Automatic Feature Selection for Biological Shape Classification in Σ YNERGOS
ODEMIR MARTINEZ BRUNO1
ROBERTO MARCONDES CESAR JUNIOR2
LUÍS AUGUSTO CONSULARO1
LUCIANO DA FONTOURA COSTA 1
Cybernetic Vision Research Group - GII - IFSC – University of São Paulo - São Carlos, SP, CP 369, 13560-970 Department of Computer Science – IME - University of São Paulo, Rua do Matão, 1010, São Paulo, SP, 05508-900
Brazil
e-mails: 1{bruno,consul,luciano}@ifsc.sc.usp.br 2cesar@ime.usp.br http://www.ifsc.sc.usp.br/visao Abstract. This work reports the development of a versatile framework allowing the characterization and analysis of computer vision techniques as well as their applications to biological shapes, with attention focused on neural cells.
The proposed framework has been implemented within the Σynergos system, a powerful imaging laboratory that includes, among other features, tools for performance assessment of computer vision techniques, image databases, real-time processing by using distributed systems and interface with the Internet. The motivations for the development of such a framework: (i) the importance of biological shape analysis; (ii) its potential as an effective tool for the systematic assessment of image processing and analysis techniques; and (iii) the possibility of conducting extensive characterizations of biological shapes. The paper describes an experiment to assess multiscale shape features for complexity characterization, which have been adopted for the classification of two types of ganglion neural cells (cat), namely α and β. This experiment involves: (1) a training stage where the k-means clustering algorithm learns the prototypes of each class from the database; (2) the neurons in the database are classified; (3) the classification results are compared to the original classes; and (4) the number of misclassifications is determined. The genetic algorithm is used as a means of effectively investigating the N-dimensional spaces defined by the parameter configurations.
Keywords: biological shape analysis; multiscale methods; neuromorphometry; genetic algorithms; image databases; performance assessment.
1 Introduction
Scientists in the natural sciences often face the problem of shape classification in order to organize and understand the phenomena they are interested in. For instance, astronomers have classified galaxies (such as spiral galaxies, and so on), star systems and planets as a preliminary step toward explaining different aspects of the structure of the universe (e.g. see [Sagan (1983); Mandelbrot (1982)])1. And yet this is but an example of the many situations where shape analysis arises in scientific research - many other examples abounding in biology, geology, physics, etc. In fact, it is not a surprise that the analysis of biological shape was one of the first applications of image analysis in computers [Ledley (1964)], a field that has received growing
1Notwithstanding the fact that shape analysis may lead to curious misinterpretations of the reality, such as in the classical Lowell canals affair [Sagan (1983)]. Percival Lowell was an important american astronomist of the XIX century that was convinced that he "saw" a set of straight lines on the surface of Mars and that those lines were due to water canals constructed by an intelligent race, i.e. the martians.
attention since then. This paper presents a new approach to biological shape classification based on automatic feature selection by genetic algorithms. It is important to note that the main contribution of this work is not a new genetic algorithm for feature selection, but the introduction of an integrated approach for biological shape analysis. This new approach includes performance assessment of features based on image databases, feature selection and tools for comparing unsupervised (objective) and supervised (subjective, based on human expertise) classification of biological shapes. The general framework of the method introduced in this paper is depicted in Figure 1 and discussed in detail in Section 3.
An especially important field of interest where biological shape analysis arises is in the morphometric analysis of neural cells, i.e. neuromorphometry [Costa et al. (1998)]. Shape analysis of neurons may involve different methods, from the estimation of simple measures such as area, number of extremities and Scholl diagrams to the characterization of spatial coverage [Murray (1995)] and the extraction of dendrograms [Cesar & Costa (1997)]. Furthermore, the application potential of such methods is vast, ranging from the characterization of the interplay between form
and function [Costa et al. (1998)] to the creation of biologically realistic neural structures [Costa et al.
(1998)].
One of the most important problems in biological shape analysis is the classification of biological entities based on their shape features. The orthodox approach to this problem is through standard statistical pattern recognition where a set of features is measured from the input images and a pattern classifier is used to carry out the recognition task [Duda & Hart (1973)]. Although such
a framework may look initially simple (feature measuring followed by statistical pattern classification), it encloses a series of intrinsic difficulties whose proper solution is always essential for the success of the application. One major difficulty regards the selection of suitable features to be used in the classification, since there is no systematic and effective methodology for this task. Indeed, feature selection is nearly always carried out based on heuristics and trial-and-error procedures [Castleman (1996)]. Furthermore, different combinations of possible feature vectors and pattern classifiers (since many classifiers can be adopted) seldom lead to the same classification results, indicating the criticality of a suitable choice of a "feature vector + pattern classifier" scheme.
