Nature has enormous power and intelligence behind its common daily appearance, and it is generous. The development of human society relies on natural resources in every area (both material and spiritual). We learn in it and from it, virtually as part of it. Nature-inspired systems and methods have a long history in human science and technology. For example, in the area of computer science, the recent well-known ones include the artificial neural network, genetic algorithm and swarm intelligence, which solve hard problems by imitating mechanisms in nature. Nature-inspired methods are also being quickly developed and applied in other areas. In this book, we just try to pick up a drop from the sea of nature’s intelligence, and apply it in a specific area. We hope that it may inspire the readers’ interest of nature’s intelligence when exploring in their own areas of science and technology.
Traditional image processing methods usually take images as data sets or mathematical functions. In our idea of nature-inspired methods, images are more like the imitation of certain natural entities (such as electric charges, currents, etc.) simulated in computer. The evolutions of such virtual entities can be simulated according to corresponding natural laws and the simulation result can be studied for possible utilization in practical image processing tasks. Nowadays, nature-inspired methods in image processing have attracted more and more attention and research efforts. Physics and biology are the two main sources from which most of such methods have derived. Related work has achieved promising results in practical tasks, which indicate that it is a direction potentially leading to breakthroughs of new image analysis techniques. Methods inspired by physical electro-magnetic field make up a branch of this field, which have been successfully applied in the practical applications including: recognition of human ear, face and gait; extraction of corner, edge, and shape skeleton in images. The existing methods inspired by electro-magnetic theory generally belong to two categories: analysis of the virtual field generated by the image (such as the “force field transform”) and deforming a shape or curve under the virtual force field generated by the image (such as the “active counter model”).
The beginning of the research introduced in this book was in 2006, after we read a paper about “force field energy functionals for image feature extraction” (David J. Hurley, Mark S. Nixon, John N. Carter, 2002). This paper inspired our strong interest of natural analogies in image processing. Since then, we have been exploring in the area of nature-inspired image analysis for years and have published a series of papers about our original methods and results. These methods are mainly inspired by the theory of electro-magnetic field, which reveal the structure properties of the image by electro-magnetics inspired transforms. In these transforms, the formulas in electro-magnetic theory are adjusted to more generalized forms in order to suit practical image analysis tasks, and some novel viewpoints which take the image as a virtual field are presented. Several types of methods have been proposed from different aspects of field theory (vector field, scalar potential field, and field source distribution), which indicates that the physics inspired virtual field is a novel way of designing new effective image transforms.
Nature-inspired methodology itself means continuous exploration in the rich resource of the intelligence shown by nature. Therefore, this book does not mean the final conclusion of the authors’on-going work. Further promising results in both theory and practice are expected and we hope our research attempts shown in the book may inspire new ideas of others, which will surely be much more valuable than the book itself.

