对数图像处理：理论与应用探索

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"Logarithmic Image Processing - Theory and Applications" 是一本深入探讨对数图像处理理论与应用的学术著作。本书由 Michel Jourlin 编辑，他来自法国圣艾蒂安大学的 Laboratoire Hubert Curien。这本书是《Advances in Imaging and Electron Physics》系列的第195卷，由学术出版社 Elsevier 出版。对数图像处理是一种在机器视觉和计算机视觉领域广泛应用的技术。其理论基础源自物理模型，特别是在图像信号的动态范围扩展、夜视增强、图像稳定和中心化等场景中，对数变换展现出显著的优势。通过对图像进行对数转换，可以有效地压缩图像的动态范围，使得原本可能被过亮或过暗部分遮蔽的细节得以显现，这对于低光照条件下的成像尤其重要，如夜间视觉应用。在工业和生物医学领域，对数图像处理技术也有着广泛的应用。例如，在工业检测中，它可以帮助识别微小的缺陷或不规则，从而提高产品质量控制的精度。在生物医学成像中，它可以改善图像对比度，使医生更容易识别组织结构或病变，这对于疾病诊断和治疗规划至关重要。书中详细介绍了基于对数定律的度量方法，这些方法对于理解和优化对数图像处理的效果至关重要。此外，还涵盖了动态范围扩张，这是一种处理高动态范围图像的技术，旨在将宽范围的亮度值适配到显示设备的能力范围内。同时，对图像稳定性的讨论涉及如何减少由于相机抖动或物体移动导致的图像模糊。中心化应用则可能涉及到图像校正，确保图像内容居中并保持清晰。通过这一专著，读者不仅可以了解到对数图像处理的理论基础，还可以掌握其在不同领域的实际应用案例，这为研究人员、工程师和学生提供了宝贵的参考资料，帮助他们在各自的领域中更好地利用对数图像处理技术解决问题。"Logarithmic Image Processing - Theory and Applications" 是一个深入了解和探索图像处理科学与实践的重要资源。

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FOREWORD: SHORT HISTORY OF THE

LIP MODEL

1. JUSTIFICATION OF THE MODEL

The first question we will answer is: Why the logarithmic image processing

(LIP) model?

In fact, when we consider preexisting logarithmic look-up tables (LUT)

we should ask what novel logarithmic tools can really bring to image

processing. Moreover, when we analyze the content of the many papers

dedicated to the LIP framework, we notice that their contribution directly

relies on the model’s nonlinearity. Particularly, most of them point out the

ability of LIP tools to enhance or process dark images or dark regions inside

an image. In fact, such tools are now well known to be practically insensitive

to lighting variations or lighting drift.

In this book, a number of applications we will expose also rely on these

capabilities of the LIP model. Nevertheless, using the strong mathematical

and physical properties of the model, we will try to understand and justify

the power of logarithmic operators. This way of reasoning permitted us to

propose many novel tools and results. For example, we invite the readers to

focus their attention on these sections:

Chapter II

–

The physical meaning of the logarithmic additive contrast and its link

with the classical Michelson contrast

– The logarithmic multiplicative contrast and its strong sensitivity in

bright regins

Chapter III:

–

The metrics associated with logarithmic contrasts

– Novel notions: the various Aspl€und’s metrics and particularly the addi-

tive Aspl€und’s metric, whose insensitivity to exposuretimeand, at a lesser

level, to diaphragm aperture variations offers a new way of processing

low-light images as well as images acquired under variable lighting.

Chapter IV:

–

Based on the mathematical vector space structure valid on the space of

images (Chapter “Gray-Level LIP Model. Notations, Recalls and

First Applications”), the use of negative gray levels as light intensifiers

permits the enhancement of very low-light images.

We have also taken care to:

–

illustrate the main results with plenty of biomedical and industrial

applications, and

– highlight the places where new research developments are required.

2. ORIGIN OF THE MODEL

In 1983, I attended a training week dedicated to image analysis at the

“Ecole des Mines de Fontainebleau.” I already worked in collaboration with

this team, called the “Fontainebleau School,” and understood the principles

and tools of “mathematical morphology.” Nevertheless, this training was an

opportunity for me to enter the formulation of the main tools of mathemat-

ical morphology in depth, and I focused my attention on the gray-level

mathematical morphology. Since my initial education was purely mathe-

matics, I was particularly interested in the set of theoretical results developed

by the Fontainebleau School on the basis of the Minkowski’s addition A B

of two binary shapes A and B. I remarked that for dilation (resp. erosion)

operator, noted A B (resp. A ⊝ B), the structuring element B and the stud-

ied shape A were of same nature (binary shapes). However, when transferred

to functions, they produce dilation/erosion operators f B and f ⊝ B

where the structuring element B remains binary.

