**Mining Lung Shape from X-Ray Images**

*Vassili Kovalev, Alexander Prus, and Pavel Vankevich*

**Abstract.** This work presents an approach for mining 2D shape of human lungs from large x-ray image archives of a national level. Images were accumulated in framework of a compulsory computerized country-wide screening programme launched few years ago which is being under development. Three study groups of images containing about 21, 18 and 39 thousands of subjects were created by sub-sampling from a test database resulted from pulmonary x-ray examinations of a total of 188 thousands people. These groups have been well balanced by age and gender according to the existing biomedical standards and subsequently used as input data for searching different kinds of regularities in 2D projective lung shape and size. The approach followed in the paper combines different methods including procrustes shape analysis, Bookstein’s baseline shape registration, multi-dimensional scaling, regression models with broken-line relationships as well as various conventional statistical procedures. As a result, interesting gender- and age-related regularities in lung shape were discovered and documented in the paper.

**1. Introduction**

Similar to data mining, the image mining can be defined as the process of extracting hidden patterns from images. More specifically, image mining deals with extraction of implicit knowledge, image data relationship or other patterns not explicitly stored in the image database. As more and more image collections are gathered, the image mining becomes an increasingly important tool for transforming these visual data into knowledge. Image mining can be applied to the visual datasets of virtually any size, and while it can discover hidden patterns, it can not discover patterns which are not already present in the image collection.

Image mining research has borrowed some ideas from such well developed areas as computer vision, image analysis, image retrieval, machine learning, and artificial intelligence. The fundamental challenge in image mining is to determine how low-level, pixel representation contained in an image can be effectively and efficiently processed to identify high-level relationships. Typical image mining procedure involves preprocessing, segmentation, feature extraction and discovering significant patterns out of the extracted features accomplished by a semantic interpretation and obtaining the final knowledge. Being applied to the large archives of biomedical images, the image mining technology allows to detect natural clusters, to find new diagnostic features and, in some cases, to discover new fundamental biomedical regularities and even decrees of nature.

In this work, we presented an approach for mining 2D projective shape of human lungs from very large x-ray image archives and reported some interesting gender- and age-related regularities discovered in the lung shape and size.

**2. Materials and Methods**

*2.1. Image segmentation and Shape Representation*

A test image database containing results of pulmonary x-ray examinations of the chest of more than 188 thousands of healthy subjects aged 20 to 84 years was used as input image data repository. Subjects’ age was measured in complete years with the precision of one year. All the original images were segmented using the lung segmentation procedure illustrated on Fig. 1 and described in the paper cited at the end of this work. Segmentation examples for different age groups are given in Fig. 2. The projective shape of each lung of every subject was represented by 500 landmark points located at the ends of corresponding rays. Along with this polar coordinate system, the equivalent representation in Cartesian coordinates was also used for lung shape description where necessary.

**Fig. 1.** General algorithm of the image segmentation procedure.

**Fig. 2.** Lung segmentation examples for subjects from different gender groups and age categories.

*2.2. Study Groups*

The first study group of images called G1 (see Fig. 3) was formed out for mining lung shape distinctions associated with age in different age categories or age ”classes”. It consisted of three sub-groups conditionally named as young (20-30 years), mid-aged (40-50 years) and aged (60-70 years) subjects. Each sub-group included images of 6930 subjects (3465 pairs of male-female subjects with the same age, 315 males and 315 females per age year), total 20790 images in the group G1.

**Fig. 3.** Composition of study groups.

The second group of images named G2 has been created for mining both age- and gender-related lung shape regularities. It was covering the wide life span between the 20 and 80 years for both genders. This age range corresponds to 60 age intervals from 20 to 79 complete years each. Similar to the above group G1, in order to achieve a perfect gender and age matching heavily favored by the existing statistical standards, group G2 was formed using pairs of male-female subjects of the same age. A total of 9000 male-female pairs were collected from the image repository, 150 pairs for each year. Thus, the group G2 consisted of 18000 x-ray images of the chest of 18000 different subjects aged 20 to 79 years, 300 images per age year (150 males plus 150 females), 9000 males and 9000 females in total.

Finally, since some interesting regularities were discovered in females of group G2 concerning dependence of lung shape and lung area on age, an additional image group G3 was created explicitly from female subjects aged 20 to 57 years, 1016 persons per age year, 38608 females in total. It should be noted that this is the first work that makes use the image data described above.

