EP1938270A2

EP1938270A2 - Method for segmentation in an n-dimensional characteristic space and method for classification on the basis of geometric characteristics of segmented objects in an n-dimensional data space

Info

Publication number: EP1938270A2
Application number: EP06806044A
Authority: EP
Inventors: Wolf Delong
Original assignee: Carl Zeiss Imaging Solutions GmbH
Current assignee: Carl Zeiss Microscopy GmbH
Priority date: 2005-10-11
Filing date: 2006-10-05
Publication date: 2008-07-02
Also published as: WO2007042195A3; US20080253654A1; US8189915B2; WO2007042195A2; DE102005049017B4; DE102005049017A1

Abstract

The invention relates to a segmentation method comprising the following steps: a single data space is selected in an n-dimensional characteristic space by the user in a first step. Said selected data space is fundamentally interpreted by the system as containing at least two categories of objects to be segmented. In the following steps, the system first determines a separating function in the n-dimensional characteristic space for differentiating the at least two categories and then applies said separating function to the entire data space or a large part of the data space. Said segmenting result is then visually presented to the user in real time. The invention also relates to a method for classifying objects on the basis of geometric characteristics of objects previously segmented according to any method in an n-dimensional data space. In a first step, at least two objects are selected as representatives of two different categories, then a number (m) of geometric characteristics per object is determined by calculating various whole wave functions, and the objects are classified on the basis of the defined number of geometric characteristics or partial quantities. The previously required segmentation of the objects can be carried out according to an inventive method.

Description

Method for segmentation in an n-dimensional feature space and method for classification based on geometric properties of segmented objects in an n-dimensional data space

The invention relates to a method for segmenting objects in an n-dimensional feature space, which is present as a data space, and to a method for classification on the basis of geometric properties of segmented objects in an n-dimensional data space.

Such methods are needed for example in image analysis or in the evaluation before radar signals. The dimension n of the data space can be any natural number. An example of a 2-dimensional data space is, for example, the amount of data associated with a phase contrast image in the microscopy, an example of a 3-dimensional data space, the amount of data associated with a color image with the color channels R-GB, and an example of a 16-dimensional data space to a radar image with 16 spectral channels associated amount of data.

In the prior art, the recognition of objects in images, e.g. using cyclic, interactive image analysis. Such a method is described in EP 1 154 369 A2 or DE 10017551 Al. In this method, the user roughly marks the image areas of interest to him and a computer program classifies the complete image areas within their correct limits. The disadvantage here is that the user must mark two areas in at least two steps, e.g. the object of interest and the background or two different objects that are adjacent. Since two image areas must be selected consecutively in time, this process is not really real-time capable.

It is a first object of the present invention to provide a method of segmentation capable of segmenting objects in an n-dimensional feature space present as a data space and requiring the user to select only a single image area. This object to provide a method for segmentation is achieved by a method having the features of claim 1. Advantageous embodiments of this method result from the features of the dependent claims 2 to 4 and 8 to 13.

It is a second object of the present invention to provide a method for classification based on geometric properties of segmented objects in an n-dimensional data space. This object is achieved by a method having the features of claim 5. Advantageous embodiments of this method result from the features of the dependent claims 6 and 7.

The two methods mentioned above should preferably be executable computer-implemented. Claim 14 specifies a suitable computer system and claim 15 specifies a suitable computer program product.

The segmentation method according to claim 1 comprises the following method steps: In a first step, the user selects a single data area in the n-dimensional feature space. This selected data area is always interpreted by the system as containing at least two classes of objects to be segmented. In subsequent steps, the system first determines a separation function in the n-dimensional feature space to distinguish the at least two classes and subsequently applies this separation function to the entire data space or a larger subset of the data space. This segmentation result is then visually presented to the user in real time.

In the segmentation method according to the invention, the results can be optimized in a real-time feedback loop using the pattern recognition capabilities of the user. Furthermore, additional features of the objects to be segmented, such as number of objects in the image, relative area of objects, minimum and maximum size, shape factors such as eccentricity, fralal dimension as a measure of the smoothness of the boundary lines or other suitable properties can be given. This information can be specified by the user as well as automatically extracted from the image by suitable methods. If the user is not yet satisfied with the segmentation result achieved, he can subsequently change the selected data area and thus visually display in each case the segmentation result changed by the system due to the then also changed separation function in real time.