There are too many possible features that can be adopted, each of them potentially suitable to specific problems while virtually useless (or even source of errors) for others. Therefore, the possible feature vectors live in high-dimensional feature spaces, and the problem of suitable feature selection may be expressed as a problem of searching such a space for the best (or at least reasonable) feature vectors. Obviously, exhaustive search (i.e. search by considering all possible feature vectors) is by far prohibitive due to the
aforementioned high-dimension of the feature space.
This work explores an alternative to circumvent this problem by using a genetic algorithm [Holland (1962)]
[Goldberg (1989)] [Sipper (1996); Tomassini (1995)] in order to carry out searches for good sets of features in multidimensional spaces. Multiscale image analysis techniques have been adopted in order to generate the possible features that define the feature space to be analysed by using the genetic algorithm.
The aforesaid considerations have motivated the
development of the Σynergos system, a framework for computer vision research that incorporates the above desired characteristics (image databases, tools for feature selection and performance assessment, to name but a few), as well as additional important resources not directly related to the scope of the present article (such as real-time implementation in distributed systems and Internet-based processing). In fact, the methods and experiments described in this work have been implemented in a prototype of the Σynergos architecture.
2 Biological Shape Classification
In general, biological shapes are associated to the physical (or biophysical) processes that generated them, subjected to physical and ecological constraints (such as evolutionary forces). As a consequence of this and of the applications that motivate the biological imaging problems, the research on biological image analysis often involves the development of techniques and measures that have physical interpretation (at least such a fact is a highly desirable goal of such research activities). For instance, an important concept for biological structures is spatial coverage (or space- CONTROL
CLASSIFIED IMAGE
DATABASE
BIOLOGICAL IMAGE
DATABASE
FEATURE EXTRACTION WHOLE
DATABASE OF ALL FEATURES
CLASSIFIED DATA
(CLUSTERING
RESULTS) PERFORMANCE ASSESSMENT
GENETIC FEATURE SELECTION K-MEANS CLUSTERING
PERFORMANCE RESULTS
Figure (1): General architecture for the experiments presented in this work.
filling) [Murray (1995)], which is related to the capacity of a biological shape to sample or fill the surrounding space, defining its interface with the exterior world.
Such a property determines diverse important qualities of the associated biological entity such as its capacity to search for food or other natural resources (think of tree roots, for example) or of influencing neighboring entities (e.g. neurons in a neural network). Therefore, measuring spatial covering properties of a biological shape is a particularly important problem, and researchers have indeed derived a number of different methods to perform such a task, mainly related to the concept of shape complexity (in the sense that the more complex is the shape, the larger is its spatial covering capacity). Examples of complexity measures are the fractal dimension and the bending and the wavelet energies [Costa et al. (1998)]. Indeed, the concept of scale plays a central role in different aspects of biological image analysis, which is also explored in this work. For instance, the analysis of neural structures may be carried out at the level of neural networks composed by thousands of neural cells (large scales), at the level of the shape of neural cells (intermediate scales), or at the level of dendritic characteristics or even of ionic channels (small scales). As above commented, this work explores the concept of multiple scales for the characterization of biological shapes.
As far as shape analysis is concerned, two typical situations can be found:
• Case 1: the shape classes are known a priori;
• Case 2: the shape classes a priori are not available or can not be determined.
In the former case the shape classes can be determined with complete confidence. An example of a problem of this kind is the classification of neurons coming from different known sources (e.g. from two different species): if the source of the neuron is known (i.e. “I know I got this neuron from the species X and that one from the species Y”), then the shape classes are exactly known. On the other hand, the latter (shape classes are not known a priori) can be characterized as a clustering problem where a given set of biological structures should be divided according to (some of) their shape properties. An example of such a case is the classification of the types of ganglion cells present in the retina of cats [Cesar et al., 1997].
Some interesting problems arise from the a priori unknown shape classes case, mainly because such classifications have been performed by (human) scientists in a predominantly subjective fashion, which often leads to disagreement between different experts.