*2.3. Integral Shape Features*

A number of commonly recognized shape features were calculated for the left and right lungs of every subject. They include lung area, dimensions of boxing rectangle, boundary length, compactness which was defined in usual way ie., as squared boundary length divided to the area as well as the size of major axis, minor axis and the eccentricity of the ellipse with equivalent area. The ellipses were fitted to the lung contours using general linear model and the statistical confidence ellipse tools. The ellipse eccentricity feature ε<1 was computed based on major and minor half-axes. In addition, the lung contour itself being represented by the vector of lengths of 500 rays ordered counter-clockwise naturally served as a polar signature of lung shape allowing computing such standard features as statistical moments.

*2.4. Shape Analysis Methods*

Statistical shape analysis is a geometrical analysis from a set of shapes in which statistics are measured to describe geometrical properties from similar shapes or different groups, for instance, the difference between male and female Gorilla skull shapes, normal and pathological bone shapes, etc. The statistical shape analysis involves methods for the geometrical study of objects where location, rotation and scale information can be removed. It is known that the key tasks of shape analysis are to obtain a measure of distance between two shapes, to estimate average shapes from a sample and to estimate shape variability in a sample.

In this work we have chosen 2D version of procrustes shape analysis described in literature and implemented in form of the “shapes” software package in framework of R, a language and environment for statistical computing. The procrustes analysis is well known as one of the advanced shape analysis methods and it considers objects made up from a finite number *k* of points in N dimensions which are called landmark points. The shape of an object is considered as a member of an equivalence class formed by removing the translational, rotational and scaling components. Specifically, the following basic algorithms of procrustes analysis were used: calculating Riemannian distance between two shapes, Bookstein’s baseline shape registration, testing for mean shape differences of groups of lung shapes with the help of Hotelling’s *T ^{2}* and Goodall’s

*F*tests. These tests were developed for examining differences in mean shape between the two independent populations and involve complex eigenanalysis and iterative generalized procrustes analysis for two dimensions.

In addition, when studying the age-related lung shape changes, a regression model with broken-line relationships suggested by Muggeo was used (please google by yourself). The method is aimed to estimate linear and generalized linear models having one or more segmented relationships in the linear predictor. Estimates of the slopes and of the possibly multiple breakpoints are provided. In this work the method was used for detecting critical age points where the trend is changed significantly.

For visualization of a set of M shapes in feature space, an M×M matrix of mutual Riemannian distances has been computed and 2D shape scatterplot was created and displayed. To accomplish this, the Multidimensional Scaling (MDS) method was utilized for reducing feature space dimensionality down to two dimensions. Note that the multidimensional scaling provides an approximate solution, which is suitable for visual examination of object scattering only.

**3. Results**

3.1 Lung Size in Different Age Categories

The lung shape distinctions caused by age were studied with the help of group G1 consisting of three sub-groups whose members were conditionally categorized to young (20-30), mid-aged (40-50) and aged (60-70) subjects. We start from very simple but yet very important, from biomedical point of view, lung feature – the lung size. The lung size is measured by its projective x-ray area and by axes of the fitted ellipse. Changes of lung area were assessed by way of pair-wise comparison of the three age sub-groups using regular two-tailed t-test. Results are summarized in Fig. 4.

**Fig. 4.** Change of mean lung area for subjects from young (20-30 years), mid-aged (40-50 years) and aged (60-70 years) groups (left plot) and its statistical significance (table on the right). Each of three age groups consist of 6930 subjects including 3465 males and 3465 females, 630 subjects per age year.

From the data presented in the figure, the following two important facts becoming immediately evident:

(a) The lung area declines with age in a non-linear manner. In particular, the reduction is more steep when transferring from young to the mid-aged group comparing to the considerably less prominent reduction when jumping for the same 10 years but from mid-aged to aged individuals. These observations are confirmed by the comparable significance values of group differences reported by *t-*test with the same degree of freedom *df* =6928 in all the occasions (see table on the right of Fig. 4). The significance scores of lung reduction for moderate 40-50 and elderly 60-70 years were nearly twice as low as in young 20-30 and mature 40-50 periods of life (*t=*16.2 and *t=*15.7 against *t=*27.4 and *t=*31.1 for males and *t=*26.1 and *t=*25.7 against *t=*44.1 and*t=*49.4 for females).