Instead of just two classes, a larger number of classes can be specified. The number of classes can also be determined by an automatic procedure. Of course, according to the desired number of classes, a data area should also be selected by the user, which contains pixels or data points of a corresponding number of classes.

The separation function can be determined by first determining a reference point of the features (Si) for each dimension of the feature space by a mathematical method, subsequently projecting all data points to all combinations of two-dimensional subspaces of the n-dimensional feature space, and finally by a two-dimensional error minimization method a phase value and an amplitude value to a predetermined wave function are determined so that a suitably defined approximation error for this wave function is minimized by a suitable method. For sinusoidal or cosine wave functions, such an approximation error is the sum of the squared differences that is minimized by the least squares method. The wave function is an integer-periodic, continuous function.

As a method for determining the separation function, as an alternative to the above-described wavefunction-based method, all methods for determining separation functions for n-dimensional data sets can be used. Examples are methods with unsupervised learning, e.g. Kohonenkarten, "Neural Gas" algorithms, ART networks.

If, for example, the n-dimensional feature space is a gray value distribution, the local average of the gray value distribution and the local variance of the gray value distribution, then the wavefunction k is greater than two with k, and the resulting k classes can be combined into at least two classes. For example, the wave function may be three-fold and the resulting three classes may be two Classes are summarized. In particular, the classes with the largest local variance of the gray value distribution can be combined.

As already mentioned, the feature space can be three-dimensional and contain RGB image data of a digital color image. Alternatively, the feature space may be four-dimensional and contain image data of four fluorescence channels acquired with four detectors at different wavelengths of light.

The method can be successively applied to different locations of an object by successively selecting different data areas belonging to the same object. By interpreting each of these data areas such that it contains at least two classes of objects to be segmented, and based thereon determining the separation function, several classes then result, at least two of which are subsequently reunited. In this way, for example, an object that is embedded in two or more different backgrounds can be segmented so that the different backgrounds are distinguished.

The above method, in which the separation function is determined from a wave function, can also be applied to a method for classification on the basis of geometric properties previously according to any method of segmented objects in an n-dimensional data space. For this purpose, first at least two objects are selected as representatives for two different classes in a first step, subsequently a number (m) of geometric features per object is calculated by calculating wavefunctions of different integer wavefunctions and finally the objects are calculated on the basis of the determined number of geometric features or Subsets thereof classified. The previously required segmentation of the objects can in principle be carried out by means of an arbitrary method, but particularly advantageously according to a method according to the present invention.

To calculate the number of geometric objects, phase values and amplitude values can be calculated from the wave functions, wherein the amplitude values characterize the shape of the objects and the phase values characterize the orientations of the objects. The amplitude values calculated from the wave functions describe the shape of the objects size-invariant, translation-invariant and rotationally invariant. A computer system suitable for carrying out a method according to the invention should have means (1) for interactively inputting and selecting image areas and a monitor for real-time visualization of the results achieved. In addition, of course, there should also be a processor and a data memory for a computer program with a software code by means of which the method according to the invention can be implemented.

Embodiments of the invention will be explained in more detail with reference to the figures. Showing:

FIG. 1: a schematic diagram of a system suitable for carrying out the invention

Computer, monitor and input unit; FIG. 2 shows a block diagram of the method steps taking place in the segmentation method according to the invention; FIG. 3 shows a block diagram of the method steps taking place in the classification method according to the invention; FIG. 4 shows a microscope image with cells as a starting point for explaining the method according to the invention;

FIG. 5 shows the segmented image generated by the system from the image in FIG. 4; FIGS. 6 to 8:

The representations of projections into two-dimensional subspaces of an RGB

image; FIG. 9: explanations of the generation of the dumbbells in FIGS. 6 to 8

Remote functions; FIG. 10: a three-dimensional representation of one derived from FIGS. 6 to 8

Separation area in RGB space;

FIG. 11: A phase-contrast image as an example of a texture image FIGS. 12 and 13: FIG.

Two from the picture in Figure 1 1 by the invention

Segmentation method generated feature spaces that are used for the detection of

Brightness dynamics in the picture in Figure 1 1 are suitable;

FIG. 14: a two-dimensional histogram of the images in FIGS. 12 and 13; FIG. 15 shows a threefold wave function; 16: the image from FIG. 11 and the feature space of the texture information for a selected pointing region FIG. 17: Images for explaining the shape recognition

FIG. 1 shows a system comprising a computer (2) with a built-in main memory (4) and processor (3). In the main memory (4) is a program loadable, which enables the processor (3) for carrying out the method according to the invention. To the computer (2) is a monitor (1) and an input means (5), e.g. a mouse, connected. Using the mouse, the user can move a pointing area raised in the image displayed by the monitor (1) relative to the image.

