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Journal of Mathematical Modelling and Algorithms 2: 277–294, 2003. © 2004 Kluwer Academic Publishers. Printed in the Netherlands.

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Automated Segmentation and Registration of Dermatological Images ILIAS MAGLOGIANNIS Department of Information and Communication Systems Engineering, University of the Aegean, 83200 Karlovasi, Samos, Greece. e-mail: [email protected] Abstract. During the last years, there has been a significant increase in the level of interest in image morphology, full-color image processing, image data compression, image recognition and knowledge based analysis systems for medical images. The present paper describes the implementation and tests the efficiency of algorithms dealing with the issues of segmentation and registration of digital images containing skin lesions. Those steps are considered of great importance in computer based characterization systems as they are responsible for the isolation of pathological findings and the matching of sequential images during follow-up studies in medical imaging. Mathematics Subject Classifications (2000): 68U10, 92C55. Key words: digital skin image, unsupervised segmentation, registration, similarity criteria.

1. Introduction Up until now, medical professionals have based the diagnosis of skin lesions on visual assessment of pathological skin and the evaluation of macroscopic features. This fact shows the high dependency of the correct diagnosis on the observer’s experience and on his or her visual acuity. Moreover, the human vision lacks accuracy, reproducibility and quantification in gathering information from an image. The quantification of tissue lesion features has been proven to be of essential importance in clinical practice, because several tissue lesions can be identified based on measurable features extracted from an image. In addition the use of digital image features may help in an objective follow up study of skin lesion progression and test the efficacy of therapeutic procedures [6, 7, 15, 13, 11]. The present paper describes the implementation and evaluates the efficiency of algorithms dealing with the issue of segmentation and registration of digital images containing skin lesions. The segmentation procedure concerns the isolation of pathological skin lesions from the surrounding healthy skin, while registration involves the matching of sequential images displaying the same skin lesion, acquired in different time periods, e.g., during follow-up studies. The paper in a first stage (Sections 2 and 3) deals with the segmentation problem while in the second stage (Sections 4, 5, 6 and 7) proposes a deterministic algorithm

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for dermatological images registration. Finally, Section 8 concludes the paper and summarizes the results.

2. Materials and Methods The set of digital skin images used for the assessment was acquired from patients with a CCD camera, a physical device that is sensitive to the visible band in the electromagnetic energy spectrum and that produces an electrical signal output proportional to the level of energy sensed. In order to avoid light reflections and to ensure the reproducibility of the images an appropriate lighting geometry with uniform lighting conditions was used and software corrections were applied to the images during the acquisition [12]. Polarizing filters were also positioned in front of the lighting sources and the camera receiver for eliminating the remaining reflections. Three types of software corrections were implemented: Calibration to Black and White, Shading correction and Median filtering. The first two concern color reproducibility, while Median Filtering is used for noise reduction due to hair, scales and light reflections. This technique was selected as it has been proved efficient in several studies [13, 9] for captured skin digital images, however any reasonable noise reduction algorithm such as a simple 3 × 3 weighted averaging mask may also be used. This procedure ends in blurring the image, which visually seems a poorer result but on the other hand assists the segmentation procedure. The segmentation of an image containing a cutaneous disease involves the separation of the skin lesion from the healthy skin. The collected set of images includes cases of malignant melanoma and dysplastic nevus. The following segmentation algorithms were utilized and compared. (A) Thresholding is the simplest approach to segmentation. It is based on the fact that the values of pixels that belong to a skin lesion differ from the values of the background. By choosing an upper and a lower value it is possible to isolate those pixels that have values within this range. The information for the upper and the lower limits can be extracted from the image histogram, where the different objects are represented as peeks. The bounds of the peeks are good estimates of these limits. (B) The use of weighted functions, which presupposes that two small windows, one inside and one outside the skin lesion area, are identified in order to calculate the weight vector. The two small windows can be identified using approximate segmentation strategy or by human intervention. Then typical values of the threecolor planes are computed for the two windows and a function is formed where the contribution of each color plane is defined by the size of variation between the two windows. (C) Region Growing is a procedure that groups pixels or subregions into larger regions. It starts with a set of “seed” pixels and grows regions from these by appending neighboring pixels that have similar properties such as gray level, color and texture [4]. In skin lesion images where the color differences are intense this

