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IEEE TRANSACTIONS ON INFORMATION TECHNOLOGY IN BIOMEDICINE, VOL. 3, NO. 1, MARCH 1999

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Automatic Retinal Image Registration Scheme Using Global Optimization Techniques George K. Matsopoulos, Member, IEEE, Nicolaos A. Mouravliansky, Konstantinos K. Delibasis, and Konstantina S. Nikita, Member, IEEE Abstract—Retinal image registration is commonly required in order to combine the complementary information in different retinal modalities. In this paper, a new automatic scheme to register retinal images is presented and is currently tested in a clinical environment. The scheme considers the suitability and efficiency of different image transformation models and function optimization techniques, following an initial preprocessing stage. Three different transformation models—affine, bilinear and projective—as well as three optimization techniques—downhill simplex method, simulated annealing and genetic algorithms—are investigated and compared in terms of accuracy and efficiency. The registration of 26 pairs of Fluoroscein Angiography and Indocyanine Green Chorioangiography images with the corresponding Red-Free retinal images, showed the superiority of combining genetic algorithms with the affine and bilinear transformation models. A comparative study of the proposed automatic registration scheme against the manual method, commonly used in the clinical practice, is finally presented showing the advantage of the proposed automatic scheme in terms of accuracy and consistency. Index Terms— Genetic algorithms, image registration, retinal images, simulated annealing, transformation models.

I. INTRODUCTION

I

N medical imaging, registration between two-dimensional (2-D) or three-dimensional (3-D) images is a common problem encountered when more than one images of the same anatomical structure are obtained, either using different imagery or performing dynamic studies. In all cases, the information present in the different images must be combined to produce fused or parametric images [1]. Registration can be performed between two modalities with anatomical information (CT-CT or CT-MRI), between anatomical atlases and dynamic studies (CT-PET, CT-SPECT, etc.) [2]–[6] or between images of the same modality, acquired at different periods of time [7]–[8]. An example of the latter is Retinal Imagery, where two techniques are widely used in the clinical practice: Fluoroscein Angiography (FA) and Indocyanine Green Chorioangiography (ICG). Ophthalmologists commonly compare Red-Free (RF) retinal images, which is a reference image taken without intravenous injection of a dye while illuminating the retina with a green light, with the corresponding FA or ICG image of the patient, acquired at different times. This is a very difficult task due to the misalignment of the retinal images caused by the geometry during the acquisition at different times and to Manuscript received June 24, 1998; revised August 1, 1998. The authors are with the Department of Electrical and Computer Engineering, National Technical University of Athens, Zografos, 15773 Athens, Greece (e-mail: [email protected]). Publisher Item Identifier S 1089-7771(99)01527-7.

possible progression of various diseases. The relative study of retinal images enhances the information on the reference RF images by superimposing useful information contained in FA or ICG retinal images and it is considered an important step toward a carefully directed laser treatment; a process that is commonly used in the clinical practice. Comparative study of RF with FA or ICG retinal images is required in order to identify dynamic aspects of the circulation and evaluate a wide variety of retinal vascular disorders. Furthermore, it guides the specialist to define the boundary of the fovea, which can be clearly observed only in the FA images and to superimpose it to the corresponding RF image. Registration of retinal images is the key process to accurately combine information using different retinal techniques. Human-interactive registration is considered as a standard method, widely used in the clinical practice. Automatic retinal registration techniques have been developed to overcome failures due to human interaction. An automatic registration of sequential FA frames was firstly reported by enhancing edges and vessel crossings and cross-correlating small windows around these features to determine optimal matching [9]. Another technique was based on identifying vessels using an adaptive thresholding technique and then applying a feature based sequential detection method to find the best match between the vessels [10]. Sequence of retinal images was also registered locally by finding corresponding triangles formed by vessel bifurcation points [11]. Registration experiments were carried out on low quality photographs of the ocular fundus, obtained with a contrast medium, implementing a phase correlation algorithm with and without a weighting function to meet the FFT hardware requirements for real time processing [12]. Only the translation component of motion was determined neglecting any rotation effects. Furthermore, an interactive method was employed to register early and late frames of FA to assess macular oedema, based on the gradient of fluorescein intensity [13]. Locally registered angiograms were also used to investigate retinal vascular occlusions. The application of a local registration method to retinal angiograms for automatic diagnosis was reported [14], whereas a real time algorithm to perform retinal tracking during photoagulation was also implemented [15]. A nonreal-time registration on monochromatic photographic and FA images by nonoptimized simple template matching or Hausdorff-distance-based algorithms was developed considering only translation and scaling factors [16]. Correlation methods have been used for retinal and medical image registration, employing very simple transformations

