Eugen Zaharescu-PROJECT STATEMENT-Morphological Medical Image Indexing and Classification in Metadata Digital Library
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This document outlines PhD. Assoc. Professor Eugen ZAHARESCU's project on developing an advanced mathematical model for analyzing and processing medical images using mathematical morphology methods. The project aims to 1) implement modern mathematical methods for solving problems in medical imaging, 2) collect, index and classify medical images and store them in a digital library, and 3) develop a software system for medical imaging using a formal model based on mathematical morphology. ZAHARESCU has done research on extending mathematical morphology to logarithmic image processing and developing new morphological operators for medical image enhancement.
![PhD. Assoc. Professor Eugen ZAHARESCU - Project Statement
Finally, I have developed algorithmic and mathematical concepts and tools used as data analysis and
modeling for machine learning, computer vision and image understanding.
In the future I would like to work on the challenging problems of multivariate image morphological
segmentation. Also I would investigate how a multi-scale decomposition could lead to a better
segmentation approach. I would like to combine the ideas of hierarchical decomposition and
variation techniques with those of other branches of mathematics and engineering to come up with
more effective way of approaching the problems in medical imagery.
3. Mathematical Morphology Theory. Basic Concepts
The Mathematical Morphology (MM) theory represents a powerful image processing framework
based on order and set theory and Euclidian geometry. The main advantage of morphological
operators lies in their inherent ability to exploit the spatial relationships of pixels. Moreover, they can
also adapt to vector strategies in order to process multivariate data. Based upon the MM theory, the
precise detection of the object’s pixels along with pertinent classification features, proved to be more
computationally efficient then other approaches (i.e. statistical methods concentrate on individual
pixel values and therefore they are more computation-intensive).
For recalling the preliminary definitions of some basic morphological operators and the theory of
MM, the reader should refer to [7] and [9].
Let f : D → T be a grayscale image, with D the discrete coordinate grid while T represents the set of
possible grey values. In short, MM studies the transformations of an image, when it interacts through
operators with a matching pattern E, called structuring element (SE). E is considered as a subset of
D. At the very basis of the MM operators pyramid are the morphological operators, dilation (E ( f ))
and erosion (E ( f)).
Subsequently, a multitude of operators is derived from dilation and erosion such as opening
E(f)=Ě(E(f)), closing E(f)=Ě(E(f)) and morphological gradient grad(f)=E(f)-E(f).
The skeleton of the set X represents the union of all intersections of the differences between the
erosion and its opening through variable sized discs E (i.e. White Top-Hat transforms) [7]:
SK ( X ) =
0 0
{ ε λE (X ) γ μE ( ε λE (X )) } (1)
The Hit-or-Miss transform, locates either pixels from erosion X-E1 (i.e. “hit") and from erosion Xc
-
E2
c
, (i.e. “miss") [9]:
HMTE(X ) = εE1
( X ) εE2
( X c
) (2)
Using these basic concepts I have developed a morphological algorithm for automated color objects
detection and classification presented in [11] (Fig. 1, 2 and 3).
Figure 1. Experiments for automated color objects classification](https://image.slidesharecdn.com/c07c9736-ea15-4af7-87cb-31f79e8d495a-160327185218/85/Eugen-Zaharescu-PROJECT-STATEMENT-Morphological-Medical-Image-Indexing-and-Classification-in-Metadata-Digital-Library-2-320.jpg)
![PhD. Assoc. Professor Eugen ZAHARESCU - Project Statement
a) Original gray-scale image. b) Segmentation by watershed c) Constrained watershed overlayed on
the original image
Figure 2. Cornea cells marking in a very poor quality microscopic image
a) Extract the lateral ventricle from an MRI image of the
brain.
b) Segmentation and separation of superposed blood cells
Figure 3. Different morphological experiments in biomedical imagery
4. New Morphological Operators in Logarithmic Image Processing Theory
The Logarithmic Image Processing (LIP) theory is a mathematical framework that provides a set of
specific algebraic and functional operations and structures that are well adapted to the representation
and processing of non-linear images, and more generally of non-linear signals, valued in a bounded
intensity range.
This very well structured theory determined using the logarithmic image representation in my
approach for defining a new set of mathematical morphology operators based upon structuring
elements with a variable geometrical shape or adaptable structuring elements.
Therefore, I have defined and analyzed new multiplicative logarithmic morphological operators used
in medical image enhancement. Finally, the experimental results reveal that this method has wide
potential areas of impact which may include: Digital X-ray, Digital Mammography, Computer
Tomography Scans, Nuclear Magnetic Resonance Imagery and Telemedicine Applications.