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technique has excellent results. The major advantage is that it allows small alterations of the skin lesion and that it ends in compact boundaries. (D) In Principal Components Transform the eigenvectors of the covariance matrix are used as a linear transform matrix on the original [RGB] vectors so that the resulting vectors have components that are uncorrelated. Geometrically this means that the primary axis has been aligned so that the variance in the data is maximal. A discriminative point (the median point) in this axis can effectively segment the image [14, 5]. (E) The CIELAB Color Space Transform is effective in measuring chromatic differences between pixels [18]. The conversion is performed using a (3 × 3)transformation matrix between RGB and XY Z color space. The matrix is calculated by measuring the RGB values of each of the 24 color patches of the Macbeth color chart with known values. Then an estimate of the color of the background is obtained from small windows in the corners and the color difference is calculated for all pixels producing the color difference image. This image is smoothed by a low-pass filter, edge detected with Sobel operator, and the image segmentation is performed by defining a threshold value for the intensity of the edge detected image. (F) The Spherical Coordinates Transform was initially developed for the identification of variegated coloring [14]. It consists of transforming the original RGB data into spherical domain, which maps the image into a color space represented by two angles, and a one-dimensional intensity space. The two angles were used then for segmenting the image.

3. Results of the Segmentation Procedure Figure 1 displays examples of skin lesions segmentation using the above described algorithms. In order to determine the success of the computer-calculated border relative to the true border we asked an expert dermatologist to determine the border manually on the digital image. The metric used for the accuracy of the algorithms was the percentage of common pixels between the two borders. We have also calculated the percentage of pixels that belong to the computer-based border and not to the manually determined border and vice-versa. The accuracy test included 50 digital images and the results are displayed in Table I.

4. Image Registration Criteria and Methods Image registration is a procedure of finding correspondence between two different images in order to correct transpositions caused by changes in camera position. This procedure is necessary for monitoring the progress and measuring the changes of skin lesions. Image registration allows the computation of border based features,

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Figure 1. Examples of image segmentation using the described algorithms.

Table I. Accuracy of the segmentation algorithms Algorithm

Common pixels between the two borders (%)

Pixels that belong to the computer-based border and not to the manually determined (%)

Pixels that belong to the manually determined border and not to the computerbased (%)

Thresholding Weighted function Region growing PCT transform CIELAB color space Spherical coordinates

60.29 79.51 69.12 83.62 73.50 79.19

19.16 7.03 22.86 7.50 16.41 9.86

20.59 13.49 8.02 9.09 3.94 10.95

which may be used as objective indexes for the progress of skin tumors and of therapeutic procedures. The input of an image registration algorithm consists of the two images and the output is the values of four parameters: Magnification, Rotation, Horizontal Shifting and Vertical Shifting [17]. The implementation involves the selection of a similarity criterion, which measures the similarity of the two images [1]. The most commonly used criteria are the correlation function, the correlation coefficient, and the sum of the absolute values of the pixel differences, defined respectively by the


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following equations [2]: f (x, y)w(x − s, y − t), C(s, t) = x

y

[f (x, y) − f (x, y)][w(x − s, y − t) − w] , 2 2 1/2 y [f (x, y) − f (x, y)] x y [w(x − s, y − t) − w]

γ (s, t) = D(s, t) =

x

x

y

|f (x, y) − w(x − s, y − t)|.