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(scaling and translations [10], [12], [17], translation, and rotation [18]). The log-polar transformation of the spatial frequency spectrum of FA images was employed to achieve automatic registration, using translation, rotation, and uniform scaling [19]. The use of this transformation removes the effects of translation and converts rotation and uniform scaling into independent shifts in orthogonal directions [20]. However, the requirement for nonuniform scale transformation models (e.g., affine, bilinear or projective) is often encountered when registering retinal images. In this paper, a new automatic registration scheme is developed, based on standard transformation models and global optimization techniques. Firstly, two retinal imagery techniques, the FA and the ICG are briefly explained along with the corresponding acquisition stage. During the preprocessing stage, a coarse segmentation of the retinal images is performed in order to identify common retinal vessels in the different retinal images. Three transformation models and their combination with two global optimization techniques are then investigated. Results of the registration of RF with FA or ICG are presented for a sufficient number of frame pairs. Finally, the automatic registration scheme is qualitatively and quantitatively compared against the manual registration technique, commonly used in the clinical practice. A. Fluorescein Angiography and Indocyanine Green ChorioAngiography Fluorescein Angiography (FA) is a clinical examination performed routinely, providing retinal information [21]. After a fast intravenous injection of a sodium fluoroscein dye (usually within 1–2 s, since this study resembles the first pass radionuclide studies), photographs of the retina are taken at a rate of one per second, during the total transient phase of the dye through the retinal vessels. The transient time as well as the time between injection and the beginning of the transient phase strongly depend on the cardiac output of the patient, the caliber and the status of his/her vessels. During the flow of the dye through the retinal vessels, fine details of the pigment epithelium and a clear picture of the retinal vessels can be recorded. The main phases of the FA are: pre-arterial, arterial, capillary, and early and late-venous phase. Indocyanine Green Chorioangiography (ICG) is a clinical procedure in which the acquired images correspond to the choroid, a layer deeper than the retina and usually obscured by pigmentation [22]. An indocyanine dye is intravenously administered and circulated through the choroid vessels, which fluoresces in the infrared spectrum. This means that it can not be seen with naked eye as the procedure is performed, whereas when it is imaged, the specialist can observe the choroid through pigmentation, fluid or blood that may exist in the retina. In ICG, the main phases can be observed, as in the FA, and it is also used in order to direct carefully laser treatment. Prior to any intravenous injection, a Red-Free (RF) image is acquired using a green filter, which causes the retinal blood vessels to appear dark. This image is the one observed by the expert during laser treatment and it is used as a reference image during the registration procedure.

RF and FA retinal images correlate significantly in nonpathological cases since retinal vessel information is highly presented in both modalities. However, in pathological cases, it is observed that abnormalities may be obscured in RF images reducing the cross image correlation. The problem of retinal image registration becomes more complicated in the case of registering RF with ICG images mainly due to the fact that retinal vessel information is obscured by choroidal circulation, especially in the late phases of the examination. In pathological cases, the visibility of the abnormalities is enhanced toward the late phases, whereas the vessel visibility, which is essential for the registration process, deteriorates rapidly. Further intravenous injection does not always resolve this problem because it may disturbs the pathological findings. II. ACQUISITION AND PREPROCESSING OF RETINAL IMAGES A. Acquisition of Retinal Images Fundus camera is the instrument of choice for FA and ICG. Retinal images were acquired using the IMAGEnet 1024 system, which is a fully functional digital imaging system for acquisition, analysis, storage, and retrieval of retinal images. 1024 were Digital FA and ICG images of size 1024 directly obtained using a CCD camera mounted on the Topcon TRX-50X, a Japanese fundus camera, providing 50 angle of coverage, 39 mm working distance and special filters for FA and ICG. The use of this motorized common camera allows image acquisition at a rate of one image every 0.8 s. The IMAGEnet system also consists of a computer (PC compatible) for display and further processing of the acquired retinal images. The IMAGEnet system is currently used to manually register retinal images; this process will be compared against our automatic registration scheme. The acquired retinal images are also driven from the CCD camera to a silicon graphics (SGI) workstation, where the developed automatic registration scheme is currently running. The automatic and the manual registration were tested on 512 512 retinal images to reduce the execution time. B. Preprocessing of Retinal Images In the case of retinal images, the objects of interest are the retinal vessels: arteries and veins. It is found that the registration algorithm operates more efficiently if the vessels are segmented, using at least a crude segmentation. Therefore, image preprocessing is required prior to registration. A simple thresholding is not sufficient, since retinal vessels and background structures are of comparable intensity. The preprocessing involves two main processes: 1) vessel enhancement and border suppression and 2) vessel detection. These processes are performed to all retinal images with the addition of an inversion procedure applied only to the RF images in order to emulate the appearance of FA and ICG images. 1) Morphological Enhancement of Retinal Images: In order to increase retinal visibility, a mathematical morphology operation is performed [23]. The retinal image is filtered using a grayscale opening using a flat structuring element of diameter larger than the maximum width of the retinal vessels. The opened image is then subtracted from the original image,

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of 30 and by rotating the kernel five times with this step, the algorithm performs the convolution six times and detects vessels of arbitrary orientation. The preprocessing algorithm can be formulated in pseudocode as follows:

Fig. 1. The kernel used to detect vertical retinal vessels for

L = 9:

 = 2 and

according to the following equation: (1) where grayscale opening; grayscale erosion operation; grayscale dilation operation; flat structuring element. The structuring element chosen for this step is a disk-shaped with a diameter of 7 pixels. This size seemed most appropriate in tests with sample images because it has a diameter greater than the largest width of the retinal vessels. Peaks of the image surface smaller than the chosen structuring element are removed by the opening operation, leaving a slowly varying background image. The resultant enchanced image (1), presents significantly suppressed background while enhances vessel visibility. It is also noted that the morphological operation suppresses pixels at the retinal image border caused by the aperture of the fundus camera. These pixels appear as image edges and it was found that they could not be discarded during the process of vessel detection. Moreover, they add noise to the measure of match, as a result of a match of the borders of two retinal images which does not correspond to the match of the anatomical structures of the retinal images. 2) Matched Filtering: A wide range of operators for edge detection has been described in the literature [24]. In this paper, the retinal vessels are detected by a matched filter, which is convoluted with the images to be registered [25]. with the vessels modeled as line The kernel is of size segments with a length of pixels. The vessels cross-sectional line profile is assumed to be of Gaussian shape: (2) and The matched filter has been where truncated along the -direction at three standard deviations left and right of the vessel segment. The requirement that the mean value of all coefficients of the convolution kernel needs to be zero, modifies (2) as follows: (3) is the mean value of the where kernel. The modified kernel can detect long vessel segments in a specific direction. Fig. 1 shows the calculated kernel and Assuming an angular resolution for

create initial kernel with and of choice for each of the possible rotated kernels by the step angle of choice for every pixel in the retinal image convolve the rotated kernel with the gray level image locate the rotated kernel with the maximum convolution response classify this pixel as belonging to a vessel oriented along the specific resolution set a threshold below which the maximum convolution response indicates no vessel The preprocessing is currently automated using standardized and threshold levels depending on the kernel size type of the retinal images (RF, FA, and ICG). Nevertheless, the expert is allowed, by the proposed implementation, to change the threshold level whenever the final visual results did not produce sufficient vessel information required for the registration. During the experiments, only two of the ICG images required changes of the threshold levels. This was due to the fact that the retinal visibility in the ICG images is inherently inferior to RF and FA images. Fig. 2 shows the segmented retinal vessels of FA and ICG images. III. REGISTRATION

OF

RETINAL IMAGES

The process of image registration can be formulated as a problem of optimizing a function that quantifies the match between the original and the transformed image. Several image features have been used for the matching process, depending on the modalities used, the specific application and the implementation of the transformation. The use of external skin markers [1], [2], [26], [27] or landmarks [1], [8], [28], [29] placed in the images are common approaches to register images from different modalities. These methods are combined with well-established transformation models such as rigid, affine and high order polynomial transformations [30]. In cases of manual registration, the match is quantified by the distance between selected pairs of markers or landmarks. Other registration approaches for both 2-D and 3-D medical images include the matching of the principal axes or template [31], distance transformation [32], chamfer matching [7] and elastic matching [33]. In the case of registering retinal images from different modalities (RF with FA or ICG), the need for an accurate registration with less human interaction, the absence of clear reference anatomical regions and the low quality of the retinal images, suggest the use of robust global algorithms. More specifically, we concentrate on the determination of the translation and rotation displacements as well as on uniform and nonuniform scaling deformation occurred during retinal image acquisition from different modalities.

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(a)

(b)

(c)

(d)

Fig. 2. Coarse segmentation of the retinal vessels: (a) original FA image and (b) its final segmentation; (c) original ICG image and (d) its final segmentation.

A. Transformation Models Three transformation models are employed for the global retinal registration [1]. 1) The Affine Transformation: This can be decomposed into a linear transformation and a simple translation. It can be shown that this transformation maps straight lines into straight lines, whereas it preserves parallelism between lines. In the 2-D case, it can be mathematically expressed as follows: (4) The affine transformation is completely defined by six for and and independent parameters 2) The Bilinear Transformation: is the simplest polynomial transformation, which maps straight lines from the original image to curves. It can be expressed for the 2-D case as (5)

The bilinear transformation is completely defined by 8 independent parameters for 3) The Projective Transformation: This maps any straight line in the original image onto a straight line in the transformed image. Parallelism is not preserved. The mathematical expression of the transformation for the 2-D case is given by (6) represents the extra homogeneous coordinate and where and are dummy variables. The projective transformation strongly resembles the bilinear and is completely defined by nine independent parameters B. The Objective Function: Measure of Match In the case of the retinal images, after the preprocessing, two and binary images of the retinal vessels are obtained, The problem is formulated as determining a transformation