(b) Despite the fact that age-related decline takes place for both lungs and both genders, male and female persons are affected differently. Namely, the rating of lung area reduction is always greater in females comparing to male subjects. Quantitatively, the joint projective area of both lungs changes from the mean value of 544 cm2 computed over the group of young males aged 20-30 years down to the value of 472 cm2 in males aged 40-50 years (reduction rate is 13.2%). In female subjects it reduces from 469 cm^{2} down to 373 cm^{2} with a noticeably greater rate of 20.5% for the same 10 years. When comparing groups of mid-aged subjects of 40-50 years old with those aged 60-70 years, corresponding lung reduction values are 472 versus 431 cm2 for males (8.7%) and 372 versus 320 cm^{2} (13.9%) for females. The observed regularity of a more quick lung area reduction in females is further confirmed by corresponding statistical significance scores provided in Fig. 4.

*3.2. Shape of Lung Ellipses in Different Periods of Life*

Statistical assessment of differences between ellipses fitted to the lungs of subjects belonging to different age groups has revealed a bit more complicated pattern of age-related changes compared to the lung areas. Although the size of major and minor ellipse axes generally behave in a way similar to the lung area, ie., decreases with age, the reduction rate varied significantly reflecting corresponding variations in global shape of lungs. Since the eccentricity feature captures mutual relationships between the two axes and describes the global elongated shape of lungs in relative units, it is worth to consider here the eccentricity instead of raw axes values.

**Fig. 5.** Significance of the eccentricity (oblongness) differences of lungs for young (20-30 years), mid-aged (40-50 years) and aged (60-70 years) subjects (top two panels) and examples of mean lung shapes and their dissimilarity (bottom two panels).

As it can be easily seen from Fig. 5, the eccentricity exhibits the non-linear character of age-related changes even more sharply than the lung area. It is especially true for the left lung, the eccentricity of which drops down dramatically from young (20-30) to mid-aged (40-50) periods of life and remains nearly unchanged over the second gap from 40-50 to 60-70 years. Similar trend can be observed for the right lung too but with a considerably lower confidence. In fact, the mean eccentricity values even slightly growing up after 40-50 years but the growth rate is close to the border of statistical significance (at this point it is good to remember that degree of freedom here is as high as *df =*6928 and the commonly-accepted minimal threshold for statistical significance is *p*<0.05 what approximately corresponds to *t>*2.0).

The significance rates supplied with the table depicted on the top-right quarter of Fig. 5 as well as pictures of mean group shapes accompanied by their dissimilarity values (see bottom two panels of Fig. 5) provide further quantitative evidences for the discovered regularity. In everyday words, all these numbers testify for a conclusion that during the ageing the lung shape tends to ”round up” and this process is mostly accomplished by the age of about 50 years. Such a behavior is more prominent in the shape of left lung.

Investigation of other global shape features of lung images of group G1 did not add anything interesting to the results reported above. In particular, the shape compactness feature ε, which admittedly might be quite useful for distinguishing image objects with sharp and rounded edges in a number of computer vision problems, has demonstrated here some inconsistent behavior. Therefore it was found to be useless for capturing any distinct trends in rather homogeneous sets of lung shapes we are dealing with.

*3.3. Lung Shape Distinctions in Different Age Categories*

Now we have arrived to the lung shape mining stage which exploits some sort of ”feature-free” methods of comparing the whole shapes. As it was described in previous section, we capitalize on the procrustes shape analysis that make use the efficient shape comparison using Riemannian distance, utilize 2D shape registration algorithms and employs specific statistical tests for examining shape differences. To this end, we have performed in a pair-wise manner both the Hotelling’s *T ^{2}* test and Goodall’s

*F*test for assessing the significance of lung shape differences in pairs of age sub-groups of group G1. Results are represented in Fig. 6 in form of a plot of Hotelling’s

*T*statistics (left panel) and in less vivid but more precise form of a table of statistical significance expressed by both Hotelling’s

^{2}*T*and Goodall’s

^{2}*F*values.

**Fig. 6.** Significance of lung shape differences for subjects from young (20-30 years), mid-aged (40-50 years) and aged (60-70 years) groups assessed using Hotelling’s *T ^{2}* test (above the line) and Goodall’s

*F*test (under line) for mean shape differences.

In all the occasions the observed shape differences were found to be highly significant that is *p-*value was much less than 0.05. Also, similar to previous experiments, the results summarized in Fig. 6 suggest that the largest portion of lung shape changes occurred from young (20-30) to mid-aged (40-50) period and the magnitude of these changes in female subjects is always greater than in males (see specific values for more details). The greater age dependence of lung shape in females can also be noticed from the example of scattering of young and aged subjects given in Fig. 7.

**Fig. 7.** Example of scattering of young and aged subjects in lung shape space reduced to 2D by multi-dimensional scaling method (Riemannian distances).