There is a number of questions that are naturally entailed by this situation:
1. Which features best discriminate the different shape class?
2. Which features were used and prioritized by the scientists during their subjective classification?
3. Do the features defined by the two questions above coincide?
While question 1 is related to unsupervised clustering of shape features and automatic (non- subjective) definition of shape classes, question 2 can be thought as a problem of expert knowledge acquisition where the system should learn which features best reflect the subjective judgements of the scientists. Finally, question 3 is important both for the development of effective systems for automatic analysis of biological images and for helping scientists in defining and understanding the classes created as consequence of their theories (or even in the detection of eventual mistakes). The next section discusses how the three questions can be approached with the aid of pattern recognition procedures.
3 Pattern Recognition, Feature Selection and Genetic Algorithms
A central problem in statistical pattern analysis is known as clustering, which basically consists in grouping feature vectors in sets (or clusters) useful for the definition of pattern classes, without supervision. As discussed in the introductory section of this paper, the analysis of feature spaces and feature selection are non- trivial application-dependent problems with no effective automatic approach, traditionally relying on heuristics and trial-and-error procedures. This paper introduces some strategies to deal with the problem of feature selection based on genetic algorithms that are motivated by the considerations presented in Section 2. The introduced approach may be better understood by considering Figure 1.
The process starts with a database containing the images to be analyzed (the Biological Image Database), from which an arbitrary large set of features is extracted, leading to a Database of All Features. The extracted features are presented in Section 3.2. The next step is to analyze the feature space stored in the correspondent database in order to select the desired subset of features, which is carried out by the Genetic Feature Selection module. It is important to emphasize that the criteria that define the “desired subset of features” depend on the particular problem under consideration. In the present case, the considered problem belongs to the class defined by question 1 in Section 2. As it will be shown, this is performed simply by defining and using different fitness functions of the genetic algorithm [Sipper (1996); Tomassini (1995)] which capture the essence of the respective questions. As it can be seen in Figure 1, feature selection is accomplished by a cooperative process between the
genetic and the k-Means Clustering [Duda & Hart (1973)] algorithms, which is also responsible for the final generation of the Classified Data Database (once the chosen feature vector has been selected). It is important to say that the feature selection may be carried out either in a supervised or in a unsupervised way, depending on the fitness function, which is the reason for the dashed line between the genetic algorithm and the Control Classified Image Database. This classified database contains the class labels for each image in the initial image database. Finally, the pre-classified database and that classified by the cluster algorithm (refer to Figure 1) may be compared by the performance algorithms in order to generate additional results, which can be used to answer the questions proposed in Section 2, as it is explained in the next section. For instance, if the pre-classification is known to be correct (case 1 in Section 2), then the classification automatically obtained by the system can be compared in order to obtain the successful recognition rates for the adopted configuration (feature vector + pattern classifier).
Figure (2): Different schemes for image analysis based on the introduced genetic approach.
3.1Genetic Algorithm
Genetic algorithms represent a recently developed paradigm for solving optimization problems typically involving large amounts of data (such as feature spaces with many dimensions). Typically, there are no means of solving such problems by exhaustive search throughout the data (because such a solution would often be computationally prohibitive), a problem the genetic algorithms attempts to circumvent by using a selective process analogous to (Darwinian) natural selection. In this paradigm, the possible solutions of the problem of interest are coded as individuals of a population of solutions. The DNA of each individual characterizes the correspondent (possible) solution of the problem. The idea underlying the genetic approach is to create a process of evolution of the population individuals based on natural selection, leading to better adapted individuals, which, by their turn, would correspond to better (sub-optimal) solutions of the problem (see [Sipper (1996); Tomassini (1995)]). The degree of how well-adapted is an individual is estimated
by a fitness value or fitness function. Finally, two genetic operators are traditionally adopted by the genetic algorithms for implementing evolution:
crossover and mutation. Crossover is the process of generating two new individuals by swapping parts of the DNA of their parents, while mutation simply changes the DNA locally according to a probability of mutation.