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Fig. 3. Two-dimensional sampling of the objective function (MOM) for a pair of RF and FA retinal images where the x and y axes correspond to the translation differences (dx and dy ) along these axes, respectively and the z axis corresponds to the value of the MOM (only translation displacements of the transformation model are allowed to vary).

that, when applied to the second image, a best match with the first is achieved. Ideally all the nonzero pixels of the transformed image should be mapped on nonzero pixels of the first image. The problem can be mathematically formulated as the maximization of the following objective function: (7) denotes the measure of match (objective funcwhere and are the transformations for the and tion) and coordinates, and is the number of nonzero pixels of Equation (7) is equivalent to the definition of the correlation function: Correlation for the binary images and According to the above correlation definition, in the binary case, only nonzero pixels from both images contribute to the value of the correlation. The choice of using (7) as an objective function was the most appropriate for the registration of retinal images whereas the implementation of other correlation methods did not performed satisfactory. For example, correlation methods based on distance measure calculations, such as distance transformation and Pelizzari’s method [1], [7], [32] provide an insensitive objective function to the changes of the registration parameters. These methods are more appropriate for registering closed contours and surfaces but they can not be applied in the case of registering retinal images where more complicate retinal vessel information exists. Furthermore, application of elastic matching methods [1], [33] may improve the registration results but they require a fine initial registration and they are computational intensive. Assuming that the nonzero pixels of the preprocessed images have a value of 255, then the absolute maximum (optimal) value of the above quantity equals 255. In general, the maximization achieved is significantly lower. The reason is not the optimization method’s inefficiency, but the fact that the two images are in most of the cases not identical and may also contain noisy pixels. In this case, there is no transformation to nonzero pixels that can match every nonzero pixel of

of Fig. 3 shows a 2-D sampling of the objective function and axes for a pair of RF and FA images, where the and along correspond to the translation differences axis corresponds to the these axes, respectively and the value of the Measure of Match. The translation differences , of the transformation model are allowed to vary, ranging from [ 80, 80] pixels, while keeping the rest of the independent parameters of the model fixed. Even when sampled in 2-D, the objective function appears containing a narrow global maximum, which corresponds to the correct translation parameters, surrounded by numerous local maxima. Such an objective function renders local search techniques inefficient, unless they are provided with a sufficient initial guess. C. Determination of the Transformation Parameters Using Global Optimization Techniques The determination of the transformation parameters strongly depends on the objective function, as well as on the retinal images to be registered. In the case of matching pairs of internal landmarks, the parameters can be calculated directly, assuming that the number of landmarks is sufficient. Furthermore, the search based methods, provide an alternative, based on the optimization of a measure of match between the original and the transformed images, with respect to the transformation parameters. If the measure of match is well behaved (is continuous and has only one extreme), simple gradient based methods (steepest descent, conjugate gradient method [34]) or downhill simplex method [35] may suffice. However, if the measure of match has multiple extrema, presents discontinuities or can not be expressed analytically, as in the case of retinal images, brute force based exhaustive search is a method that guarantees successful determination of the parameters. An exhaustive search in the case of an affine transformation model was proposed in order to register remote sensing images, assuming that some of the unknown parameters can be estimated one at a time, in a serial manner, thus converting the multidimensional search into a sequence

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of optimization problems of lower dimensionality [36]. Under this assumption, the authors were forced to narrow the range of the parameters in order to accelerate the execution of the program. However, in cases of nontrivial transformations with many independent parameters, exhaustive search is not possible. The most attractive solution for search methods using nontrivial transformations is based on global optimization techniques. In this work we consider the use of two global optimization techniques, simulated annealing (SA) [37] and genetic algorithms (GA’s) [38]. The transformation models employed in the case of 2-D retinal images, introduce six, eight, and nine independent parameters (corresponding to the affine, bilinear and projective transformation models, respectively), defined over a wide range of values to achieve robustness. This fact, combined with the presence of multiple local extrema of the objective function, necessitates the use of global optimization techniques. The necessity for the use of global optimization techniques to register retinal images, without any assumption reducing the robustness of the approach, was indicated by the initial application of the downhill simplex method (DSM) [35], as a standard optimization method. The DSM was implemented in conjunction with the affine transformation model. The experimental results indicated that the performance of the DSM was strongly affected by the initial guess. The method performed adequately only in cases where the initial guess was defined very close to the correct solution. For instance, if translation displacement of the initial guess was more than 5 pixels, the method was confined to a local maximum rather the global one. However, the registration of retinal images was experimentally shown to require translation displacements of the order of 100 pixels. Therefore, the use of global optimization techniques is required and a brief introduction of the two proposed in the paper has been given in the next sections. 1) Simulated Annealing (SA): Simulated annealing presents an optimization technique that can process cost functions with arbitrary degrees of nonlinearities and arbitrary boundary conditions. SA has been successfully applied to image processing [39], molecular biology [40], biological signal processing [41], neural network training [42], etc. described by the vector A function of a system’s state, is minimized (respectively maximized) using a process called annealing. The system searches while adding to the for optimal values of the function function a noise component, whose magnitude is a descending function of time. For every minimization problem, a quantity known as “temperature,” is defined as a descending function is called annealing schedule. A of time and the function standard definition of the annealing schedule is the following [43], [44]:

is evaluated. The is then modified by and is affects the system, since reevaluated. The temperature is affected by the Faster annealing schemes, such as the following, have shown to behave optimally in several cases [45]. • Very Fast SA (VFSA), where (9) • Exponential SA (ESA), where (10) In the case of a multidimensional cost function, a different could be assigned to each of the independent temperature parameters of the transformation model used. This type of SA is called adaptive simulated annealing (ASA) [44]. In the case of retinal registration, the adaptive ESA scheme (10) was proven to be marginally superior than the standard adaptive (8) and the adaptive VFSA (9) schemes. 2) Genetic Algorithms (GA’s): Genetic algorithms (GA’s) are global optimization methods, inspired by Darwinian evolution [38]. The method starts by creating a population of random solutions of the optimization problem. A solution to the problem usually consists of the values of the independent parameters of the function to be optimized (objective function). These values are often converted to binary and concatenated to a single string, called individual. In several cases it has been shown that this conversion does not offer substantial advantages and real encoding is used instead. The method treats each individual as an organism, assigning to it a measure of fitness. Each individual’s fitness is estimated by the value of the objective function calculated over the values of the parameters that are stored in the individual. Using the principle of the survival of the fittest, pairs of fit individuals are selected to recombine their encoded parameters to produce offspring. The most basic genetic operators that act on the individuals are crossover and mutation, although a number of others have been proposed [38]. In this way a new generation of solutions is produced which replaces the previous one. This process is formulated in pseudocode as follows: initialize the first generation of n individuals randomly while (termination condition is false) calculate the objective function of the n individuals select N/2 pairs of individuals apply crossover and mutation operator to produce offspring replace the current generation by the n offspring

(8) is a time index and is a starting value, large where is enough to cover the search space. An initial guess, made for the set of the unknown parameters and the function

Because of the global search they provide, without the necessity for an optimal initial guess, GA’s are powerful tools in optimizing multidimensional, non linear objective functions which present many local extrema. In such problems, the local

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TABLE I THE AVERAGED VALUES OF THE OBJECTIVE FUNCTION ACHIEVED USING BOTH GLOBAL OPTIMIZATION METHODS (SA AND GA’s) AND FOR EACH OF THE THREE TRANSFORMATION MODELS (AFFINE, BILINEAR, AND PROJECTIVE) FOR 26 RETINAL IMAGE PAIRS AND AFTER 10 INDEPENDENT EXECUTIONS. (THE BEST AVERAGED VALUES OF THE OBJECTIVE FUNCTION ARE SHOWN IN BOLD)

search based methods will fail, unless an initial guess is given close to the required solution. GA’s have been effectively used to numerous applications, including biology [46], chemistry [47], medical physics [48], medical image processing [49], [50], etc. IV. IMPLEMENTATION OF THE RETINAL REGISTRATION SCHEME AND EXPERIMENTAL RESULTS A. Implementation of the Transformation Models Three transformation models have been considered: the Affine, the Bilinear and the Projective in order to register retinal images. The allowed ranges of the parameters are determined during the experimental phase and are presented. These values cover the majority of the retinal image pairs and can be redefined by the user in situations where extreme transformation is required. Affine Affine Affine Bilinear Bilinear Bilinear Bilinear Projective Projective

Projective Projective Projective Projective It can be observed that in both affine and bilinear transformation, the parameters controlling the contribution of coordinate to the transformed and the contribution of coordinate to the transformed are symmetrically 0.1. Also, the parameters controlling kept in the range 1 to the transformed coordinate and the contribution of are symmetrically kept in the range 0 vice versa, 0.01. The translation parameters for both transformations, and are kept within the range [ 150, 150]. For the bilinear transformation, the parameters controlling term to the transformed and the contribution of the coordinates, are kept into a very narrow range of [ 0.0001, 0.0001]. For the projective transformation, the range of the parameters is determined using similar principles. B. Implementation of Simulated Annealing The details of the implementation of SA are summarized in the following. Annealing Schedule Exponential Initial guess

Eq. (10) Random

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TABLE II PARAMETERS OF BILINEAR TRANSFORMATION MODEL OBTAINED BY APPLYING THIS TRANSFORMATION IN CONJUNCTION WITH THE GAS IN ALL RETINAL IMAGE PAIRS [EIGHT INDEPENDENT PARAMETERS ACCORDING (5)]

Multidimensional implementation Number of Temperatures Total number of function evaluations

One temperature for each parameter 7 20 000

C. Implementation of Genetic Algorithms The details of the implementation of GA’s are summarized in the following: Population Number of generations Total number of function evaluations Probability of crossover Probability of mutation/parameter Parameter encoding Selection Type of crossover Hybridization First generation Speciation