An example of a practical image is shown in FIG. The pointing area is here provided with the reference numeral (24). The pointing area (24) should be positioned relative to the image such that the pointing area (24) comprises a part of the object (23) to be segmented and a part of the image background (22).

The running segmentation process will be explained below with reference to FIG. 2 using the example of a color image. The starting point in this case is the image (7), which exists as color brightness information in the three primary colors red, green and blue as a function of the two spatial coordinates x, y. In a first step (8), the user selects a region in the image (7) which should contain the object to be segmented and image background or image parts of two objects to be distinguished. The image information in this selected pointing region is interpreted by the system in a subsequent step (8) such that at least two classes of objects are contained in the selected pointing region. In the following steps, a separation function is determined on the basis of the image information in the pointing area. For this purpose, suitable features such as color brightness values in the three primary colors are analyzed and in a step (10) a reference point of the various features is determined. Then, in a step (11), all data points are projected onto all two-dimensional subspaces of the feature space. From this projection, which will be described in more detail below, phase values and amplitude values that determine the separation function as a wave function result in a subsequent step (12). In a subsequent step (13), this separation function is applied to the entire data space - or the subspace thereof to be segmented - and the result of the segmentation is displayed in real time in a step (14). As already stated above, the user first roughly points to the boundary between an object (23) and the background (24) or to the boundary between two different adjoining objects as indicated in FIG. As in the aforementioned EP 1 154 369 A2, the user selects an arbitrarily shaped area (22), z. A circle, and positions that pointing area to cover a portion of the object (23) and at the same time a portion of the background (24). The segmentation system can therefore assume that the boundary of an object runs within the circle. In addition, as in EP 1 154 369 A2, it can be assumed that both the texture / color of the object and the texture / color of the background are present in the pointing area. So this is not only a simplification of the necessary work steps, but at the same time an increase in the information content, namely the information about different textures / colors on the one hand and the border between the textures / colors on the other. The set of selected pixels should be such that it can be decomposed into two (or more) disjoint subsets of which one can be assigned to exactly one of several objects or the background. This increased information content can, for example, be exploited so that the recognition of an object can take place online while the user travels the pointing area over the image. The pointing area can be controlled, for example, by a mouse, a touchpad, a touch screen, a trackball, a joystick or other pointing device used to move the cursor on computers, and then a separation function is determined based on the texture / color in the pointing area The result of the segmentation is shown in Fig. 5. As the separation function, a wave function is preferably used, and the determination of a suitable separation function will be described below in more detail by an example.

The user has in the process of the invention during the movement in the image with the pointing area the immediate feedback of the computer program (in real time), whether this has correctly detected the object sought, or if corrections are necessary at some edge points of the object. Thus, for example, the mean value important for the classification can be optimized by shifting the pointing region, and likewise the representative selection of the relevant pixel subsets can be optimized. In the case of images which exhibit strong inhomogeneities, it is optionally possible to select a further pointing region which is used to expand the pixel quantity to be examined by further representative data. This results in N separation planes, from which a local classifier for the segmentation is determined for each pixel by a suitable method. Such methods are: a) the selection according to the distance of the local point to the known separation planes or their centers of gravity, b) the interpolation between the planes using the relative image coordinates of the example objects and the current picture element (morphing), c) the use of self-learning approaches such as linear or non-linear neural networks or d) the application of all separation planes and the use of the maximum distance. In addition to these four mentioned methods, however, other methods are possible.

Compared with the prior art, the present invention has the further advantage that it works in arbitrarily high-dimensional feature spaces. An example here is the three-dimensional color space with the colors red, green and blue. Another, even higher-dimensional example would be radar images with 16 or more spectral channels.

It should be expressly understood that the method is not limited to image processing. It works in any higher-dimensional feature space described by locally changing scalar fields.

The constructed classifier for the separation areas is by constructionem invariant against translation, rotation and extension. With suitable further processing, this also applies to the design recognition described in more detail later. Such invariance properties are only possible by the usual methods by complex mathematical treatments such as e.g. To achieve local Fourier analyzes or Gabor wavelets, whereby the serious advantage of real-time capability is lost.