*3.4. Gender-Related Differences in Lung Shape*

In previous sections we have been mostly concentrated on the assessment of the influence of age factor to the lung shape. Nevertheless, studying the effect of age, we have performed all the evaluations for male and female subjects separately and therefore already contributed towards disclosing some of gender-related regularities. In this section the gender-related differences will be investigated further based on the well-balanced sample of 9000 males and 9000 females of group G2 densely and evenly covering a good portion of the life span from 20 to 79 years inclusive.

It is obvious that the male and female lungs are different in their size. When comparing lung shapes visually or using quantitative features sensitive to size, these differences may confuse results and cause various miss-interpretations. Thus, it is worth to start with an estimation of size-induced differences. This may be done, for instance, by looking at the male/female lung shape differences with and without scaling. Fig. 8 presents mean lung shapes for male and female subjects of group G2 computed by a straightforward averaging (top left panel) and with the help of Bookstein’s base line registration of all 18000 shapes(top right panel). As it can be seen from the figure, the base line registration makes the existing gender-related shape differences very explicit. In particular, it can be noticed that the greatest cross section of lower lung aperture is wider in males comparing females. This is more prominent in the right lung which also appears to be slightly shorter and wider in males what reﬂects the known fact of their more brachymorphic structure of the chest.

**Fig. 8.** Gender-related differences in lung size and lung shape as revealed by comparison of mean (top left) and registered (top right) lung contours of 18000 subjects along with the Hotelling’s *T ^{2}* significance score of gender-related lung shape differences by life tetrads (plot underneath).

In order to reliably estimate the significance of lung shape differences between male and female subjects in different ages, the whole study period of 20-79 years was subdivided into tetrads and the Hotelling’s test for shape differences was performed on every subset of 1200 lung images (600 males plus 600 females) for each of 15 tetrads. The resultant significance scores *T ^{2}* plotted at the bottom of Fig. 8 suggest that the gender-related shape differences keeping highly signiﬁcant (

*p-*values were also much less than 0.05) for every tetrad of the examined period of life. It can be noticed that the shape of the right lung appears to be more distinct in male and female subjects than the shape of the left one. However, this regularity holds true till the age of 60-64 years and switches to opposite afterwards. Looking to the shape of significance curve depicted in Fig. 8, one can also note that the significance of gender-related differences tend to keep relatively low in young and in opposite – the elderly periods of life with more high values in between and a confident bump of yet unknown nature within 52-64 years.

*3.5. Lung Area Changes during Ageing*

Our previous experience suggest that the new knowledge on ageing process of the human body and its functional systems always attracting a lot of attention from both scientific and general public domains. In many occasions changes in organ’s size are proven to be a very important sign of pathology and/or age-related decline. Thus, in context of this image mining study it is very interesting to try to find out how exactly the lung size changes during the normal ageing and whether these changes going synchronously for both genders or not.

A simple correlative analysis shows that the lung size significantly correlates with age of 18000 subjects of group G2 with the correlation coefficient*k _{L}* = −0.43 for the left lung and

*k*= −0.45 for the right one. When considering genders separately, the correlations were

_{R}*k*= −0.39 and

_{L}*k*= −0.40 for the left and right lungs of males versus

_{R}*k*= −0.56 and

_{L}*k*= −0.58 in females. It is easy to see from these numbers that correlation of lung projective area with age is greater in females what confirms once more the fact of more significant age-related changes characteristic for female subjects that was discovered earlier in this work with the help of study group G1.

_{R}After the above general observations, let us take a closer look at the age-related dependence of lung area and its diversity by gender. For this purpose, the whole study period from 20 to 79 complete years was first subdivided into tetrads and statistical box-and-whiskers graphs plotted separately for the area of left and right lungs over the resultant 15 tetrads (see the right lung areas of males and females illustrated in Fig. 9 as an example). As it can be qualitatively concluded from the figure, female’s right lung clearly demonstrates some specific, non-linear behavior during the ageing while male’s lung area staying approximately linear. (It should be noted that corresponding measurements have confirmed that both left and right lungs behave in pretty much the same way and this is why the only right lung plots are presented in Fig. 9. Such left-right synchronism is not surprising given that the correlation of left/right lung area is as high as 0.93 in males and 0.94 in females of group G2.)

**Fig. 9.** Changes of lung area with normal ageing in 9000 male (left plot) and 9000 female (right plot) subjects. Statistical data are presented by age tetrads for reliability.