100 200 20 000 1.0 0.01–0.1 encoded into the individual real values tournament selection linear and arithmetic no uniformly random no

D. Experimental Results The experimental work is concerned with the application of the automatic registration scheme on a number of retinal image

pairs. A comparative study of the three transformation models (affine, bilinear and projective) in conjunction with the two global optimization techniques (SA and GA’s) is performed on 26 retinal image pairs. In order to obtain comparable results, the following assumptions are made: a) same total number of function evaluations (in our case 20 000) and b) same allowed range for the independent parameters of the transformations, as they are defined above. Especially, for the SA, the initial is suitably adjusted for each independent parameter. We have adopted the use of the adaptive ESA schedule (10), as it was indicated by preliminary experiments. Table I shows the values of the objective function (7) achieved by both global optimization methods and for each of the three transformation models for 26 retinal image pairs. The higher values of the objective function performed by these methods are highlighted in bold. Pairs 1–12 correspond to the registration of RF with FA images, Pairs 13–18 to the registration of RF with ICG images, while Pairs 19–26 to the registration of the three types of retinal images for various retinal pathologies identified by an expert. It becomes evident that the GA’s achieved better optimization than the SA for the majority of the retinal image pairs. The SA, combined with the affine transformation, performed better than the GA’s for only three pairs (Pairs 11, 16, and 18) and equally for the Pair 13. Poor optimization results are achieved using the bilinear and the projective transformations with SA for all the retinal pairs. In terms of transformation models, the affine and the bilinear transformations, combined with the

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(a)

(b) Fig. 4. Performance of the automatic registration technique for retinal image Pair 4: (a) GA’s (continuous line) versus SA (dotted line) versus DSM (dashed line) in conjunction with the bilinear transformation model. (b) Performance of the three transformation models (affine (AFF-dotted line) versus bilinear (BIL-continuous line) versus projective [PRO-dashed line)] with GA’s.

GA’s, appeared both superior in 23 pairs. Specifically, using the GA’s, the affine transformation achieved better results than the other transformations in eight pairs, the bilinear in nine pairs while in four pairs both these transformations performed equally. The projective transformation performed equally with the affine and bilinear only for the Pair 5 and with affine only for the Pair 13. The above results are averaged over 10 independent executions for all retinal pairs to compensate for the stochastic (randomized) nature of the optimization methods. Furthermore, the experimental results showed a significant reproducibility with a standard deviation averaged over ten executions for all retinal image pairs using the GA’s, in conjunction with the bilinear transformation model, of around 9%. The above observations, in terms of transformation models used, showed the superiority of the affine and bilinear transformations for the majority of the retinal image pairs. In the practical implementation of the automatic scheme, the bilinear transformation model was finally chosen because of its optimal performance in the pathological cases and its property to compensate for more complex deformations than the affine, by using eight independent parameters. On the other hand, the projective transformation, despite of its increased complexity, did not perform in most of the cases as expected and may

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be used in registering other modalities. Also, it is important to observe the different values of the objective function achieved, having a higher mean value for the RF and FA registration, a slightly lower mean value for the RF and ICG registration and a low mean value for the various retinal pathologies pairs. This was due to the different imaging techniques used for the acquisition of the retinal images. Based on the above observations, the values of the optimized parameters, using the GA’s, in conjunction with the bilinear transformation model, are listed in Table II for all retinal image pairs. Eight independent parameters for 1, 2, 3 were obtained according to the (5). In Fig. 4(a), the two global optimization methods, SA and GA’s, as well as the downhill simplex method (DSM), as a widely applied optimization technique, using the bilinear transformation, are compared by plotting the values of the objective function (measure of match) against the number of function evaluations, for the Pair 4. In Fig. 4(b), the three transformation models, using the GA’s, are also compared by plotting the MOM against the number of function evaluations. The measure of match is averaged for ten different program executions. It becomes evident from Fig 4(a) that the DSM, although it converges very fast (e.g., typically in 300 function evaluations), it was usually trapped in local maxima, failing to locate the global one. It can also be observed that the GA’s performed better than the SA with significantly higher convergence rate. The convergence to the optimal value of the objective function, using the GA’s, is achieved for less number of function evaluations than the SA, which required the total number of function evaluations to approximate the optimal value. This advantageous property of the GA’s was utilized in the clinical application of the registration scheme, reducing the total number of function evaluations and therefore the execution time. Furthermore, the superiority of the affine and bilinear transformations in Fig. 4(b) is evident for the retinal image Pair 4, both in terms of numerical performance and convergence rate. These results are typical for the majority of the experimental results (Table I). V. CLINICAL RESULTS The proposed automatic retinal registration scheme is currently running on an Indigo SGI workstation, installed at the Ophthalmological Diagnostic, Therapeutic and Research Center in Athens. RF, FA, and ICG retinal images with 1024 are acquired using the fundus camera size 1024 and digitized by the CCD camera mounted on the system. The automatic registration scheme is based on the bilinear transformation, in conjunction with GA’s and applied on 512 retinal images. The parameter ranges of the 512 transformation model are kept as they were defined during the experimental process of the scheme and the total number of function evaluations has been reduced to 10 000. Fig. 5 shows the result of the automatic registration scheme on RF and FL retinal images. In Fig. 5(a) and (b), the preprocessed (binary) RF (white colored vessels) and the FL (gray colored vessels) retinal images are shown. Fig. 5(c) shows the registration performed by the best individual of the first generation of the GA’s whereas the final result of the