Segmentation by means of circular wave functions:

The image is taken from the color values of a certain environment for which a difference is to be calculated. In the example of the color image, these are the 3 color channels with the indices 1, 2, 3. So, in this example, there are 3 dimensions, and for each dimension, a number of metrics corresponding to the number of image pixels in the pointing area. The Characteristics Snm divided by measured values and dimension form an n * m matrix in the general case

Dimensions 1 ... n Measured values 1 ... m

1st calculation step:

First, the mean values of the features in each dimension are calculated:

1 ^m mean, = - * Σs _lk

These mean values form reference points in the feature space. Instead of averaging the reference points can also be determined otherwise.

2nd calculation step:

In a subsequent second step, the coefficients of a phase matrix and an amplitude matrix are calculated for all two-relationships ij with j> i between the dimensions from the features Sij. In the example of three colors, these are the phase coefficients φ ₁₂ , φ ₁₃ and φ ₂₃ , as well as the amplitude coefficients amp _n , amp _u and amp ₂₃ for the relations red-green, red-blue and green-blue {re _IJ = ^ amp * cos (2φ)

in _tJ = Σamp * sin (2φ) k = \ with φ = arctan ^s , _k ^{~ m} ,

amp = τ] {s _lk - m, f + (s _ß - m _] J in .. φ = 0.5arctan (- -) re "

}

In the above equations, m; and ni _j the mean values calculated in the first calculation step in the individual dimensions.

An alternative is to omit the weighting of re and im by the amplitudes amp. The choice of the method results from the given boundary conditions, especially the nature of the image recording method (phase contrast, multi-channel fluorescence, etc.). The 3-dimensional color values are clearly projected into the levels red-green, red-blue and green-blue. This is shown in Figures 6 to 8. In each of these planes, a cosine (2φ) is fitted in polar coordinates after the smallest error square. These dumbbell-shaped entities (26, 29) divide the color values into two classes, the black measured values (28) and the white measured values (25). In this case, the center (27, 30) of the dumbbells (26, 29) is in each case the mean value from the first calculation step.

As shown in Figure 9, the dumbbells arise by plotting 2 sine waves instead of Cartesian coordinates over a circle of radius r. The dumbbells arise in this form if r is chosen equal to the amplitude amp of the sine wave. The rotation of the dumbbell relative to the axes results from the respectively associated phase values. The dumbbell value d from the center of rotation of the polar coordinates is then:

d (a) - r + amp * cos (2α - φ)

3rd calculation step:

In a third calculation step, a separation area (31) in the 3-dimensional color space is now calculated. This separation surface is shown in FIG. 10 in 3D. The separation area is determined by the fact that the mean value from calculation step 1 lies at this level. The following operations still determine the normal vector of the separation surface.

The components of the interface result from the maxima of the amplitudes in the amplitude matrix. In this case, the plane (two-dimensional subspace of the feature space) with the largest amplitude maximum is started, and the plane coefficients for the individual planes are subsequently calculated in the order of decreasing amplitude maximum. If the largest amplitude is in the green-blue plane, the area components c2 and c3 result in: c2 = amp * cos (φ) c3 = amp * sin (φ)

If the next larger amplitude lies in the red-green plane, then the last missing surface component cl results: cl = amp * cos (φ)

In the case of higher-dimensional data, corresponding further plane coefficients are then to be calculated in descending order of the amplitude values.

4th calculation step:

The result of the calculation steps 1 to 3 are 2 vectors, namely the vector mean from the coordinate origin to the mean on the separating surface and the vector plane perpendicular to the separating surface. This makes it possible to decide for each pixel on the basis of its color value Sk, on the softer side of the separating surface it lies, or to which object to be segmented it belongs. For this purpose, a threshold is first calculated, which is given by the scalar product of the two vectors mean and plane.

Threshold = scalar product (meα / -z, /? / ΑA7e)

This then results in:

The color value lies before the separation surface if the scalar product (Sk, p / ö «e) is smaller than the threshold and the color value lies behind the separation surface if the scalar product (Sk, p / ύ7" ze) is greater than or equal to the threshold ,

In the special case of gray images (= one-dimensional feature space), the calculation steps 2 and 3 can be omitted. The threshold from calculation step 4 is then equal to the mean value from calculation step 1, since the plane from calculation step 3 thereby shrinks to a point. In a two-dimensional feature space, the plane of calculation step 3 shrinks to a straight line.

As a result, the above method corresponds to the result of the known method for segmenting gray scale images by determining an optimized threshold (Calculation of the mean value, division of the pixel quantity into two subset with the mean value as threshold, calculation of the mean values of the two subsets, these mean values correspond to the emphases in the indicated procedure).