Finally, for detecting ”critical” age points where the trend in lung size reduction (ie., in the slope of regression line) is changed significantly, we employed regression model with broken-line relationships recently suggested by Muggeo. The three series of experiments on 9000 female subjects were subsequently performed using projective area or the left lung, right lung, and the total lung area (ie., the sum of both lungs) as regression response and the age as a predictor. Two age points, 34 and 50 years inspired by plot in Fig. 9 were set as an initial guess of broken line location required by the method. As a result, the following values of estimated breakpoints and significance scores were obtained.

(a) Left lung: 33.3 years (t =−11.8) and 47.8 years (t =8.6). The ”improved” location of these points computed under condition of null left slope gave 33.2 and 47.8 years respectively.

(b) Right lung: 33.1 years (t =−11.2) and 47.5 years (t =8.9). With the hypothesized null left slope: 33.1 and 47.5 years respectively.

(c) Both lungs: 33.2 years (t = −11.7) and 47.6 years (t = 9.0). With the hypothesized null left slope: same 33.2 and 47.6 years.

Additional experimentations performed with initial guess values varying in a reasonably wide age range of about 6-7 years have demonstrated good reliability of the output breakpoint estimates the method always converged to. Detailed analysis of the linear slopes including bordering slope values of 95% confidence intervals suggest that the left shoulder of the piece-wise linear regression standing before 33 years may be considered as a plateau (no confident positive or negative slope) whereas the right one (after 48 years) is going slightly upwards. No significant breakpoints were found in male lung size regressions.

Since the above regularities discovered on the study group G2 were found to be very interesting, they were examined further on the group G3 consisting of 38608 females. The resultant age points obtained with the help of G3 were similar, namely: 34.2 and 49.1 years (left lung), 35.4 and 51.4 years (right lung) and 34.9 and 49.6 years (both together). Contrary to the G2, the right shoulder beginning around 50 years was found to be rather flat. Thus, summarizing the results we may conclude that the normal ageing process of adult female subjects accompanied by a decline of lung projective area which is non-even across the adult life span. The temporal pattern of lung size reduction can be roughly described as «plateau–slope–plateau». The accelerated lung size reduction starts around 33-35 years and lasted till approximately 48-50 where the decline process starts to slow down. This regularity was not confirmed for male subjects.

**4. Conclusions**

1. The image mining approach reported with this study allows to manage large collections of x-ray data, reliably extract projective lung shape, and run 2D shape mining procedures for discovering new regularities from large image databases of a national level.

2. It was found that the lung projective area declines with age in a non-linear way. The significance scores of lung reduction from moderate 40-50 to elderly 60-70 years were nearly twice as low as from young 20-30 to mature 40-50 periods of life. The rating of lung area reduction is always greater in females comparing to male subjects. The temporal pattern of lung size reduction in females can be roughly described as «plateau–slope–plateau». The accelerated decline starts around 33-35 years and lasted till 48-50 where the process begins to slow down.

3. The procrustes analysis suggest that similar to the size, the largest portion of lung shape changes occurs from young (20-30) to mid-aged (40-50) period and the magnitude of these changes in female subjects is always greater than in males. During the ageing, the lung shape tends to «round up» (the eccentricity of fitted ellipses decreases). This process is mostly accomplished by the age of about 50 years. Such a behavior is more prominent in the shape of left lung.

It is anticipated that future work will be concerned with discovering reliable markers of biological age using both shape and intensity information derived from X-Ray and CT lung images as well as directed towards searching for new diagnostic features based on lung texture mining.

*This material is largely based on the following paper:*

Kovalev V., Prus A., Vankevich P. Mining lung shape from X-ray images. In: Int. Conf. on Machine Learning and Data Mining (MLDM-2009), Leipzig, Germany, P.Perner (Ed.), LNAI, vol. 5632, Springer Verlag, 2009, pp. 554-568.

### A method for highlighting tumor borders in lung CT images

## Purpose

Computed tomography is the primary modality for imaging lung cancer patients. However, the problem is that in the native CT scans the lung regions with the atelectasis and with the malignant tumors have quite similar attenuation values. The mean intensity of atelectasis area is 36.9±6.5 Hounsfield units (HU) while for the malignant tumors it is varies in a window of 37.0±7.7 HU. Therefore the visual discrimination and separation of the atelectasis and tumor is hardly possible.

Recently, some advanced methods of detecting hardly visible borders between the random image textures have been suggested. Moreover, it was experimentally proven that these methods capitalizing on so-called “generalized gradient” are able to highlight the border which is poorly visible or completely invisible for human eye.

