Artificial intelligence and pattern recognition techniques in microscope image processing and analysis

BONNET N. Artificial intelligence and pattern recognition techniques in microscope image processing and analysis. Advances in Imaging and Electron Phy...
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BONNET N. Artificial intelligence and pattern recognition techniques in microscope image processing and analysis. Advances in Imaging and Electron Physics. (2000) 114, 1-77 Artificial intelligence and pattern recognition techniques in microscope image processing and analysis Noël Bonnet INSERM Unit 514 (IFR 53 "Biomolecules") and LERI (University of Reims) 45, rue Cognacq Jay. 51092 Reims Cedex, France. Tel: 33-3-26-78-77-71 Fax: 33-3-26-06-58-61 E-mail: [email protected] Table of contents I.

Introduction

II: An overview of available tools originating from the pattern recognition and artificial intelligence culture A. Dimensionality reduction 1. Linear methods for dimensionality reduction 2. Nonlinear methods for dimensionality reduction 3. Methods for checking the quality of a mapping and the optimal dimension of the reduced parameter space B. Automatic classification 1. Tools for supervised classification 2. Tools for unsupervised automatic classification (UAC) C. Other pattern recognition techniques 1. Detection of geometric primitives by the Hough transform 2. Texture and fractal pattern recognition 3. Image comparison D. Data fusion III: Applications A. Classification of pixels (segmentation of multi-component images 1. Examples of supervised multi-component image segmentation 2. Examples of unsupervised multi-component image analysis and segmentation B. Classification of images or sub-images 1. Classification of 2D views of macromolecules 2. Classification of unit cells of crystalline specimens C. Classification of "objects" detected in images (pattern recognition) D. Application of other pattern recognition techniques 1. Hough transformation

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2. Fractal analysis 3. Image comparison 4. Hologram reconstruction E. Data fusion IV. Conclusion Acknowledgements References

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I : Introduction Image processing and analysis play an important and increasing role in microscope imaging. The tools used for this purpose originate from different disciplines. Many of them are the extensions of tools developed in the context of one-dimensional signal processing to image analysis. The signal theory furnished most of the techniques related to the filtering approaches, where the frequency content of the image is modified to suit a chosen purpose. Image processing is, in general, linear in this context. On the other hand, many nonlinear tools have also been suggested and widely used. The mathematical morphology approach, for instance, is often used for image processing, using gray level mathematical morphology, as well as for image analysis, using binary mathematical morphology. These two classes of approaches, although originating from two different sources, have interestingly been unified recently within the theory of image algebra (Ritter, 1990; Davidson, 1993; Hawkes, 1993, 1995). In this article, I adopt another point of view. I try to investigate the role already played (or that could be played) by tools originating from the field of artificial intelligence. Of course, it could be argued that the whole activity of digital image processing represents the application of artificial intelligence to imaging, in contrast with image decoding by the human brain. However, I will maintain throughout this paper that artificial intelligence is something specific and provides, when applied to images, a group of methods somewhat different from those mentioned above. I would say that they have a different flavor. People who feel comfortable in working with tools originating from the signal processing culture or the mathematical morphology culture do not generally feel comfortable with methods originating from the artificial intelligence culture, and vice versa. The same is true for techniques inspired by the pattern recognition activity. In addition, I will also try to evaluate whether or not tools originating from pattern recognition and artificial intelligence have diffused within the community of microscopists. If not, it seems useful to ask the question whether the future application of such methods could bring something new to microscope image processing and if some unsolved problems could take advantage of this introduction. The remaining paper is divided into two parts. The first part (section II) consists of a (classified) overview of methods available for image processing and analysis in the framework of pattern recognition and artificial intelligence. Although I do not pretend to have discovered something really new, I will try to give a personal presentation and classification of the different tools already available. Then, the second part (section III) will be devoted to the application of the methods described in the first part to problems encountered in microscope image processing. This second part will be concerned with applications which have already started as well as potential applications. II: An overview of available tools originating from the pattern recognition and artificial intelligence culture The aim of Artificial Intelligence (AI) is to stimulate the developments of computer algorithms able to perform the same tasks that are carried out by human intelligence. Some fields of application of AI are automatic problem solving, methods for knowledge representation and knowledge engineering, for machine vision and pattern recognition, for artificial learning, automatic programming, the theory of games, etc (Winston, 1977). Of course, the limits of AI are not perfectly well defined, and are still changing with time. AI techniques are not completely disconnected from other, simply computational, techniques, such as data analysis, for instance. As a consequence, the list of topics included in