In the paper [12] I have presented several possibilities of defining structuring elements with a
variable geometrical shape within the logarithmic image processing theory, i.e. using only vector-
oriented operations with images represented as gray-tone functions operands.
In fact, we can demonstrate that all the classical mathematical morphology operators are solely a
particular case of the logarithmic mathematical morphology operators, based upon the definition of
the structuring elements with a variable geometrical shape or adaptable structuring elements.
At least three categories of mathematical morphology operators can be defined within the context of
a logarithmic image representation:
1. Multiplicative logarithmic morphological operators;
2. Additive logarithmic morphological operators;](https://image.slidesharecdn.com/c07c9736-ea15-4af7-87cb-31f79e8d495a-160327185218/85/Eugen-Zaharescu-PROJECT-STATEMENT-Morphological-Medical-Image-Indexing-and-Classification-in-Metadata-Digital-Library-3-320.jpg)
![PhD. Assoc. Professor Eugen ZAHARESCU - Project Statement
3. Additive-multiplicative logarithmic morphological operators;
As an example, here are the definitions of multiplicative logarithmic morphological operators from
the basic levels of their pyramid following the classical morphological paradigm.
4.1 Multiplicative Logarithmic Morphological Erosion
Definition 1: Multiplicative logarithmic morphological erosion for the image f by structuring
element g, represents the gray-tone function defined as follows:
(f ML ğ)( x ) = inf{ k (f ( y) - g( y-x )) | y 2
} . (3)
where ğ is defined as: xn
, ğ(x)=g(-x) and represents LIP product of a gray-tone function
with a real scalar.
Within LIP model we will obtain the following definition:
( f ML ğ)( x ) =inf{
( ( ( ) - ( - ))) - ( - ( ( ) - ( - )))
( ( ( ) - ( - ))) ( - ( ( ) - ( - )))
k k
k k
M f y g y x M f y g y x
M
M f y g y x M f y g y x
| y2
} .
(4)
4.2 Multiplicative Logarithmic Morphological Dilation
Definition 2: Multiplicative logarithmic morphological dilation for the image f by structuring
element g, represents the gray-tone function defined as follows:
(f ML ğ)(x) = sup{k(f (y) + g( y-x ))| y2
} . (5)
where ğ is defined as: xn
, ğ(x)=g(-x) and represents LIP product of a gray-tone function
with a real scalar.
Within LIP model we will obtain the following definition:
( f ML ğ)( x )= =sup{
( ( ( ) ( - ))) - ( - ( ( ) ( - )))
( ( ( ) ( - ))) ( - ( ( ) ( - )))
k k
k k
M f y g y x M f y g y x
M
M f y g y x M f y g y x
| y2
}
(6)
Using these basic concepts I have developed new logarithmic morphological operators for color
image enhancement as presented in [12] (Fig. 4).
a) Contrast and sharpness enhancement using logarithmic
morphological transforms in a color image of eye retina
b) Contrast and sharpness enhancement using logarithmic
morphological transforms in a color image of blood vessels
Figure 4. Experiments for logarithmic morphological enhancement in medical imagery](https://image.slidesharecdn.com/c07c9736-ea15-4af7-87cb-31f79e8d495a-160327185218/85/Eugen-Zaharescu-PROJECT-STATEMENT-Morphological-Medical-Image-Indexing-and-Classification-in-Metadata-Digital-Library-4-320.jpg)
![PhD. Assoc. Professor Eugen ZAHARESCU - Project Statement
5. References
[1] J. Angulo, J. Serra, "Color segmentation by ordered mergings", Proc. of IEEE International Conference on Image
Processing (ICIP'03), IEEE, Vol. 2, Barcelona, Spain, Sept. 2003, p. 125-128.
[2] A. Hanbury, J.Serra, "Color Image Analysis in 3D-polar coordinates", Dans Proc. of DAGM symposium, Vienna,
April 2003.
[3] A. Hanbury and J. Serra, Morphological Operators on the Unit Circle, IEEE Transactions on Image Processing,
10(12) (2001) 1842-1850.
[4] M. Jourlin, J.C. Pinoli, “Logarithmic Image Processing. The mathematical and physical framework for the
representation and processing of transmitted images”, Advances in Imaging and Electron Physics, vol. 115:130-
196, 2001.