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(b)

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(d)

Fig. 5. Clinical result of the automatic registration scheme on RF and FL retinal images: (a) preprocessed RF image (white colored vessels); (b) preprocessed FL image (gray colored vessels); (c) registration performed by the best individual of the first generation of the GA’s; (d) final result of the registration (produced by the best individual of all generations).

registration (produced by the best individual of all generations) is shown in Fig. 5(d). Regions of Interest (ROI) from the FL and ICG images, as rectangular areas, are superimposed on the corresponding RF images and the results are shown in Fig. 6(a) and (b), respectively. The accuracy of the registration is evident by the continuity of the retinal vessels along the borders of the superimposed ROI. The automatic registration scheme is also applied on a pathologic pair of RF and FL images of a male patient suffering from Harada’s Syndrome (Pair 22). Fig. 6(c) shows the registered FL image of the patient with three boundaries traced by the expert: one corresponding to the fovea (best fitting ellipse) and the other two to the areas of the abnormality (free drawing). These boundaries are easily identified only in the FL image and are of extreme importance in directing the laser treatment procedure. Since the laser treatment planning is based on the RF image of the retina, these

boundaries are traced by the ophthalmologist on the registered FL image and simultaneously placed on the corresponding RF image, displayed besides, according to the implementation of the scheme [Fig. 6(d)]. VI. AUTOMATIC RETINAL REGISTRATION VERSUS MANUAL REGISTRATION The method commonly used for retinal image registration in clinical practice is the manual approach. The ophthalmologist, using the IMAGEnet system, identifies points of vessel bifurcation (landmarks), common to both images that are to be registered. At least three such points are required for the transformation model installed in the software of the system, however, the specialist is allowed to enter any number of points. In clinical practice, four points are usually placed in each retinal image. The choice for the number of points placed by the experts seemed the appropriate for

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(a)

(b)

(c)

(d)

Fig. 6. Accuracy of the automatic registration: (a) superposition of an area of the registered FL image on the corresponding RF image; (b) superposition of an area of the registered ICG image on the corresponding RF image; (c) a registered pathological FL image with three boundaries traced by an expert; (d) superposition of the boundaries on the corresponding RF image.

most cases in order to registering the retinal images and to reduce the program’s execution time. Furthermore, in cases where the visibility of the vessel information is poor, it was observed that the identification of corresponding points from both retinal images was very difficult, even for an expert, reducing the number of the manually selected points. Then, the coefficients of the transformation are calculated directly. The disadvantages of this human-interactive approach include inaccuracy in the placement of landmarks, inconsistency of the registration results and increased interaction time between the expert and the system. The automatic retinal registration scheme is compared to the manual registration for all the pairs of Table I, both visually and numerically. Fig. 7 shows randomly selected areas of registered FA images superimposed on the corresponding RF images, for two pairs, using the automatic [Fig. 7(a) and (c)]

and the manual [Fig. 7(b) and (d)] registration techniques. It can be observed that the manual registration failed to preserve the continuity of the vessels along the borders of the superimposed regions, whereas the proposed automatic approach achieved registration of all vessels. A quantitative analysis between automatic and manual retinal registration methods has also been performed. Three independent experts, using the IMAGEnet system, performed manual registration of all the retinal pairs of Table I, and the average value of objective function (7) for the three trials and for all pairs, was evaluated. The results were then compared to the average objective function values obtained by the automatic registration scheme (ten independent executions) and are displayed in Fig. 8, against all the retinal image pairs. The values of the objective function of all manual trials are significantly lower than the one achieved by the automatic

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(a)

(c)

(b)

(d)

Fig. 7. Qualitative comparison between the automatic and the manual registration of RF and FA retinal images: (a) and (c) automatic registration; (b) and (d) manual registration.