The purpose of this particular paper is to present results of an experimental study of the ability of the generalized gradient method to highlight hardly visible tumor borders under condition of adjacent atelectasis in native CT images of lung cancer patients.

## Methods

### Materials

In this study we used 40 CT images of the chest of patients with lung cancer and the atelectasis of a portion of the lung as diagnosed by a qualified radiologist and confirmed histologically. Thirty three of them were males and remaining seven were females. The age of patients ranged from 41 to 80 years with the mean value of 61.7 years and standard deviation of 8.7 years.

CT scanning was performed on a multi-slice Volume Zoom Siemens scanner with the standard clinical kV and mA settings during the one-breath hold. The voxel size of 9 tomograms was in the range of 0.65-0.74 mm in the axial image plane with the slice thickness equal to the inter-slice distance of 1.5 mm. The voxel size of 31 remaining tomograms was 0.68 mm in the axial image plane with the slice thickness equal to the inter-slice distance of 5.0 mm. No intravenous contrast agent was administered before the collection of scan data what is a significant detail of present study.

### The generalized gradient method

The generalized gradient method was first introduced as so-called classification gradient and slightly improved afterwards. The generalized gradient method treats the voxel values taken from halves of appropriately sized sliding window as two samples that need to be compared by a suitable way. Once it is done, the value of corresponding dissimilarity measure is treated as a “gradient” value at the current sliding window position for given orthogonal orientation X, Y and Z. The sets of voxels may, for example, be compared in a statistical manner using conventional *t-*test or using some classification procedure of comparing two samples of voxels. Also in order to achieve the resultant dissimilarity estimate as precise as possible, a bootstrap multi-step meta-procedure can be employed. The example of generalized gradient maps for synthetic images is presented in Fig. 1.

**Fig. 1.** a) original synthetic image; b) GG map using t-test; c) GG map using SVM, sliding window parameters R=3, d=1; d) GG map using SVM, sliding window parameters R=4, d=2.

The evaluation procedure

The ability of the generalized gradient method to highlight tumor borders under condition of adjacent atelectasis was examined in two steps.

(a) The total of 40 gradient maps with voxel-by-voxel correspondence to original native CT scans were calculated using unpaired *t-*test as the elementary procedure of quantification of the difference between the voxel sets sampled from window halves.

(b) The gradient maps were visually examined synchronously with original CT images by a chief radiologist of an oncology hospital. Examination of each particular map resulted in an integral expert categorization of the map to one of the following three categories: the map is definitely useful for detecting tumor border (“yes”), the map is useless (“no”), and the intermediate case where the utility of gradient map in highlighting tumor border remains unclear by one or other reason (“unclear”).

## Results

Quantitative assessment of the utility of generalized gradient maps in highlighting lung tumor borders was performed separately for the first subgroup of 31 native CT images with the slice thickness of 5.0 mm and remaining 9 images of the second subgroup with the slice thickness of about 1.5 mm. Typical examples of original CT image ROIs and corresponding gradient map regions are presented in Fig. 2.

As a result of experimentation, on the first subgroup of patients it was revealed that the generalized gradient maps were definitely useful for detecting tumor border in 17 patients (54.8%) whereas in 9 other cases (29.0%) they did not provide any help for solving the problem of separation the malignant tumor from adjacent atelectasis. The efficacy of maps in the rest 5 cases (16.1%) was found to be unclear.

The results of similar examination of CT scans with reasonably thin slices of about 1.5 mm suggest that it appears to be unlikely the slice thickness is an important parameter for the method. In particular, the distribution of cases between the “yes”, “no”, and “unclear” categories was 5 (55.6%), 3 (33.3%), and 1 (11.1%) respectively.

**Fig. 2.** Example ROIs of the original CT images of lungs (left column) and corresponding generalized gradient maps (right column). The first row represent case where the gradient map is definitely useful for detecting tumor border whereas the second and the third rows illustrate cases where the utility of maps is unclear and useless respectively.

## Conclusions

Results obtained with this experimental study of the ability of generalized gradient method to highlight lung tumor borders based on a sample of 40 CT scans allow to draw the conclusions that the generalized gradient maps *provide* useful information for detecting hardly visible border between the malignant tumors and adjacent atelectasis areas of lung CT images in 55.0% of cases and therefore may be considered as an additional source of visual data for tumor segmentation, measurement and radiotherapy planning.

** Acknowledgements** – This work was partly funded by the National projects IT11/4-04 and CRDF project BOB 1-31055-MK-11.