[5] V. Pătraşcu, V. Buzuloiu, “A Mathematical Model for Logaritmic Image Processing”, The 5-th World Multi-
Conference on Systemics, Cybernetics and Informatics, SCI2001, July 22-25, 2001, Orlando, USA
[6] P. Salambier, "Morphological Multi-scale Segmentation for Image Coding", Signal Processing, Vol. 38, pp. 359-
386, 1994.
[7] J. Serra, “Image Analysis and Mathematical Morphology” Academic Press, London, 1982.
[8] J. Serra, Morphological Segmentation of Color Images by Merging of Partitions, in Proc. of International
Symposium on Mathematical Morphology (ISMM '05), Kluwer, 2005,151-176.
[9] P. Soille, “Morphological Image Analysis”, Springer-Verlag, Berlin, Heidelberg, New York, 1999.
[10]C. Vertan, M. Zamfir, E.Zaharescu, V.Buzuloiu, C. Fernandez-Maloigne, “Nonlinear Color Image Filtering by
Color to Planar Shape Matching”, ICIP 2003, Barcelona, Spain, 2003.
[11]E. Zaharescu, "Morphological Algorithm for Color Objects Classification", IEEE Computer Society Proceedings
of the Fourth Balkan Conference in Informatics, 17-19 September 2009, Thessaloniki, Greece, pag.152-156,
Library of Congress No. 2009934322, (ISBN 978-0-7695-3783-2)
[12]E. Zaharescu, “Morphological Enhancement of Medical Images in a Logarithmic Image Environment”, IEEE
Proceedings of International Symposium on Signals Circuits and Systems-ISSCS 2007, Iaşi, Romania, 2007,
pag.352-356 (ISSN 1-4244-0968-1) ISI-Inspec® http://ieeexplore.ieee.org/xpl/
[13]E. Zaharescu, M. Zamfir, C.Vertan: “Color Morphology-like Operators based on Color Geometric Shape
Characteristics”, Proc. of International Symposium on Signals Circuits and Systems SCS 2003, Iaşi, Romania,
2003.](https://image.slidesharecdn.com/c07c9736-ea15-4af7-87cb-31f79e8d495a-160327185218/85/Eugen-Zaharescu-PROJECT-STATEMENT-Morphological-Medical-Image-Indexing-and-Classification-in-Metadata-Digital-Library-5-320.jpg)
Eugen Zaharescu-PROJECT STATEMENT-Morphological Medical Image Indexing and Classification in Metadata Digital Library
- 1. PhD. Assoc. Professor Eugen ZAHARESCU - Project Statement Morphological Medical Image Indexing and Classification in Metadata Digital Library - Project Statement - PhD. Assoc. Professor Eugen ZAHARESCU 1. Project Research Objectives The main research activity of this project will be focused on the development of an advanced mathematical model that can be used for the analysis and processing of the medical images (e.g. obtained by medical ultrasonography). By involving researchers from Mathematics, Medicine, Informatics and Electronics this project has wide interdisciplinary and multi-institutional characteristics. The first project research objective is the implementation of modern mathematical methods for the solution of difficult problems arising in the field of medical imagery. Subsequently, a complex set of experiments will be accomplished in order to validate the theoretical models proposed. By developing a complex formal model based on the mathematical morphology, I will build the theoretical basis for the development of a complete and modern software system for medical imagery (e.g. virtual medical ultrasonography). The secondary project research objectives will include data/image collection, selection, indexing and classification. Subsequently, they will be stored in a hypermedia repository and they will be integrated in a metadata digital library. A Web portal will facilitate the access to this knowledge base throughout Internet/Intranet network for every member of academic and scientific community. Moreover this can be used to implement an expert system for virtual medical imagery. Fundamental theoretical research methods will be applied in mathematical morphology. Mathematical morphology is a recent algebraic theory based on the Lattice structure and that proposes a shape driven image processing approach. Mathematical morphology leads to methods and processes that simplify the structure of an image by eliminating irrelevant details whatsoever, but that maintain the main shape characteristics, by the end. Likewise, the mathematical morphology combined with the logarithmic images processing theory can produce very useful methods for nonlinear image enhancement. Possible extensions of the morphological methods in the framework of logarithmic images representations appear to be very promising. Using multiplicativ-logharithmic morphological operators, the common classical medical imagery will be transformed into virtual medical imagery. 2. Statement of Research Interest My research interest ranges from mathematical morphology, used in image analysis and processing, to large scale image ontology generation. I have started with the extension of mathematical morphology theory to multivariate images and I have continued with the exploration of adapting the whole set of morphological operators for the images represented in a logarithmic environment.