Thus, I thought that it would likely be interesting (at least intellectually)

to imagine new operators f }}g and f }⊝}g where g could play the role of a

functional structuring element, ie, could be chosen as a simplified function

dedicated to the study of an image f, as it is commonly done for binary

shapes. Moreover, as a former mathematician converted to image

processing, I had in mind that the laws }} and }⊝} would not be limited

to a mathematical formulation, but would possess a tangible usefulness. This

is the reason why my first concern was to think about a realistic situation in

image processing where the sum of two images could have a physical mean-

ing. This reflection directed me toward images acquired in transmission

(microscopy, tomography, scanner, etc.) where the observed object appears

often as the superimposition of various components. For example, the sim-

ple observation with a microscope of the nucleolus of a cell consists of the

stacking of the cell cytoplasm, of the nucleus and the nucleolus. The

resulting image is then nothing but the addition, in transmission, of the

images corresponding separately to each component.

In such conditions, I decided to define first the law }} in the context of

transmitted signal (images acquired in transmission), ie, when the observed

xvi Foreword

object is located between the source and the sensor. I finally noted this addi-

tion law with the symbol ⨹ so as not to lead to confusion with the standard

morphological operators.

The first research on this subject permitted me to effectively introduce

an internal addition law ⨹ on the space ID,0,M½Þ½ð of images defined on

the same spatial support D and with values in the same gray scale 0,M½½ .

Such a law is the well-known transmittance law expressed in terms of gray

levels (cf. following Chapter “

Gray-Level LIP Model. Notations, Recalls

and First Applications”). A classical reflex for a mathematician when

he disposes of an addition law is to deduct a scalar multiplication ⨻ by

stacking n times the object corresponding to the image f:

f ⨹ f ⨹ ⋯ ⨹ f ¼n ⨻ f . Once established for integers, this law is then

extended to every real number λ. At this moment, we dispose of two

laws, one permitting to add two images ( f ⨹ g), the other to multiply

an image by a real number λ ⨻ f

ðÞ

: Having done this “physical” reasoning

based on the transmittance law, I returned to a mathematical point of

view, which consisted of asking what the properties of these laws are

in terms of associativity, neutral element, opposite, commutativity,

distributiveness, etc.

All these properties are satisfied when the space ID,0,M½Þ½ð of images is

extended to the space FD,ð∞, M½Þ of functions defined on the same

domain D with values in ∞, M½. In fact, the introduction of possible neg-

ative values allows us to define the opposite ⨺ f of an image f, representing

the function, which results in the neutral element 0 when added to the image

f : f ⨹⨺fðÞ¼0.

The set of these properties structures FD,ð∞, M½Þ,⨹,⨻Þ as a vector

space, allowing the use of the numerous tools available in such spaces, such as

interpolation, gauges, norms, scalar products, etc.

In conclusion, we dispose of a strong physical and mathematical frame-

work to perform image processing in good conditions.

I do not know if the reader is unfamiliar with the LIP model considered

at this step, or whether it is interesting to pursue these first developments, but

I will say that when I proposed this subject to my PhD students, no one was

enthusiastic. I most strongly insisted until one of them, J.C. Pinoli, demon-

strated some interest. I must admit that nobody, not even myself, had the

least idea of the subject’s extent at this period.

After I published the first results with J.C. Pinoli and R. Zeboudj

(1985-89), I had some contact with researchers interested in the LIP model.

I remember particularly the visit in Lyon of Professor Cahill (La Trobe

xviiForeword

University, Australia) who had the courtesy to ask my agreement before

beginning a PhD on the LIP subject with his student, Dennis Deng.

To refer to the most important milestones punctuating the LIP pro-

gresses, I must cite:

–

In the biomedical domain, the collaboration I developed with Professor

J€org Sch€upbach (University of Zurich) concerning the three-dimensional

(3D) visualization of T4-lymphocytes cultured in presence of HIV virus.

T4-lymphocytes were removed from the culture and fixed in an epoxy

block before being cut into very thin slices (thickness: 40 nm) with an

ultramicrotome. Each slice was then imaged with an electron microscope

in transmission and the role of the LIP was to interpret some missing cuts

(logarithmic interpolation) and to normalize the lighting changing

observed on the cuts due to thickness variations. This research took place

between 1985 and 1989 and resulted in a scientific prize (Plano Prize,

Salzburg, 1989).

– In the research domain, I had a lasting collaboration with the team created

and led by Professor Vasile Buzuloiu (Polytecnica, Bucaresti), including

the works of V. Patrascu, E. Zaharescu, C. and L. Florea, C. Vertan,

among others.

– In research-development and industrial applications, I am working with a

start-up called NT2I, which has integrated the set of logarithmic tools and

tests the final tools as we proceed in their creation. I have headed two

PhD theses prepared by research engineers from NT2I and we work

together daily.

2.1 Spirit and Goals of the Book

It’s a pleasure for me to recall the long and fruitful collaboration I developed

with Peter Hawkes: thanks to him, it was possible to publish extended papers

dedicated to the LIP model. I had already the occasion to emphasize the

particular role of AIEP Serial in the “jungle” of scientific journals, where

it is customary today to publish papers mostly devoted to abstract, introduc-

tion, notations, recalls, conclusion, perspectives, and references, with very

little space for research itself. On the contrary, AIEP Serial permits me to

present extended papers that allow in-depth study of a subject. With Peter

Hawkes agreement, I decided that this book’s contents would not be the

simple aggregation of previous papers. It seemed more interesting to sum-

marize the main existing results (which remain accessible to the interested

reader) and to highlight the novel ones, as well as application examples.

xviii Foreword

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