Image Reconstruction Ugo Jardonnet EPITA Research and Development Laboratory
CSI Seminar, January 2009 The Olena Project
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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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Bootstrap
Image reconstruction Aim at displaying information from different modalities into a single image.
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.
N-clustering Min/Max tree Attribute image Tarjan Union Find N-clustering Algorithm
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Conclusion
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Image Reconstruction N-clustering Min/Max tree
Image as a 3d Surface
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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
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.
N-clustering Min/Max tree Attribute image Tarjan Union Find N-clustering Algorithm
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Conclusion
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Image Reconstruction N-clustering Attribute image
Attribute Filtering
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cutting point
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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.
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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 )|)
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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
N-clustering Min/Max tree Attribute image Tarjan Union Find N-clustering Algorithm
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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.
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.
Algorithm 3-Clustering of a sample image: 128 156 165 117
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131 108 151
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118 109 167
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125 157 117
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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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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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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.
Efficient computation of the singular value decomposition with applications to least squares problems. Technical Report CS-94-257, institut, Knoxville, TN, USA,.
Edit distance. Implementation. Python Implementation import numpy as np def levenshtein(s1, s2):. "Calculates the Levenshtein distance between a and b.".
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