- 2. PhD. Assoc. Professor Eugen ZAHARESCU - Project Statement Finally, I have developed algorithmic and mathematical concepts and tools used as data analysis and modeling for machine learning, computer vision and image understanding. In the future I would like to work on the challenging problems of multivariate image morphological segmentation. Also I would investigate how a multi-scale decomposition could lead to a better segmentation approach. I would like to combine the ideas of hierarchical decomposition and variation techniques with those of other branches of mathematics and engineering to come up with more effective way of approaching the problems in medical imagery. 3. Mathematical Morphology Theory. Basic Concepts The Mathematical Morphology (MM) theory represents a powerful image processing framework based on order and set theory and Euclidian geometry. The main advantage of morphological operators lies in their inherent ability to exploit the spatial relationships of pixels. Moreover, they can also adapt to vector strategies in order to process multivariate data. Based upon the MM theory, the precise detection of the object’s pixels along with pertinent classification features, proved to be more computationally efficient then other approaches (i.e. statistical methods concentrate on individual pixel values and therefore they are more computation-intensive). For recalling the preliminary definitions of some basic morphological operators and the theory of MM, the reader should refer to [7] and [9]. Let f : D → T be a grayscale image, with D the discrete coordinate grid while T represents the set of possible grey values. In short, MM studies the transformations of an image, when it interacts through operators with a matching pattern E, called structuring element (SE). E is considered as a subset of D. At the very basis of the MM operators pyramid are the morphological operators, dilation (E ( f )) and erosion (E ( f)). Subsequently, a multitude of operators is derived from dilation and erosion such as opening E(f)=Ě(E(f)), closing E(f)=Ě(E(f)) and morphological gradient grad(f)=E(f)-E(f). The skeleton of the set X represents the union of all intersections of the differences between the erosion and its opening through variable sized discs E (i.e. White Top-Hat transforms) [7]: SK ( X ) = 0 0 { ε λE (X ) γ μE ( ε λE (X )) } (1) The Hit-or-Miss transform, locates either pixels from erosion X-E1 (i.e. “hit") and from erosion Xc - E2 c , (i.e. “miss") [9]: HMTE(X ) = εE1 ( X ) εE2 ( X c ) (2) Using these basic concepts I have developed a morphological algorithm for automated color objects detection and classification presented in [11] (Fig. 1, 2 and 3). Figure 1. Experiments for automated color objects classification
- 3. PhD. Assoc. Professor Eugen ZAHARESCU - Project Statement a) Original gray-scale image. b) Segmentation by watershed c) Constrained watershed overlayed on the original image Figure 2. Cornea cells marking in a very poor quality microscopic image a) Extract the lateral ventricle from an MRI image of the brain. b) Segmentation and separation of superposed blood cells Figure 3. Different morphological experiments in biomedical imagery 4. New Morphological Operators in Logarithmic Image Processing Theory The Logarithmic Image Processing (LIP) theory is a mathematical framework that provides a set of specific algebraic and functional operations and structures that are well adapted to the representation and processing of non-linear images, and more generally of non-linear signals, valued in a bounded intensity range. This very well structured theory determined using the logarithmic image representation in my approach for defining a new set of mathematical morphology operators based upon structuring elements with a variable geometrical shape or adaptable structuring elements. Therefore, I have defined and analyzed new multiplicative logarithmic morphological operators used in medical image enhancement. Finally, the experimental results reveal that this method has wide potential areas of impact which may include: Digital X-ray, Digital Mammography, Computer Tomography Scans, Nuclear Magnetic Resonance Imagery and Telemedicine Applications. In the paper [12] I have presented several possibilities of defining structuring elements with a variable geometrical shape within the logarithmic image processing theory, i.e. using only vector- oriented operations with images represented as gray-tone functions operands. In fact, we can demonstrate that all the classical mathematical morphology operators are solely a particular case of the logarithmic mathematical morphology operators, based upon the definition of the structuring elements with a variable geometrical shape or adaptable structuring elements. At least three categories of mathematical morphology operators can be defined within the context of a logarithmic image representation: 1. Multiplicative logarithmic morphological operators; 2. Additive logarithmic morphological operators;