The genetic algorithm reported here is based in the following scheme. Recall that the problem of interest consists in selecting a good subset (feature vector) among the total set of possible features. Let fm denotes the m-th feature, m = 1..M, where M is the number of total possible features (i.e. the initial feature space is M- dimensional). Therefore, each individual DNA Im, m = 1..M, of the genetic algorithm is defined as an arbitrary sequence of 0’s and 1’s (e.g. 0010100110…010) of length M, which defines a feature vector in the total feature space composed by the features fm for which Im
= 1. Obviously, the information coded in the DNA of each individual is enough to specify the k-means algorithm with the feature vector defined by the respective DNA code. Different fitness functions can be defined depending on each specific problem:
1. Which features best discriminate the different shape classes?
Basically, the answer of this question corresponds to the feature vector obtained by the genetic algorithm based on an unsupervised approach, where the fitness function analyzes the feature space per se, attempting to minimize dispersion within each cluster while maximizing the distance between clusters. In this approach, the expert classification underlying case 2 of Section 2 is simply disregarded, and an exclusively data-driven fitness function is used instead. An example is the class separation distance [Castleman (1996)] between two clusters (denoted as 1 and 2), defined as D1,2 = |µ1 - µ2 | / (σ12 - σ22)1/2, where µ1 and µ2 are the means of the clusters 1 and 2, respectively, while σ1 and σ2 are the respective standard deviations.
On the other hand, if case 1 of Section 2 is being considered (i.e. the shape classes are known a priori), then the results of the k-means classification only need to be compared to the a priori classification, and the mean correct recognition rate may be used as the fitness function;
2. Which features are used by the scientists during their classification?
This question refers to case 2 of Section 2 and can be thought as a problem of extracting knowledge from an expert. Its answer is the feature vector obtained by the genetic algorithm taking as fitness function the mean correct recognition rate between the expert classification and the cluster algorithm;
3. Do the features defined by questions 1 and 2 above coincide?
It suffices to compare the answers to the above questions 1 and 2.
Figure 2 summarizes the different aforesaid problems that may be approached by genetic algorithm framework proposed in this work. In that figure, the two cases discussed in Section 2, as well as the two possible approaches for the definition of the fitness value (i.e.
supervised, where the fitness depends on the human pre-classification of the images; and unsupervised, where the fitness do not depend on human opinions and an objective measure, such as the class separation distance, is used instead). The simple pairwise combination of the boxes of Figure 2 defines an approach for solving a specific problem: (1) if the classes are known and the fitness function is supervised, then the method is used for assessing the characterization capabilities of each assessed feature;
(2) if the classes are known and the fitness function is unsupervised, the assumption that a suitable feature vector has been chosen allows the evaluation of the clustering (classification) method; (3) if the classes are unknown and the fitness function is supervised, then the best feature vectors reflect the criteria used by the expert in his classification, which characterizes an expert knowledge acquisition method; and (4) if the classes are unknown and the fitness function is unsupervised, then the clustering algorithm allows the search for partitioning the (particular) shape space in a way that the shape classes optimize pre-defined criteria.
3.2Adopted Features
As observed in Section 2, the concept of multiple scales play a central role in image analysis (in biological applications in particular), and the here considered problems reflect this fact. One of the nice properties of the multiscale approach is that it allows the measure to incorporate spatial neighborhood information in the measure. Take, for example, the standard definition of the variance of an image. It clearly depends only on the value of each pixel, without taking their disposition into account. Two binary images containing an equal number of black and white pixels (say, half black and half white) but with two entirely different spatial distributions (say, one with its half right portion composed by black pixels and the other half white; and the other with the pixels disposed as a chessboard) present the same variance. On the other hand, if the two images are filtered by a gaussian kernel, the two resulting smoothed images will present different variances, for the local disposition of the black and white pixels will be reflected in the convolution operation.
Four families of multiscale features are represented in the total feature space analyzed by the experiments described in this paper, namely Minkowsky sausage areas [Costa et al. (1998)] and the multiscale entropy, variance and circularity. The Minkowsky sausages are defined by the convolution of the input image with a family of multiscale functions defined as h(x, y, a) = {1 if (x2 + y2) < a2; 0 otherwise}, a = 1, 2, 3, …, A, where A is the larger analyzing scale. Let f(x, y) denote the input image. Then, the Minkowsky sausage areas S(a) are defined as the number of non-zero pixels of the 2D convolution f(x, y) * h(x, y, a) for each fixed value of a.
