Image Reconstruction - Ugo Jardonnet

Bibliography. Bibliography II. R. Jones. Connected filtering and segmentation using component trees. Computer Vision and Image Understanding,.
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Image Reconstruction

Image Reconstruction Ugo Jardonnet EPITA Research and Development Laboratory

CSI Seminar, January 2009 The Olena Project

Image Reconstruction

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Image Reconstruction

Bootstrap Collaboration: IGR - Olena The Gustave Roussy Institute is the first European center of fight against the Cancer. Olena is the image processing team of the EPITA Research and Development Laboratory. Objective Image reconstruction of medical images.

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Image Reconstruction

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Image Reconstruction

Bootstrap

Image reconstruction Aim at displaying information from different modalities into a single image.

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Image Reconstruction

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Image Reconstruction

Bootstrap

Segmentation

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Registration

Image Reconstruction

Information Fusion

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Image Reconstruction

Bootstrap

Segmentation

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Registration

Image Reconstruction

Information Fusion

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Image Reconstruction

Bootstrap

Segmentation

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Registration[2]

Image Reconstruction

Information Fusion

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Image Reconstruction

Bootstrap

Segmentation The Olena Project

Registration Image Reconstruction

Information Fusion 7 / 36

Image Reconstruction

Bootstrap

Segmentation The Olena Project

Registration Image Reconstruction

Information Fusion 8 / 36

Image Reconstruction

Outline 1

Watershed Segmentation Watershed Algorithm Segmentation

2

N-clustering Min/Max tree Attribute image Tarjan Union Find N-clustering Algorithm

3

Conclusion

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Image Reconstruction Watershed Segmentation Watershed Algorithm

Outline 1

Watershed Segmentation Watershed Algorithm Segmentation

2

N-clustering Min/Max tree Attribute image Tarjan Union Find N-clustering Algorithm

3

Conclusion

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Image Reconstruction

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Image Reconstruction Watershed Segmentation Watershed Algorithm

Watershed Algorithm

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Image Reconstruction Watershed Segmentation Watershed Algorithm

Defect: Oversegmentation

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Image Reconstruction Watershed Segmentation Segmentation

Outline 1

Watershed Segmentation Watershed Algorithm Segmentation

2

N-clustering Min/Max tree Attribute image Tarjan Union Find N-clustering Algorithm

3

Conclusion

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Image Reconstruction Watershed Segmentation Segmentation

Segmentation

Segmentation techniques based on watershed 1

A gradient image is computed.

2

The gradient image is filtered to suppress inconsistent mimima.

3

A watershed transform is applied on the filtered gradient image.

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Image Reconstruction Watershed Segmentation Segmentation

Results

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Image Reconstruction Watershed Segmentation Segmentation

What if we want only one object?

What if we want only one object? Depending on the filter and its parameters the segmentation will produce more or less clusters. It is not possible to directly obtain an N-cluster segmentation using this process.

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Image Reconstruction N-clustering Min/Max tree

Outline 1

Watershed Segmentation Watershed Algorithm Segmentation

2

N-clustering Min/Max tree Attribute image Tarjan Union Find N-clustering Algorithm

3

Conclusion

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Image Reconstruction

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Image Reconstruction N-clustering Min/Max tree

Image as a 3d Surface

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Image Reconstruction

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Image Reconstruction N-clustering Min/Max tree

Components Inclusion

At a given z level λ, we are able to compute the following set: Sλ = {p | f (p) ≤ λ}, where p ∈ D(f )

Note that we have the following property: Sλ1 ⊂ Sλ2 ⊂ . . . ⊂ Sλn−1 ⊂ Sλn Image’s level sets can be represented by a component tree where node parenthood maps component inclusion. The Olena Project

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Image Reconstruction N-clustering Min/Max tree

Component Tree[4]

240 190 190 240 240 190 120 120 240 240 190 190 120 240 240

ABCDE S240 BDE

C

S190

120 190 240 240 240 S120

D

E

240 190 240 190 190

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Image Reconstruction N-clustering Min/Max tree

Min Tree[1]

In order to avoid redundancy, nodes may be used to store points of Sλi − Sλi+1 [3] This compact form of the component tree is called the min tree since leaf nodes represent image min values.

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Image Reconstruction N-clustering Min/Max tree

Min Tree[1]

A

B

B

A

A A

S240 B

D

D

A

A

B

B

D

A

A

E

B

A

A

A

S190 S120 D

A

B

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A

C

c

B

E

C

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Image Reconstruction N-clustering Min/Max tree

Min/Max Tree

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Image Reconstruction N-clustering Attribute image

Outline 1

Watershed Segmentation Watershed Algorithm Segmentation

2

N-clustering Min/Max tree Attribute image Tarjan Union Find N-clustering Algorithm

3

Conclusion

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Image Reconstruction N-clustering Attribute image

Attribute Filtering

0

1

2

3

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Image Reconstruction

cutting point

4

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Image Reconstruction N-clustering Attribute image

Attribute image Let’s consider a given image ima: 1

We compute the min tree representation of ima.

2

The volume of a given component at a given level, represented by a node p, is defined as follows. For all pi such as parent(pi ) = p, X X volume(p) := volume(pi ) + (pi ∗ |ima(p) − ima(pi )|)

3

Finally, we produce an output image where output(p) = volume(p).

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Image Reconstruction N-clustering Attribute image

Attribute image Local minima are minimum values of the attribute image

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Image Reconstruction N-clustering Tarjan Union Find

Outline 1

Watershed Segmentation Watershed Algorithm Segmentation

2

N-clustering Min/Max tree Attribute image Tarjan Union Find N-clustering Algorithm

3

Conclusion

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Image Reconstruction N-clustering Tarjan Union Find

Union Find

Union Find Algorithm Segments a set of elements into several disjoint sets. Mainly performs two operations: Find: determines which set a particular element belongs to. Union: merges two sets into a single set.