Texture segmentation:

With the above steps 1 to 4 can be segmented objects that are distinguishable by their color or gray value from the background. But now there are pictures in which the objects can not be distinguished from the background by their color or gray value, but by their brightness distribution. An example of this is the image of cancer cells as shown in Figure 11. In normal light, these cancer cells are largely transparent. Polarized light makes the cells visible in so-called phase contrast. The objects are distinguished by their brightness dynamics and not by a brightness range from the homogeneous background.

With the aid of the above steps 1 to 3, first of all a feature space adapted for this task is generated. The image is transformed before editing so that the real-time capability is restored using three classes. For this purpose, a pointing region of the size of, for example, 3 by 3 pixels or larger is automatically applied for each pixel i, j of the image to be processed. Instead of reconstructing the object in the image as in calculation step 4, its distance from the separation surface is calculated for each pixel of the pointing region. All these distances are added up correctly according to the location of the pointing area. Let: mean, _} mean of the pointing region at the point i, j plane, _} plane vector of the pointing region at the point i, j thresh _t] = slalar product (mean _l} , plane,) Then:

Dist i, _j = ^ ^ scalar {S, _ _ _kj, _plane; ) - thresh, _} k = - \ I = -]

The result Dist i, j is shown in FIG.

In addition, the lengths of the plane vector plane are also added to the correct position. Plenary, _j = J scalar product {plane, _} , plane, _:) Then: fc = + l / = + 1

^Plen u = Σ ΣP ^len , -kj-i k = - \ / = - 1

The result Plen i, j is shown in FIG

FIGS. 12 and 13 now illustrate a two-dimensional feature space which is used for the

Detection of the brightness dynamics is suitable. First, the feature space must still be normalized, so that both dimensions of the feature space comprise the same number range, e.g. the range of numbers between 0 and 1 has to be particularly favorable

sigmoid

; / = l / (l + exp (-g (x-x ₀ )).

Let m be the number of pixels, then

1 ^m meand = - * ^ Dist _k ^m t = i

1 ^m meanp = - * ^ Plen _k ^m k = \ and the normalization via the sigmoid function is performed by using the numerical values of Dist and Plen for x and x ₀ meand or meanp for x.

As a two-dimensional feature space, it can be imaged as a two-dimensional histogram, which is shown in FIG. The pixels form a triangle in the feature space, with the pixels at the top at the top are the pixels of the background, right below the bright pixels within the objects and lower left are the dark pixels of the cells. Such a triangular shape can be recognized with a wave function of period 3. For this purpose, a cosine (3φ) is fitted according to exactly the same scheme as in the above calculation step 2. Such a wave function of period 3 is shown in FIG. 15 on the left in Cartesian coordinates and in FIG. 15 on the right in polar coordinates. The right-hand part of the image in FIG. 16 shows the feature values Dist and Plen for the pointing region 31 in the left-hand part of FIG. 16. In the image, then the pixels in the phase range of the upper oscillation belong to the background and the pixels in the phase range of the two lower oscillations belong to the object. The amplitude of the oscillation is a measure of the quality of detection. According to the prior art, a possible alternative is the use of a Kohonen neural network with 3 classes as described in T. Kohonen, Self-Organizing Maps, Springer Verlag, ISBN 3-540-62017-6. The background is then the class with the smallest class variance and the object is the other two classes. The disadvantage here is that no quality of the classification is recognizable.

Shape recognition:

The method of using wavefunctions can also be used for the character recognition or for the classification of objects. The corresponding method is shown in FIG. In this method, the starting point (15) is the already segmented image. In this method, at least two objects to be distinguished are selected by the user in a subsequent step (16). In a subsequent step (17), a number of geometric features are calculated by calculating wave functions. Phase values and amplitude values are again calculated from the wave functions in a subsequent step (18), and the objects are subsequently classified in a step (19) on the basis of the geometric features. The classification result is visualized in a step 20 in real time.

This classification method can be used, for example, for design recognition. In the example of FIG. 17, worms in a phase contrast recording are recognized above via texture segmentation. These worms exist in two forms, stretched (alive) (see left part of picture) and rolled up (dead) (see right part of picture). The pointing area necessary for the wave functions is the object itself and the feature space are directly the pixel coordinates of the objects. In the example of FIG. 17, the wave functions 2 (fit of a cosine (2φ)) to 7 (fit of a cosine (7φ)) are calculated. From this, the shape coefficients (from the phase values and the amplitude values of the wave functions) are calculated:

The presentation is made below in program form. The procedure is completely identical to the above calculation step 2.