Fig. 8. Quantitative comparison between the automatic (continuous line) and the manual (dotted line) registration for 26 retinal image pairs.

registration scheme for all retinal image pairs (except for the Pair 9). The mean and the standard deviation of the objective function for the automatic registration scheme were 138.34 and 40.63, respectively, for all retinal image pairs, whereas the mean and the standard deviation of the objective function for the manual registration of all retinal image pairs were 104.23 and 41.82, respectively. The above findings confirm the advantage of the proposed automatic registration scheme in terms of accuracy against the manual method. It was also noticed that the values of the objective function obtained by the three manual registration trials differ substantially

for all retinal image pairs. When the landmarks are placed close to each other, the manual registration algorithm seems to perform local than global registration, whereas when the landmarks are distributed over the whole image, the manual registration seems to improve. This confirms the inconsistency characteristic of the method due to human intervention. In terms of execution time, the manual registration method requires a minimum of 3.5 min for each retinal image pair, with size 512 512. The proposed automatic registration scheme, running currently on an Indigo SGI, requires minimum human interaction, only during the preprocessing stage,

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with an overall execution time of 4.5 min for the same size of retinal images.

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VII. DISCUSSION An automatic retinal image registration scheme was presented in this paper. According to the scheme, a successful coarse segmentation of the retinal images was firstly obtained and retinal vessels were identified. Three transformation models (affine, bilinear and projective) as well as three optimization methods (downhill simplex method, simulated annealing and genetic algorithms) had been evaluated in terms of accuracy and efficiency for retinal image registration. Results were presented in the form of evolution of the optimization with the number of function evaluations, averaged over an independent number of executions to compensate for the stochastic nature of the techniques. Results were presented in the form of the best achieved registration, both numerically and visually, for a sufficient number of data, applied on three different retinal images: Red-Free, Fluoroscein Angiography, and Indocyanine Green Chorioangiography images. The experimental results showed the superiority of Genetic Algorithms as a global optimization process in conjunction with the affine or bilinear transformation models. The automatic registration scheme was implemented on SGI workstation and installed on a clinical setting, requiring minimum human interaction. It allowed registration of retinal images within a wide range of translation and rotation displacements and scaling deformations. The proposed scheme was finally compared, both visually and numerically, to the currently used manual registration method and the superiority of the automatic registration was evident from the real clinical trials in terms of accuracy and consistency. In terms of execution time, the proposed automatic registration algorithm was 1 minute slower than the manual registration, for retinal 512. images of size 512 Currently, our work is directed toward implementation of the automatic registration scheme for a PC compatible version, concentrated more on reducing the execution time and incorporating other retinal images (e.g. monochromatic or color photographic images). It is investigated the reduction of the retinal image size to lower resolution levels, using multiresolution techniques [51], and the application of the above registration scheme to these images. ACKNOWLEDGMENT The authors would like to express their gratitude to Dr. P. Papadopoulos and Dr. D. Katsavavakis, ophthalmologists, at the Ophthalmological Diagnostic, Therapeutic and Research Center in Athens, Greece, for supplying the retinal image data, testing the new automatic registration scheme and evaluating the results.

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George K. Matsopoulos (M’97) received the diploma in electrical engineering in 1988 from the National Technical University of Athens (NTUA), Athens, Greece. He received the M.Sc. degree in 1989 and the Ph.D. degree in bioengineering in 1993 from the University of Strathclyde, U.K. He is currently an Assistant Professor, Institute of Communication and Computer Systems, NTUA. His interests are nonlinear image processing applied to medical applications, 2-D and 3-D registration of medical images and computer vision applications. Dr. Matsopoulos is a member of the Technical Chamber of Greece and the Hellenic Society of Biomedical Engineering.

Nicolaos A. Mouravliansky was born in Athens, Greece, in 1973. He received the diploma in electrical engineering in 1996 from the Technical University of Athens (NTUA). He received the Ph.D. degree in medical image processing from NTUA. His research interests include development of mathematical interpolation techniques, 3-D segmentation, 3-D and 4-D visualization, medical image registration, and fusion. Mr. Mouravliansky is a member of the Technical Chamber of Greece.

Konstantinos K. Delibasis was born in Athens, Greece, in 1967. He received the B.Sc. degree in physics from the University of Athens in 1989, and the M.Sc. degree in medical physics and Ph.D. degree in medical imaging from the University of Aberdeen, Aberdeen, U.K., in 1991 and 1995, respectively. He is currently a Research Assistant, Institute of Communication and Computer Systems, National Technical University of Athens. His research interests include image processing, pattern recognition, optimization techniques, and Web-based telemedicine applications.

Konstantina S. Nikita (M’96) received the diploma in electrical engineering and the Ph.D. degree from the National technical University of Athens (NTUA), Athens, Greece, in 1986 and 1990, respectively. She also received the M.D. degree from the University of Athens in 1993. Since 1990, she has been a Researcher, Institute of Communication and Computer Systems, NTUA. In 1996, she joined the Department of Electrical and Computer Engineering, NTUA, where she is currently an Assistant Professor. Her current research interests include applications of electromagnetic waves in medicine, electromagnetic scattering, diffraction tomography, medical imaging and image processing, and nonlinear optimization algorithms and applications. Dr. Nikita is a member of the Technical Chamber of Greece, the Athens Medical Association, and the Hellenic Society of Biomedical Engineering.