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Image Reconstruction N-clustering N-clustering Algorithm

Outline 1

Watershed Segmentation Watershed Algorithm Segmentation

2

N-clustering Min/Max tree Attribute image Tarjan Union Find N-clustering Algorithm

3

Conclusion

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Image Reconstruction N-clustering N-clustering Algorithm

Algorithm

Scan points in the increasing order of attribute. Current point is unified with points previously processed only. If union result in merging two segments, decrease the counter of remaining segment.

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Image Reconstruction N-clustering N-clustering Algorithm

Algorithm 3-Clustering of a sample image: 128 156 165 117

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90

131 108 151

87

118 109 167

73

125 157 117

Image Reconstruction

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Image Reconstruction N-clustering N-clustering Algorithm

Algorithm 3-Clustering of a sample image: 128 156 165 117

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90

131 108 151

87

118 109 167

73

125 157 117

Image Reconstruction

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Image Reconstruction N-clustering N-clustering Algorithm

Algorithm 3-Clustering of a sample image: 128 156 165 117

The Olena Project

90

131 108 151

87

118 109 167

73

125 157 117

Image Reconstruction

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Image Reconstruction N-clustering N-clustering Algorithm

Algorithm 3-Clustering of a sample image: 128 156 165 117

The Olena Project

90

131 108 151

87

118 109 167

73

125 157 117

Image Reconstruction

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Image Reconstruction N-clustering N-clustering Algorithm

Algorithm 3-Clustering of a sample image: 128 156 165 117

The Olena Project

90

131 108 151

87

118 109 167

73

125 157 117

Image Reconstruction

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Image Reconstruction N-clustering N-clustering Algorithm

Algorithm 3-Clustering of a sample image: 128 156 165 117

The Olena Project

90

131 108 151

87

118 109 167

73

125 157 117

Image Reconstruction

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Image Reconstruction N-clustering N-clustering Algorithm

Algorithm 3-Clustering of a sample image: 128 156 165 117

The Olena Project

90

131 108 151

87

118 109 167

73

125 157 117

Image Reconstruction

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Image Reconstruction N-clustering N-clustering Algorithm

Algorithm 3-Clustering of a sample image: 128 156 165 117

The Olena Project

90

131 108 151

87

118 109 167

73

125 157 117

Image Reconstruction

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Image Reconstruction N-clustering N-clustering Algorithm

Algorithm 3-Clustering of a sample image: 128 156 165 117

The Olena Project

90

131 108 151

87

118 109 167

73

125 157 117

Image Reconstruction

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Image Reconstruction N-clustering N-clustering Algorithm

Algorithm 3-Clustering of a sample image: 128 156 165 117

The Olena Project

90

131 108 151

87

118 109 167

73

125 157 117

Image Reconstruction

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Image Reconstruction N-clustering N-clustering Algorithm

Algorithm 3-Clustering of a sample image: 128 156 165 117

The Olena Project

90

131 108 151

87

118 109 167

73

125 157 117

Image Reconstruction

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Image Reconstruction N-clustering N-clustering Algorithm

Algorithm 3-Clustering of a sample image: 128 156 165 117

The Olena Project

90

131 108 151

87

118 109 167

73

125 157 117

Image Reconstruction

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Image Reconstruction N-clustering N-clustering Algorithm

Algorithm 3-Clustering of a sample image: 128 156 165 117

The Olena Project

90

131 108 151

87

118 109 167

73

125 157 117

Image Reconstruction

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Image Reconstruction N-clustering N-clustering Algorithm

Algorithm 3-Clustering of a sample image: 128 156 165 117

The Olena Project

90

131 108 151

87

118 109 167

73

125 157 117

Image Reconstruction

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Image Reconstruction N-clustering N-clustering Algorithm

Algorithm 3-Clustering of a sample image: 128 156 165 117

The Olena Project

90

131 108 151

87

118 109 167

73

125 157 117

Image Reconstruction

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Image Reconstruction N-clustering N-clustering Algorithm

Algorithm 3-Clustering of a sample image: 128 156 165 117

The Olena Project

90

131 108 151

87

118 109 167

73

125 157 117

Image Reconstruction

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Image Reconstruction N-clustering N-clustering Algorithm

Algorithm 3-Clustering of a sample image: 128 156 165 117

The Olena Project

90

131 108 151

87

118 109 167

73

125 157 117

Image Reconstruction

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Image Reconstruction N-clustering N-clustering Algorithm

Algorithm 3-Clustering of a sample image: 128 156 165 117

The Olena Project

90

131 108 151

87

118 109 167

73

125 157 117

Image Reconstruction

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Image Reconstruction Conclusion

Conclusion

N-clustering Produces N distincts object.

We don’t control how clusters grow. We still have unexpected results.

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Image Reconstruction Conclusion

Outstanding Points and Future Work

We are able to compare segmentations using different attributes.

Use same tools to perform filtering, and then apply the Watershed transform.

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Image Reconstruction

Bibliography

Bibliography I C. Berger, Th. Géraud, R. Levillain, N. Widynsky, A. Baillard, and E. Bertin. Effective component tree computation with application to pattern recognition in astronomical imaging. IEEE International Conference on Image Processing., 2007. U. Jardonnet. Fast image registration. Technical report, Laboratoire de Recherche et Développement d’EPITA, 2008.

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Image Reconstruction

Bibliography

Bibliography II

R. Jones. Connected filtering and segmentation using component trees. Computer Vision and Image Understanding, 75(3):215–228, 1999. Fernand Meyer. Levelings, image simplification filters for segmentation. jmiv, 20(1–2):59–72, 2004.

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