The specific criteria take into account directly the pixel values of the images. Therefore they work correctly when the compared images are very similar but frequently lead to misregistrations when significant dissimilarities are present. In dermatological images the healing process has frequently as result the alteration of the lesion colour, making the use of such criteria inappropriate. In this paper it is demonstrated that the use of another family of criteria, the sign change criteria leads to algorithms with better performance [16]. The sign change criteria involve calculations on sign changes and not on pixel values of a subtraction image. The criteria used in the utilized algorithms are: • The Stochastic Sign Change Criterion (SSC). • The Deterministic Sign Change Criterion (DSC). • The Window Change Criterion (WinC). The SSC criterion was introduced for the registration of nuclear medicine images [17]. Lets consider two images, F1 (x, y) and F2 (x, y) of the same object. Suppose that F1 (x, y) and F2 (x, y) only differ because of the noise measurement, which is assumed to be additive zero mean with a symmetric density function. Let D(x, y) = F1 (x, y) − F2 (x, y) be the subtraction image. If there was no noise the D(x, y) pixel values would fluctuate around 0. The probability of a negative or positive sign of these pixel values is 0,5. Consider the sign sequence of a D(x, y) line (for example − − + − − + +_ + . . .). The sign changes are frequent because for each pixel the probability of sign change is 0.5. If the two images F1 (x, y) and F2 (x, y) strongly differ in a zone, in this zone the D(x, y) pixel values are all negative or all positive. Thus the more similar the two images are, the more large the number of sign changes is. The SSC criterion is therefore defined as the number of sign changes in the D(x, y) pixel values scanned line by line or column by column. For the definition of DSC criterion we suppose the two images F1 (x, y) and F2 (x, y) without noise. The D(x, y) pixel values are null and the SSC criterion value is zero. In this case a third image F3 (x, y) is calculated adding a periodic pattern to F2 (x, y) according to the following: F3 (x, y) = F2 (x, y) + q F3 (x, y) = F2 (x, y) − q

if x + y is even, if x + y is odd

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(where q is a small real or integer number). The subtraction image is now defined as D (x, y) = F1 (x, y) − F3 (x, y) and the DSC criterion as the number of changes in D (x, y). The WinC criterion uses the same consept. Let w be a small integer or real number in compare with the mean pixel value of the two images. If F1 (x, y) and F2 (x, y) are identical, then obviously all pixel values in the subtraction image D(x, y) = F1 (x, y)−F2 (x, y) will fluctuate among the window defined as |p| < w or −w < p < w. In case the second image is shifted the density function of the pixel values in D(x, y) will have a mean different than zero. The possibility of some D(x, y) pixel values to be outside the bounds [−w, w] is now bigger. Thus the more the two images F1 (x, y) and F2 (x, y) differ, the more large the number of D(x, y) pixel outside the window is. The WinC criterion is defined as the number of D(x, y) pixel values that are inside the window [−w, w]. 5. The Proposed Algorithm The most important step in the registration procedure is the utilization of an optimization algorithm, which maximizes the similarity criterion. The complexity of the problem, imposed by the existence of at least four independent parameters, makes the use of exhaustive algorithms ineffective. The use of random search algorithms is a generally acceptable technique for the optimization of nonlinear problems. Their major advantage is easy implementation. On the other hand, their efficiency is based on probability factors and their behavior is not predictable. In the paper we describe a very effective deterministic algorithm that uses the crosscorrelation of the log-polar Fourier spectrum, that overcomes the complexity of the problem [3]. The Fourier transformation spectrum is independent of horizontal and vertical shifting, while the use of the log-polar transform eliminates the dependency on magnification and rotation. If the two compared images are f (x, y) and f (x, y), they are connected through a four-parameter geometric transformation, which is described by the following equation: f (x, y) = f (a(x cos b + y sin b) − x, a(−x sin b + y cos b) − y), where Dx and Dy are the horizontal and vertical shifting respectively, a is the magnification factor and b is the rotation angle. The Fourier spectrums of the two images are connected by the following equation: 1 (u cos b + v sin b) (−u sin b + v cos b) , |F (u, v)| = 2 F a a a which displays the independence of horizontal and vertical shifting. Then the logpolar transformation is performed by two equations: 1 r , θ + b , |F (r, θ)| = 2 F a a


where r=

u2 + v 2 ,

θ = tan−1

283

v u

and |F (ρ, θ)| =

1 , F (ρ − ln(a), θ + b) a2

where ρ = ln(r). The next step is the use of the cross-correlation function or correlation-coefficient to find the scale factor and the rotation angle that maximizes the corresponding criterion: XC(R, T ) =