Preface iii

Acknowledgements iv

1 Review 1

1.1 Literature Review 1

1.2 Overview of The Book 3

2 Electro-Statics Inspired Methods 5

2.1 The Relative Potential Field Inspired by Physical Electro-Static Field 5

      2.1.1 The Relative Potential Field of Gray-Scale Images 6

      2.1.2 The Property of The Relative Potential Field 7

      2.1.3 Image Segmentation Based on The Relative Potential Field 9

2.2 Vector Field Methods Inspired by Electro-Static Field 17

      2.2.1 The Diffusing Vector Field of Gray-Scale Images 18

      2.2.1.1 The Diffusing Vector Field of Gray-Scale Images 18

      2.2.1.2 The Diffusing Vector Field of Images 19

      2.2.1.3 The Primitive Area In The Diffusing Vector Field 22

      2.2.1.4 Diffusing Centers in The Primitive Area 22

      2.2.1.5 Primitive Area Extraction by The Area-Expanding Method 23

      2.2.1.6 Gray-Scale Image Segmentation Based on The Primitive Area Extraction 25

      2.2.2 The Compressing Vector Field of Gray-Scale Images 27

      2.2.2.1 The Definition of The Compressing Vector Field 27

      2.2.2.2 Additional Border Force for Compressing Vector Field in Border Regions 28

      2.2.2.3 The Extraction of Region Center Points 32

      2.2.2.4 The Extraction of Primitive Regions 34

      2.2.2.5 Gray-Scale Image Segmentation in The Compressing Vector Field 34

2.3 Electro-Statics Inspired Source Reversing for Gray-Scale Images 36

      2.3.1 The Relationship Between the Electro-Static Field and The Field Source 36

      2.3.2 The Source-Reverse Transform for Digital Images 37

      2.3.3 The Virtual Field Source as the Representation of Image Structure 38

      2.3.4 Region Border Detection Based on The Source-Reverse Transform 41

      2.3.5 The Opposite Transform From The Virtual Source to The Restored Image 42

      2.3.6 Data Reduction of The Virtual Field Source 43

3 Magneto-Statics Inspired Methods 45

3.1 The Virtual Edge Current in Gray-Scale Images 45

      3.1.1 The Spatial Property of The Magnetic Field Generated by Stable Currents 45

      3.1.1.1 The Magnetic Field of The Current in A Straight Wire and Its Spatial Property 45

      3.1.1.2 The Magnetic Field of The Current in A Closed Wire With Arbitrary Shape and Its Spatial Property 46

      3.1.2 The Tangent Edge Vector for Simple Image Regions 47

      3.1.2.1 The Definition of The Tangent Edge Vector 48

      3.1.2.2 The Spatial Property of The Virtual Magnetic Field Generated by The Set of Tangent Edge Vectors 49

      3.1.3 The Virtual Edge Current in Digital Images 52

      3.1.4 Image Segmentation Based on The Virtual Edge Current 55

      3.1.5 The Influence of Different Edge Intensity Thresholds on Border Formation 58

3.2 The Curling Vector Field Transform of Gray-Scale Images 60

      3.2.1 The Definition of The Curling Vector 60

      3.2.2 The Definition of The Curling Vector Field Transform 61

      3.2.3 Image Segmentation in The Curling Vector Field 63

      3.2.3.1 The Rotating Direction and Base Points of Rotating Expansion 63

      3.2.3.2 Primitive Region Extraction in The Curling Vector Field 65

      3.2.3.3 Real World Image Segmentation Based on The Curling Vector Field 66

3.3 The Curl Source Reversing for Digital Images 68

      3.3.1 The Relationship Between The Magnetic Field and Its Field Source 68

      3.3.2 The Virtual Curl Source Reversing 68

      3.3.3 The Spatial Properties of The Virtual Curl Source for Digital Images 70

      3.3.4 The Opposite Transform Form The Virtual Curl Source to The Restored Image 75

4 Relative Field Method on Image Sequence Processing 79

4.1 The 3D Relative Potential Field of Image Sequences 79

      4.1.1 The Electro-Static Potential and Its Spatial Property 80

      4.1.2 A General Form of Virtual Potential Field for Images 80

      4.1.3 The Definition of 3D Relative Potential Field 81

4.2 The Spatial Characteristics of The 3D Relative Potential Field 81

4.3 3D Segmentation of Image Sequence in The Relative Potential Field 88

      4.3.1 The 3D Segmentation Results for The Testing Image Sequences 88

      4.3.2 The 3D Segmentation Results for The Real-World Image Sequences 93

5 Relative Field Method on Color Image Processing 129

5.1 The Definition of The Relative Potential for Color Images 129

      5.1.1 A general form of virtual potential field for 2D images 129

      5.1.2 The Relative Potential Field for Color Images 130

5.2 The Spatial Property of The Color Relative Potential Field 133

5.3 Color Image Segmentation in The Color Relative Potential Field 135

5.4 The Preprocessing of Brightness Normalization 141

6 Summary and Discussion 151

6.1 The Transformation Among Different Patterns (The Diffusing, Whirling, and Shrinking Patterns) of Vector Field 151

6.2 The Source-Reverse Transform and The Laplacian Operator 155

6.3 Summary 156

References 159

Subject Index 164

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