The other three multiscale families of features are calculated from the convolution of the input image with a family of multiscale gaussians g(x, y, a) = exp( -(x2 + y2) / (2 a2) ). Let f(x, y, a) = f(x, y) * g(x, y, a) be the family of multiscale (blurred) images indexed by the scale parameter a and obtained by 2D convolutions between f and g for each fixed value of a. Then the following three multiscale features are defined:
1. Multiscale Entropy: defined as
=∑
j pj a pj a
a
E( ) ( )ln ( )
where pj(a) is the relative frequency of the j-th gray level in the blurred image f(x, y, a) for each value of a;
2. Multiscale Standard Deviation: defined as the square root of the variance of f(x, y, a) for each scale a;
3. Multiscale Circularity: defined as perimeter to the power two divided by the area of the (smoothed) cell (see [Castleman (1996)] for further information). This is a measure of shape complexity;
4 The Σynergos System
Some of the main aspects discussed in this work have motivated the recent development of a new framework for research in computer vision named Σynergos, a system aimed at unifying a series of modern concepts in a cooperative and synergistic way.
The main modules of Σynergos are:
1. Computer Vision Research: this module includes the traditional tools for computer vision and image processing, such as Fourier and other transform methods, edge detection, image segmentation, etc.;
2. Biological Vision Research: tools for different activities related to the investigation of biological vision, such as psychophysics and synthesis and modeling of biological structures, are included in this module;
3. Data Analysis and Classification: this topic deals with procedures such as pattern classifiers and clustering algorithms, including statistical functions,
which are useful for many tasks such as those included in the next section;
4. Validation/Evaluation: this module comprehends the methods for verifying the correctness of the implemented routines, as well as for performance assessment of algorithms;
5. Databases: databases, both for images and for general data, provide the basic ground on which different routines, such as those for performance assessment, automatic feature selection and data mining, should act;
6. Off-the-Shelf Applications: this module is responsible for allowing Σynergos to interface and interact with other applications, such as MatLab or ADOBE PhotoShop, endowing Σynergos with a versatile environment for imaging investigation;
7. Artificial Intelligence: routines for knowledge acquisition, both from experts and from the experiments run within Σynergos, as well as more general procedures for learning and planning, are implemented here;
8. Data Mining: this module refers to functions for finding general laws in datasets, which may be used for modeling of biological structures and for expert knowledge acquisition, for instance;
9. Visualization and GUI: the procedures here are responsible for visualization and user interfacing;
10. Internet: Σynergos has been designed to interact with the Internet in at least the three following different ways: (i) synthesis, i.e. automatic generation of WWW documents; (ii) analysis, i.e.
processing images and data coming from the WWW; (iii) processing, i.e. application running through the Internet (via cgi-bins, for instance);
11. Distributed Systems: this module is responsible for the implementation of real-time applications through parallelization in (PC-based) distributed systems.
One of the ideas underlying the whole approach is that the result obtained by joining several computer approaches in a single system can be greater than the sum of its parts, since the relative advantages and disadvantages of each module could complement one another. While these modules are not explained here because of space limitations, a more complete
motivation and description of Σynergos will be published opportunely. A main feature of Σynergos is that it attempts not only to include tools for the aforesaid modules but to develop powerful experiments based on the interaction between the modules. As a matter of fact, the architecture described in Figure 3 is an example of such an interaction: databases + computer vision + validation/evaluation (i.e.
performance analysis) + data classification (k-means clustering) + artificial intelligence (the genetic approach). This provide a nice example that more powerful research schemes may arise from the interaction of the different modules. A prototype of the Σynergos system has been implemented using the Delphi programming environment in the Windows/95 platform. The Delphi environment, which includes tools for visual programming, databases, and an object- oriented language, has greatly contributed for the effective implementation of the ideas behind the Σynergos.
As far as implementation is concerned, different computational issues have been taken into account at the design stage. Firstly, considering that the investigated techniques have to be applied over large databases, it is essential to use parallel computer systems in order to achieve reasonable execution times (or to analyze more data during a specific time interval).
The adoption of a distributed system of IBM-PC compatible machines, as well as the Windows NT/95 operating system, have been based on the following principal reasons: (i) IBM-PC compatibles have reached a high-level of performance (e.g. Pentium 333MHz);
(ii) portability and popularity of hardware and software;
(iii) low-cost. In order to achieve good efficiency levels, Borland Delphi was chosen as the development platform, which includes pre-defined database management tools and object-oriented support. The parallelization of the system, which is interconnected by a standard network, has been implemented by using the CVMP (Cybernetic Vision Message Passing) tool, corresponding to a group of Delphi components developed for implementation of distributed parallel systems [Bruno & Costa (1997)]. This task has been largely facilitated by the object-oriented nature of Delphi. Moreover, the very own parallelization tool I/O (GUI'S)
MANAGER
PROGRAMS PROPRIETARY LIBRARY
DATABASES INTERNET APPLICATIONS REMOTE COMPUTERS
USER
Figure (3): General architecture of the Σynergos system.