ρmax 2π

F (ρ + R, θ + T )F (ρ, θ),

ρ=ρmin θ=0

where the parameters are the log-difference of the scale factors R and the difference of the rotation angle T . The use of the corellation coefficient is more appropriate as it is a normalized criterion. An important issue in the implementation procedure is the selection of samples number in log-polar space Nρ · Nθ . Figure 2 displays an example of representation from the orthogonal Fourier spectrum to the log-polar space. It should be noted that only a ring with an inner radial rmin and an outer rmax is finally transformed. Logpolar transform is space dependent. This is clear in Figure 2, where the two black areas, although they have the same shape in Fourier space they have different size in log-polar space. An approach to the calculation issue of the spatial dependency in log-polar space resolution is to consider the minimum log-polar resolution equal to the resolution in Fourier space. The resolution in log-polar space is defined as: θ =

l , r

ρ =

r . r

The minimum resolution in log-polar space depends on the minimum value of θ and ρ. Taking into account the resolution in the orthogonal space it can be shown that: (l)min 1 = , rmax rmax (r)min 1 = = , rmax rmax

θmin = ρmin

where θmin is radians, ρmin is log units and rmax is the outer radial we consider for the orthogonal space.

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Figure 2. Representation in the log-polar space.

The necessary number of samples for the log-polar space in order to maintain the information can be calculated as following: π = rmax · π, θmin ln(rmax ) − ln(rmin ) rmax = = rmax · ln . ρmin rmin

Nθ = Nρ

Let’s suppose an image 512 × 512 pixel with Fourier spectrum an image with the same dimensions. If the ring we described above has an inner radial rmin = 1 and an outer rmax = 255, thus the whole spectrum, according to the above equation the log-polar space would be an image with dimensions 800 × 1400 pixels. This means that the number of samples is increased significantly in the log-polar space. The complexity of calculations may be reduced if we limit the range between rmin and rmax . The selection of the bounds rmin and rmax should be the cutoff frequency points from where the energy of the image is insignificant and the information is preserved. From experimental results we found that for images 256×256 a selection rmax = 85 and rmin = 20 corresponding to Nϑ = 256 and Np = 128 concentrates a significant percentage of the energy spectrum and it is sufficient for the registration algorithm. An example of this procedure is also depicted in Figure 3. The problem is now reduced to finding the horizontal and vertical shifting, which is much simpler, as it involves only two independent parameters [8]. 6. Vertical and Horizontal Shifting Registration Exhaustive methods may be used for the calculation of vertical and horizontal shifting because the problem variables are now reduced to two. This procedure includes the calculation of the above described similarity criteria between two windows:

(m, m) . . . . . . . . . . . . . . . . . . . (m, k − m + 1) of the first image and (k − m + 1, m) . . . (k − m + 1, k − m + 1)


(a)

(b)

(c)

(d)

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(e) Figure 3. Image registration procedure: (a) Fourier spectrum of a dermatological image; (b) Fourier spectrum of the same image rotated by 20 degrees and scaled down by a factor 0.8; (c) Log polar transform of image A; (d) Log polar transform of image B (NB: The magnification and rotation have been transformed to horizontal and vertical shifting); (e) Apply of the cross-correlation coefficient to find the scale factor and the rotation angle that maximizes the corresponding criterion.

(m + i, m + j ) . . . . . . . . . . . . . . . . . . . (m + i, k − m + 1 + j ) (k − m + 1 + i, m + j ) . . . (k − m + 1 + i, k − m + 1 + j ) of the second image,

where i, j = −p, . . . , 0, . . . , p (p is the assumed limit of shifting).

