 Summary: 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 ε B ( f )( y ) = ∧{ f ( x ) , x − y ∈ B ( y ) } (2) where ∧ the infimum (minimum) operator. f(x) x 1D erosion example.

Segmentation of X-ray tuffeau images September 4, 2008 19 de 1 Summary: Morphological tools : Opening and Closing Opening operator γ : γ B = δ B ◦ ε B f(x) x 1D opening example. Closing operator ϕ : ϕ B = ε B ◦ δ B f(x) x 1D closing example.

Segmentation of X-ray tuffeau images September 4, 2008 20 de 1 Summary: Application to µ -tomography image of tuffeau : Opening and Closing filtering original image. After application of ϕ B 1 γ B 1 .

Segmentation of X-ray tuffeau images September 4, 2008 21 de 1 Summary: Application to µ -tomography image of tuffeau : Opening and Closing filtering original image. ϕ B 2 γ B 2 ϕ B 1 γ B 1 .

Segmentation of X-ray tuffeau images September 4, 2008 22 de 1 Summary: Application to µ -tomography image of tuffeau : Opening and Closing filtering original image. ϕ B 3 γ B 3 ϕ B 2 γ B 2 ϕ B 1 γ B 1 .

Segmentation of X-ray tuffeau images September 4, 2008 23 de 1 Summary: Application to µ -tomography image of tuffeau : Opening and Closing filtering original image. ϕ B 4 γ B 4 ϕ B 3 γ B 3 ϕ B 2 γ B 2 ϕ B 1 γ B 1 .

Segmentation of X-ray tuffeau images September 4, 2008 24 de 1 Summary: Application to µ -tomography image of tuffeau : Opening and Closing filtering 4e+07 3.5e+07 3e+07 2.5e+07 2e+07 1.5e+07 1e+07 5e+06 0 0 50 100 150 200 250 grey-level histogram of a filtered image

Segmentation of X-ray tuffeau images September 4, 2008 25 de 1 Summary: Morphological tools : Morphological Gradient g ( x ) = δ B f ( x ) − ε B f ( x ) (3) f(x) x 1D gradient example.

Segmentation of X-ray tuffeau images September 4, 2008 26 de 1 Summary: Morphological tools : Morphological Gradient g ( x ) = δ B f ( x ) − ε B f ( x ) (4) f(x) x 1D gradient example : 1-dilatation.

Segmentation of X-ray tuffeau images September 4, 2008 27 de 1 Summary: Morphological tools : Morphological Gradient g ( x ) = δ B f ( x ) − ε B f ( x ) (5) f(x) x 1D gradient example : 2-erosion.

Segmentation of X-ray tuffeau images September 4, 2008 28 de 1 Summary: Morphological tools : Morphological Gradient g ( x ) = δ B f ( x ) − ε B f ( x ) (6) f(x) x g(x) x 1D gradient example

Segmentation of X-ray tuffeau images September 4, 2008 29 de 1 Summary: Application to µ -tomography image of tuffeau : Morphological gradient original image 1024 pixels. gradient : structuring element 3 pixels

Segmentation of X-ray tuffeau images September 4, 2008 30 de 1 Summary: Morphological tools : Watershed The goal is to identify the influence area of gradient minima. To start the watershed, usually one takes min( g ) f(x) x g(x) x 1D gradient example : gradient.

Segmentation of X-ray tuffeau images September 4, 2008 31 de 1 Summary: Morphological tools : Watershed We propose to take : (max( h ) ∨ min( h )) ∧ min( g ) f(x) x g(x) x watershed.

Segmentation of X-ray tuffeau images September 4, 2008 32 de 1 Summary: Morphological tools : Watershed We propose to take : (max( h ) ∨ min( h )) ∧ min( g ) f(x) x g(x) ��� ��� �� �� �� �� � � ��� ��� ��� ��� �� �� �� �� � � ��� ��� x watershed.

Segmentation of X-ray tuffeau images September 4, 2008 33 de 1 Summary: Morphological tools : Watershed We propose to take : (max( h ) ∨ min( h )) ∧ min( g ) f(x) x g(x) ���������� ���������� ������� ������� �������� �������� ������ ������ ����� ����� ���������� ���������� ������� ������� �������� �������� ������ ������ ����� ����� ���������� ���������� ������� ������� �������� �������� ������ ������ ����� ����� ���������� ���������� ������� ������� �������� �������� ������ ������ ����� ����� x watershed.