- 4. PhD. Assoc. Professor Eugen ZAHARESCU - Project Statement 3. Additive-multiplicative logarithmic morphological operators; As an example, here are the definitions of multiplicative logarithmic morphological operators from the basic levels of their pyramid following the classical morphological paradigm. 4.1 Multiplicative Logarithmic Morphological Erosion Definition 1: Multiplicative logarithmic morphological erosion for the image f by structuring element g, represents the gray-tone function defined as follows: (f ML ğ)( x ) = inf{ k (f ( y) - g( y-x )) | y 2 } . (3) where ğ is defined as: xn , ğ(x)=g(-x) and represents LIP product of a gray-tone function with a real scalar. Within LIP model we will obtain the following definition: ( f ML ğ)( x ) =inf{ ( ( ( ) - ( - ))) - ( - ( ( ) - ( - ))) ( ( ( ) - ( - ))) ( - ( ( ) - ( - ))) k k k k M f y g y x M f y g y x M M f y g y x M f y g y x | y2 } . (4) 4.2 Multiplicative Logarithmic Morphological Dilation Definition 2: Multiplicative logarithmic morphological dilation for the image f by structuring element g, represents the gray-tone function defined as follows: (f ML ğ)(x) = sup{k(f (y) + g( y-x ))| y2 } . (5) where ğ is defined as: xn , ğ(x)=g(-x) and represents LIP product of a gray-tone function with a real scalar. Within LIP model we will obtain the following definition: ( f ML ğ)( x )= =sup{ ( ( ( ) ( - ))) - ( - ( ( ) ( - ))) ( ( ( ) ( - ))) ( - ( ( ) ( - ))) k k k k M f y g y x M f y g y x M M f y g y x M f y g y x | y2 } (6) Using these basic concepts I have developed new logarithmic morphological operators for color image enhancement as presented in [12] (Fig. 4). a) Contrast and sharpness enhancement using logarithmic morphological transforms in a color image of eye retina b) Contrast and sharpness enhancement using logarithmic morphological transforms in a color image of blood vessels Figure 4. Experiments for logarithmic morphological enhancement in medical imagery
- 5. PhD. Assoc. Professor Eugen ZAHARESCU - Project Statement 5. References [1] J. Angulo, J. Serra, "Color segmentation by ordered mergings", Proc. of IEEE International Conference on Image Processing (ICIP'03), IEEE, Vol. 2, Barcelona, Spain, Sept. 2003, p. 125-128. [2] A. Hanbury, J.Serra, "Color Image Analysis in 3D-polar coordinates", Dans Proc. of DAGM symposium, Vienna, April 2003. [3] A. Hanbury and J. Serra, Morphological Operators on the Unit Circle, IEEE Transactions on Image Processing, 10(12) (2001) 1842-1850. [4] M. Jourlin, J.C. Pinoli, “Logarithmic Image Processing. The mathematical and physical framework for the representation and processing of transmitted images”, Advances in Imaging and Electron Physics, vol. 115:130- 196, 2001. [5] V. Pătraşcu, V. Buzuloiu, “A Mathematical Model for Logaritmic Image Processing”, The 5-th World Multi- Conference on Systemics, Cybernetics and Informatics, SCI2001, July 22-25, 2001, Orlando, USA [6] P. Salambier, "Morphological Multi-scale Segmentation for Image Coding", Signal Processing, Vol. 38, pp. 359- 386, 1994. [7] J. Serra, “Image Analysis and Mathematical Morphology” Academic Press, London, 1982. [8] J. Serra, Morphological Segmentation of Color Images by Merging of Partitions, in Proc. of International Symposium on Mathematical Morphology (ISMM '05), Kluwer, 2005,151-176. [9] P. Soille, “Morphological Image Analysis”, Springer-Verlag, Berlin, Heidelberg, New York, 1999. [10]C. Vertan, M. Zamfir, E.Zaharescu, V.Buzuloiu, C. Fernandez-Maloigne, “Nonlinear Color Image Filtering by Color to Planar Shape Matching”, ICIP 2003, Barcelona, Spain, 2003. [11]E. Zaharescu, "Morphological Algorithm for Color Objects Classification", IEEE Computer Society Proceedings of the Fourth Balkan Conference in Informatics, 17-19 September 2009, Thessaloniki, Greece, pag.152-156, Library of Congress No. 2009934322, (ISBN 978-0-7695-3783-2) [12]E. Zaharescu, “Morphological Enhancement of Medical Images in a Logarithmic Image Environment”, IEEE Proceedings of International Symposium on Signals Circuits and Systems-ISSCS 2007, Iaşi, Romania, 2007, pag.352-356 (ISSN 1-4244-0968-1) ISI-Inspec® http://ieeexplore.ieee.org/xpl/ [13]E. Zaharescu, M. Zamfir, C.Vertan: “Color Morphology-like Operators based on Color Geometric Shape Characteristics”, Proc. of International Symposium on Signals Circuits and Systems SCS 2003, Iaşi, Romania, 2003.