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Figure 4. A typical criterion surface.

Figure 5. Ideal criteria surface.

Thus we examine the similarity criterion 4 · p 2 times in a window of (k − 2 · m) ×(k − 2 · m) pixels. This could be a complex and resources consuming problem in case we select a big value for p. Therefore we propose a more sophisticated algorithm. The description of the proposed algorithm is based on similarity criteria surfaces. For simplicity reasons we consider intersection of the surfaces, thus onedimensional diagrams. Analyzing a typical criterion diagram we find three types of fluctuations: regional aberrations, regional maximums, and a global maximum. Our goal is the detection of the global maximum. Observing the above constructed typical criterion surface we can extract the following simplifying remarks: (1) The area around the global maximum of the criterion usually shows the symmetry displayed in Figures 5 and 6. (2) There is a relationship between the regional and the global maximums displayed in Figure 7, which shows an incremental direction in parallel to the axis movements. (3) The regional aberrations may be encountered as regional maximums that hinder the detection of the global maximum. The above observations show that theoretically the global maximum may be detected with alternated parallel to axis movements. Each movement is to the direction of positive surface gradient. An example of parallel movements that end in the global maximum is shown in Figure 8. Let’s suppose an intersection of the area around a global maximum displayed in Figure 9. Let also “α” be a temporary point of criteria control and suppose that


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Figure 6. Symmetry around global maximum.

Figure 7. Relationship between the regional maximums and the global maximum.

the global maximum is located on the right of “α”. From the point “α” we move on the right with initial step λ. We calculate the similarity criterion for the point C(α + λ) and we compare it with C(α). If C(α) < C(α + λ) we continue moving right until we found a k where C(α +2k−1 λ) > C(α +2k λ). This way we bound the maximum in the first axis between the interval [α +2k−1 λ, α +2k λ] (Figure 9). The same procedure is followed for locating the maximum in the second (y) axis. The direction of the movement is decided by calculating points in the neighborhood

Figure 8. Alternated parallel to axis movements for detection of the global max.

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Figure 9. Movement in the area around maximum.

Figure 10. Direction of movement.

of α. For example we calculate C(α − λ) and C(α + λ) in order to see in which direction the similarity criterion increases as it is shown in Figure 10. The value of λ should be a sufficient number of pixels, so that local aberrations could not juggle the algorithm. On the other hand λ determines the accuracy in finding the global maximum, so the use of big λ have negative side effect to the accuracy of the algorithm. A solution to this problem is to reduce the value of λ for the area around the global maximum. After experimenting with a set of images we found that good choices for λ are values between 3 and 5. When the algorithm reaches a point where it can not find augmentation of the similarity criterion in any direction, it starts to decrease the value of λ until λ = 1. This way the desired accuracy is achieved. During the testing of the proposed algorithm we found some cases where a local maximum is miscalculated as global. Figure 11 is displaying such a case, where the algorithm is trapped in a regional maximum. This effect may be encountered by adding momentum to the algorithm: After the location of the maximum the algorithm considers it as temporal and continues seeking for a number of steps,


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Figure 11. Entrapment in regional maximum.

Figure 12. Escape from a regional maximum.

e.g., 5. If the “mount” of the global maximum is near, there is good possibility that the algorithms escapes from the regional maximum, as shown in Figure 12. There is although a case where the parallel movements are unable to locate the global maximum and the trap is inevitable. Such a case is displayed in Figure 13. In order to keep the algorithm simple and efficient we have decided not to include solutions for this case but to “apply” the algorithm for several randomly selected starting points. In case the algorithm converges to the same point it is obvious that the result is correct. Figure 14 depicts the flowchart of the proposed algorithm.

Figure 13. Inevitable trap in regional maximum.

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Figure 14. Vertical and horizontal registration algorithm flowchart.