(CVMP) is itself object-oriented, which implies in several desirable properties such as modularized integrability, portability, adaptability and life-time maintenance.
5 Experimental Results
The genetic approach to expert knowledge acquisition described in Section 3 has been implemented in Σynergos in order to assess the neuroscientists-based classification of retinal ganglion cells (cat). A total of 49 ganglion cells were digitized from the literature (see [Cesar et al., 1997] for further detail) and stored in an image database. These cells were originally classified by (expert human) neuroscientists in two morphological classes, namely α- cells (23 cells) and β-cells (26 cells). The mulsticale features described in Section 3.2 (Minkowski sausage areas for 34 scales; multiscale entropy, standard deviation and circularity for 18 scales each one, including the 0 scale) were calculated for the cells in this database. Therefore, an 88-dimensional feature space is defined through which the genetic algorithm has to search for good (at least sub-optimal) combination of feature vectors, i.e. the feature vectors which best represents the knowledge used by the neuroscientists. The genetic algorithm has been executed with a population of 200 individuals, a mutation rate of 0.01 and a probability of crossover of 0.7. After 77 generations, the genetic algorithm has achieved a mean successful recognition rate of 95% for some individuals whose DNA corresponding to feature vectors with two components: a sausage area for a specific scale and a circularity.
A typical GUI interface in Σynergos is shown in Figure (4), including the list of considered neural cells (dimensions and clipped images at the righthand side); a 3-D representation of the feature space and obtained classification with respect to entropy, sausages (upper left); and the spatial scales selected for each of these features (lower left). The clusters corresponding to α- (black diamonds) and β-cells (squares) resulted reasonably well-separated. Though being just a possible example of the GUI interfaces in Σynergos, this case well illustrates the importance and convenience typically allowed by the integration of several computational principles. In this particular case, the operator can easily inspect the feature space in terms of 3-D projections with respect to different spatial scales. The dynamic visualization (rotation and scaling) also contributes to the effective familiarization and structure of the data under analysis. Such interfaces also allow the direct verification of correspondences between each specific sample and the feature space.
Moreover, such reasonably friendly interfaces much
contributes to motivate the operator to inspect and analyse the obtained results.
The obtained result indicates that feature vectors containing information about the size (sausage area) and shape complexity (circularity) best describes the knowledge used by the human experts in their subjective classification of the considered neural cells.
Although limited by the ensemble of considered features (there is an infinite number of shape measures which could have been used instead, the tendency of such features to become correlated increasing with the number of considered measures) and adopted classification method, the obtained result is highly relevant not only for its practical value in defining an effective means for ganglion cell classification and as an illustration of the potential of the synergetic nature of Σynergos, but also for its implications for neuroscience. In fact, to our best knowledge, this is the first time the subjective criteria adopted by neuroscientists for the classification of ganglion cells, an important issue in itself, has been formally and comprehensively investigated by using computational methods. The fact that the best sets of features identified by Σynergos does correspond to the main criteria used by neuroscientists in their subjective classification procedures provides a cogent indication that their approach seems to be coherent and reasonable.
Figure (4) – One of the GUI interfaces in Σynergos illustrating the valuable role of integrated approaches (in this case image database, visualization, and classification) in making the analysis and investigation of the results more friendly and effective.
Yet, there is a further aspect of the obtained results deserving special attention. It concerns the overall spatial distribution of the samples, especially the α-
cells. As clearly shown in Figure (4), the region of the feature space occupied by the considered ganglion cells is constrained to a narrow and elongated strip. One of the principal motivations behind Σynergos was precisely the identification of such trends in the feature space, aimed at suggesting the existence of possible constraints of biological origin deserving further attention. In addition to such data mining possibilities, such results are also important in helping the extension of graph-theoretical approaches to biological shape generation (e.g. Costa et al., 1998) in the sense of producing shapes statistically equivalent as far as global measures (e.g. area, fractal dimensions, elongation, etc.) are concerned.
6 Concluding Remarks
This work has introduced a novel framework for pattern analysis of biological images based on a genetic approach, which has been implemented as a part of the Σynergos system. When implemented in Σynergos, the introduced framework provides the tools for the effective investigation of four different problems:
feature selection, assessment of clustering algorithms, expert knowledge acquisition and unsupervised shape classification. An example of an experiment for expert knowledge acquisition for automatic classification of ganglion cells has been described and successful results have been reported. The remaining experiments are among our ongoing work and the new results will be reported in due time.