Let xc, yc be the center of gravity of the object. The calculation takes place after calculation step 1 as the mean value in the individual dimensions x and y. Calculation step 2 as a program: For each pixel x, y of the object

{zx = x - xc; zy = y - yc;

phi = atan2 (zy, zx); dist = sqrt (zx * zx + zy * zy); distsum + = dist;

Sum for the coefficients

for (k = 0; k <ncoefficient; k ++)

{dcos [k] + = dist * cos (k * phi); dsin [k] + = dist * sin (k * phi);

}} Normalization for (k = 0; k <ncoefficient; k ++)

{amp [k] = sqrt (dcos [k] * dcos [k] + dsin [k] * dsin [k]) / distsum;

} amp [k] are the shape coefficients

In Figure 17, below, the shape coefficients (numbers between 0 and 1) are shown as a block diagram. This block diagram in turn represents a six-dimensional feature space (shape space). For the distinction of the two worm forms, the above segmentation method can now be used again by calculating the separation surface between the worm forms in this six-dimensional shape space by means of wave functions. One worm shape then lies on one side of the separation surface and the other worm form on the other side of the separation surface. The above classification is invariant to translation, rotation, mirroring, enlargement, and reduction without a previous elaborate transformation of image space into an invariant property space.

Claims

claims:

A method of segmentation in an n-dimensional feature space existing as a data space, comprising the steps of: a) selecting a single data area, b) interpreting the selected data area such that it contains at least two classes of objects to be segmented, c) determining d) generalize by applying the separation function or the separation function resulting from local interpolation of the separation functions to the entire data space or a larger subset of the data space, and e) real-time visualization of the data space by the generalization achieved result.

2. The method of claim 1, wherein the separation function is determined by f) determining a reference point of the features (Si) for each dimension of the feature space by a mathematical method, g) all data points on all combinations of two-dimensional subspaces of the n-dimensional one Feature space, and h) a phase value and an amplitude value to a predetermined wavefunction are determined by a two-dimensional error minimization method so that the approximation error in each of the subspaces becomes minimal.

The method of claim 2, wherein the wavefunction is an integer-periodic, continuous function.

4. Method according to one of claims 1-3, with the following additional intermediate steps between steps c) and d): c1) carrying out steps a) to c) in an interactive feedback loop until the local separation function has been optimized for the application, and c2) Repetition of steps a) to cl) for other objects in the image and collecting and storing the resulting separation functions.

5. A method of classifying based on geometric properties of segmented objects in an n-dimensional data space, comprising the steps of: a) selecting at least two objects as representatives of two different classes, b) determining a number (m) of geometric features per object Calculating wavefunctions of various integer wavefunctions and, c) classifying the objects based on the determined number of geometric features or subsets thereof.

The method of claim 5, wherein phase values and amplitude values are calculated from the wave functions, and wherein the amplitude values characterize the shape of the objects and the phase values characterize the orientations of the objects.

7. The method of claim 5 or 6, wherein amplitude values are calculated from the wave functions, which describe the shape of the objects size invariant, translation invariant and rotationally invariant.

8. The method of claim 2, 3 or 4, wherein the n-dimensional feature space is a gray value distribution, the local average of the gray value distribution and the local variance of the gray value distribution, the wavefunction k- is greater than two with k, and the resulting k Classes of at least two classes are summarized.

9. The method of claim 8, wherein the wavefunction is three-fold and the resulting three classes are grouped into two classes.

10. The method of claim 8 or 9, wherein the classes are summarized with the largest local variance of the gray value distribution.

1. The method of claim 1, wherein the feature space is three-dimensional and includes RGB image data of a digital color image.

The method of any one of claims 1-4, wherein the feature space is four-dimensional and includes image data of four fluorescence channels acquired with four detectors at different wavelengths of light.

13. The method of claim 1, wherein the object is selected at more than one location, the method of steps b) and c) is performed for each of the selected object areas, and at least two of the resulting classes are subsequently merged.

A computer system suitable for carrying out a method according to any one of claims 1 to 13, comprising means (1) for interactively inputting and selecting image areas and a monitor for real-time visualization of the results obtained.

A computer program product loadable into the memory of a digital computer and having software code for performing a method comprising the steps of any one of claims 1 to 13 when the program is run on the computer.