7. Results of the Registration Procedure The proposed algorithm was applied to follow-up images containing skin lesions in healing procedure. The results showed that Log-Polar Fourier Transform had good performance in measuring small rotations up to 10 degrees. For bigger rotations the algorithm had a tendency to calculate greater rotation values than the real ones. Regarding the calculation of the scale factor the algorithm had better accuracy for values below 1.0, thus for diminution of the image. Figure 15 shows results produced by applying the log-polar Fourier algorithm for a number of manually specified rotation and magnification values. The bulleted curve corresponds to the measured rotation and magnification, while the line represents the correct values. From the application of the new class similarity criteria it was found that all the sign change criteria showed better performance for high altered images. The behavior of DSC and WinC criteria is almost identical, resulting to the conclusion that they are more appropriate for very high altered images, while SSC has better performance for lower alterations between the follow-up images. MSV criterion


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Figure 15. Accuracy of the log-polar Fourier transform in calculation of the rotation and scale factor.

Figure 16. Typical behavior of the similarity criteria in low altered images.

did not converge in high altered images, but had better performance for images with high levels of similarity. Figures 16 and 17 show typical criteria surfaces produced by applying the introduced similarity criteria in two couples of images, one containing a low altered and one containing a high altered skin lesion. The two sets of images were intentionally shifted by −12 to +12 pixels with a step 2 pixel to both directions, vertical and horizontal. For each shifting, the 4 mentioned criteria (SSC, DSC, WinC and MSV) were calculated and 4 matrixes were populated containing 13 × 13 criteria values, as many as the shifting combinations are. From the above procedure it is obvious that the criteria surface should have a peak in the central point of the

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Figure 17. Typical behavior of the similarity criteria in high altered images.

matrix, which corresponds to zero horizontal and vertical shifting, and is the point with coordinates (7, 7). The diagrams depict that for the set of low altered images the MSV criterion has the sharpest peak in the correct point (7, 7). The sign change criteria do not fail as they indicate the same maximum point, but they have smoother peaks. As it is shown in Figure 17, for the set of high altered images the use of MSV criterion is maximized in another point (13, 1), failing to indicate the correct maximum (7, 7). Regarding the remaining part of the proposed algorithm dealing with the location of the global maximum, the only problem encountered is the entrapment in regional maximum points. It showed good performance for initial step value λ = 3 and for limit value of momentum iterations equal to 4. During our experiments, we applied the algorithm starting from random points and terminate the procedure until the same spot was found 3 times. In all the test cases the algorithm found correctly the global maximum 3 times as required. It should be noted though, that the starting points should not be neighboring and they should cover all four quarters of the examined rectangle.

8. Conclusions The present paper is proposing several algorithms for the segmentation and a complete algorithm for the registration of dermatological images. The results showed


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that the Principle Components Transform and the transformation to spherical coordinates can improve the correct separation of the skin lesions from healthy skin in dermatological images. The Log-Polar representation of the Fourier spectrum has also been proved a powerful tool for the registration of two dermatological images as it separates such a complicated task in two independent phases and diminishes the computational complexity of the problem. The introduction of a new family similarity criteria, the sign change criteria, overcome the problem of the high alterations encountered in dermatological imaging between follow ups. The use of such criteria helps the convergence of the optimization algorithms incorporated in registration, as it was proved during experimentation on the proposed by the paper algorithm, even if the input images differ a lot. The set of algorithms, which proposes the present paper, may be integrated in a complete knowledge based image analysis system, intended to serve as a diagnostic tool for dermatologists or general practitioners [10]. The use of a computer-based system will help in avoiding human subjectivity and in performing specific reproducible measurement according to a number of criteria, concerning the progress of a skin disease or the efficiency of a therapeutic procedure.

Acknowledgement The skin lesion images used for the algorithms efficiency tests were acquired from patients in the General Hospital of Athens G. Gennimatas with the help of the medical personnel of the department of Plastic Surgery and Dermatology.

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