# Advances in Image Analysis -free research papers-2011

In electro-static fields and magneto-static fields, the field and its source are two indivisible parts of a physical system. The field is derived from the source, and it naturally reflects the characters of the source distribution. On the other hand, the source may be mathematically inverted from the field. Therefore, the field and its source can be regarded as two domains of a special transform, and either of them can represent the characters of the other. The potential and the field intensity have a similar relationship, which means they are two different presentations of a same physical system. Images can be regarded as a two-dimensional distribution of data. Image transform is the basic technique in image analysis, which finds a clearer and more convenient representation in the transform domain for better analyses. The natural transforms implied in the theory of physical electro-magnetic field just satisfy the need of the transform and feature extraction in image analysis. Moreover, the mathematical forms of electro-magnetic formulas have a unique advantage of the balance between local and global analysis, which is needed in many practical tasks.

In recent years, there have been increasing research efforts in nature inspired methods for image

analysis. Promising results have been obtained in edge detection, corner detection, shape skeletonization,

ear recognition, etc. Existing research focuses on scalar potential field, but the work on vector field

transform is rare. The direct application of the formulas of physical fields is common, but there is much less

work of adjusting and altering the forms of physical formulas to suit practical applications better. Moreover,

most of the existing work in this area takes the image as the source and produces its virtual field, but the

inverse transform from the image as a field to its virtual source is not investigated in previous research

work. In the paper series of this book volume, the authors try to widen the research of physical field

inspired methods in image analysis.

This book volume is the collection of the authorsâ€™ recent original work mainly in the area of physicsinspired methods for image analysis, which provide a new kind of natural representation of image structure

imitating the electro-magnetic field. Three virtual vector field transforms (diffusing vector field, curling

vector field, compressing vector field) are proposed based on the electro-static or magneto-static analogy. A

scalar virtual potential field (relative potential field) is also proposed for image analysis. Besides, two

different virtual source reverse methods (potential source reverse, curling source reverse) are proposed

imitating the physical fields derived from the static charges and static current distribution. The edge vector

field is also presented, and the virtual magnetic field generate by it is also investigated. In the above work,

the basic properties of the virtual fields are analyzed and experimentally investigated, and their possible

applications in image analysis are also studied by experiments. The experimental results indicate the

impressive research value of physical field inspired methods in image analysis.

Other methods proposed in this book volume include: an image segmentation method inspired by

physical deformable grid, a biological swarm inspired method for feature extraction, fractal representation

of image local feature, and a social insect inspired method for task allocation in parallel processing tasks.

The experimental results of the proposed methods show the promising wide application of nature inspired

methods in practice.

Diffusing Vector Field of Gray-Scale Images for Image Segmentation 1

Xiaodong Zhuang, Nikos E. Mastorakis

The Curling Vector Field Transform of Gray-Scale Images: A Magneto-Static Inspired

Approach

9

Xiaodong Zhuang, Nikos E. Mastorakis

Region Shrinking and Image Segmentation based on the Compressing Vector Field 17

Xiaodong Zhuang, Nikos E. Mastorakis

A Novel Field-Source Reverse Transform for Image Structure Representation and Analysis 25

Xiaodong Zhuang, Nikos E. Mastorakis

A Magneto-Statics Inspired Transform for Structure Representation and Analysis of Digital

Images

37

Xiaodong Zhuang, Nikos E. Mastorakis

The Relative Potential Field as a Novel Physics-Inspired Method for Image Analysis 47

Xiaodong Zhuang, Nikos E. Mastorakis

Image Analysis based on the Discrete Magnetic Field Generated by the Virtual Edge Current in

Digital Images

60

Xiaodong Zhuang, Nikos E. Mastorakis

The Local Fuzzy Fractal Dimension as a Feature of Local Complexity for Digital Images and

Signals

75

Xiaodong Zhuang, Nikos E. Mastorakis

Image Processing with the Artificial Swarm Intelligence 86

Xiaodong Zhuang, Nikos E. Mastorakis

The Scale-Rate as the Measurement of Local Spatial and Temporal Complexity in Medical

Images

95

Xiaodong Zhuang, Nikos E. Mastorakis

A Physics-Inspired Model of Image Structure Representation by Deformable Elastic Grid 101

Xiaodong Zhuang, Nikos E. Mastorakis

Task Allocation in Multi-Agent Systems with Swarm Intelligence of Social Insects 107

Xiaodong Zhuang, Nikos E. Mastorakis

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