Acknowledgements
Luciano da Fontoura Costa is grateful to FAPESP (Procs. # 96/05497-3 and 94/04691-5) and CNPq (Proc. # 301422/92-3) for financial support. Roberto M. C. Junior is grateful to Roberto Lotufo and to Jean-Pierre Antoine for the partial computational support, and to FAPESP (97/04186-7) for the financial support.
References
[Bookstein (1991)] F.L. Bookstein, Morphometric Tools for Landmark Data: Geometry and Biology, Cambridge University Press, Cambridge, 1991.
[Bruno & Costa (1997)] O. Bruno & L. F. Costa, Versatile real-time vision based on a distribuited system of personal computers, Proc. IEEE International Conference on Engineering of Complex Computer Systems, Como, Italy, September 8-12, pp 174-179, 1997.
[Castleman (1996)] K.R. Castleman, Digital Image Processing, Prentice-Hall, Englewood Cliffs, NJ, 1996.
[Cesar & Costa (1997)] R.M. Cesar Jr. and L. da F. Costa, Semi-automated Dendrogram Generation for Neural Shape Analysis, Proc. Simpósio Brasileiro de Computação Gráfica e Processamento de Imagens (SIBGRAPI-97, Campos do Jordão, SP, Out 1997), IEEE Computer Society Press, 147- 154, 1997.
[Cesar et al., 1997] R.M. Cesar Junior, R.C. Coelho and L. da F. Costa, Automatic Classification of Retinal Ganglion Cells, Proc. II Workshop on Cybernetic Vision, IFSC - USP, (São Carlos , SP, Brazil, 9-11 December 1996), IEEE Press, pp 51- 56, 1997.
[Costa et al. (1998)] L. da F. Costa, R.M. Cesar Jr., R. C.
Coelho and J. S. Tanaka, Perspective on the Analysis and Synthesis of Morphologically Realistic Neural Networks, In R. Poznanski (Ed.) Modeling in the Neurosciences: From Ionic Channels to Neural Networks, Gordon and Breach Science Publishers, 1998 (in press).
[Duda & Hart (1973)] R.O. Duda e P. E. Hart, Pattern Classification and Scene Analysis, John Wiley & Sons, NY, 1973.
[Goldberg (1989)] D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison- Wesley, Reading, Massachussetts, 1989.
[Holland (1962)] J. H. Holland, Outline for a logical theory of adaptive systems, J. Assoc. Comput. Mach., vol. 3, pp.297- 314, 1962.
[Ledley (1964)] R.S. Ledley High-Speed Automatic Analysis of Biomedical Pictures, Science, 146:216-223, October, 1964.
[Mandelbrot (1982)] B. Mandelbrot, The Fractal Geometry of Nature, W.H. Freeman and Company, New York, 1982.
[Mokhtarian & Mackworth (1992)] F. Mokhtarian and A.
Mackworth, A theory of multiscale, curvature-based shape representation for planar curves, IEEE Trans. Patt. Anal.
Mach. Intell., 14:789-805, 1992.
[Murray (1995)] J.D. Murray, Use and Abuse of Fractal Theory in Neuroscience, The Journal of Comparative Neurology, 361:369—371, 1995.
[Sagan (1983)] C. Sagan, Cosmos, Random House, 1983.
[Shen et al. (1994)] L. Shen, R.M. Rangayyan, and J.E.L.
Desautels, Application of shape analysis to mammographic calcifications, IEEE Transactions on Medical Imaging, 13(2):263-274, 1994.
[Sipper (1996)] M Sipper, A Brief Introduction to Genetic Algorithms: http://lslwww.epfl.ch/~moshes/ga_main.html, 1996.
[La Recherche (1996)] Special Issue – Voir dans le Cerveau, La Recherche, 289, Jul/Ago, 1996. (in French)
[Tomassini (1995)] M. Tomassini. A survey of genetic algorithms. In D. Stauffer, editor, Annual Reviews of Computational Physics, volume III, pages 87-118. World Scientific, 1995.
(http://lslwww.epfl.ch/pages/staff/tomassini/).
[Young et al. (1974)] I.T. Young, J.E. Walker and J.E., Bowie, An Analysis Technique for Biological Shape. I, Information and Control, 25:357--370, 1974.