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this review is somewhat arbitrary. I chose to include the following ones: dimensionality reduction, supervised and unsupervised automatic classification, neural networks, data fusion, expert systems, fuzzy logic, image understanding, object recognition, learning, image comparison, texture and fractals. On the other hand, some topics have not been included, although they have some relationships with artificial intelligence and pattern recognition. It is the case, for instance, of methods related to the information theory, to experimental design, to microscope automation and to multi-agents system. The topics I have chosen are not independent of each other and the order of their presentation is thus rather arbitrary. Some of them will be discussed in the course of the presentation of the different methods. The rest will be discussed at the end of this section. For each of the topics mentioned above, my aim is not to cover the whole subject (a complete book would not be sufficient), but to give the unfamiliar reader the flavor of the subject, that is to say, to expose it qualitatively. Equations and algorithms will be given only when I feel they can help to explain the method. Otherwise, references will be given to literature where the interested reader can find the necessary formulas. A. Dimensionality reduction The objects we have to deal with in digital imaging may be very diverse: they can be pixels (as in image segmentation, for instance), complete images (as in image classification) or parts (regions) of images. In any case, an object is characterized by a given number of attributes. The number of these attributes may also be very diverse, ranging from one (the gray level of a pixel, for instance) to a huge number (4096 for a 64x64 pixels image, for instance). This number of attributes represents the original (or apparent) dimensionality of the problem at hand, that I will call D. Note that this value is sometimes imposed by experimental considerations (how many features are collected for the object of interest), but is also sometimes fixed by the user, in the case the attributes are computed after the image is recorded and the objects extracted; think of the description of the boundary of a particle, for instance. Saying that a pattern recognition problem is of dimensionality D means that the patterns (or objects) are described by D attributes, or features. It also means that we have to deal with objects represented in a D-dimensional space. A “common sense” idea is that working with spaces of high dimensionality is easier because patterns are better described and it is thus easier to recognize them and to differentiate them. However, this is not necessarily true because working in a space with high dimensionality also has some drawbacks. First, one cannot see the position of objects in a space of dimension greater than 3. Second, the parameter space (or feature space) is then very sparse, i.e. the density of objects in that kind of space is low. Third, as the dimension of the feature space increases, the object description becomes necessarily redundant. Fourth, the efficiency of classifiers starts to decrease when the dimensionality of the space is higher than an optimum (this fact is called the curse of dimensionality). For these different reasons which are interrelated, reducing the dimensionality of the problem is often a requisite. This means mapping the original (or apparent) parameter space onto a space with a lower dimension (ℜD→ℜD’; D’µjk ∀j≠i} Specific criteria have been suggested for estimating the quality of a partition in the context of the fuzzy logic approach. Most of them rely on the quantification of fuzziness of the partition after convergence but before defuzzification (Roubens, 1978; Carazo et al., 1989; Gath and Geva, 1989; Rivera et al., 1990, Bezdek and Pal, 1998). Information theoretical concepts (entropies for instance), can also be used for selecting an optimal number of classes. Several variants of the FCM technique have been suggested, where the fuzzy set theory is replaced by another theory. When the possibility theory is used, for instance, the algorithm becomes the possibilistic C-means (Krishnapuram and Keller, 1993), which has its own advantages but also its drawbacks (Barni et al., 1996; Ahmedou and Bonnet, 1998). d. Parzen/watersheds The methods described above share an important limitation; they all consider that a class can be conveniently described by its center. It means that hyperspherical clusters are anticipated. Replacing the Euclidean distance by the Mahalanobis distance makes the method more general, because hyperelliptical clusters (with different sizes and orientations) can now be handled. But it also makes the minimization method more susceptible to sink into local minima instead of reaching a global minimum. Several clustering methods have been proposed that do not make assumptions concerning the shape of clusters. As examples, I can cite: - a method based on "phase transitions" (Rose et al., 1990) - the mode convexity analysis (Postaire and Olejnik, 1994) - the blurring method (Cheng, 1995) - the dynamic approach (Garcia et al., 1995) I will describe in more details the method I have worked on, which I will name the Parzen/watersheds method. This method is a probabilistic one; clusters are identified in the parameter space as areas of high local density separated by areas of lower object density. The first step of this method consists in mapping the data set to a space of low dimension (D'

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