Lesion Detection Using Morphological Watershed Segmentation and

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subjected to a model-based inverse filtering to determine ... Keywords: Brain images, lesion detection, morphological watershed segmentation, model-based.
Lesion Detection Using Morphological Watershed Segmentation and Modelbased Inverse Filtering Marc Macenko, Mehmet Celenk, and Limin Ma School of Electrical Engineering and Computer Science Stocker Center, Ohio University, Athens, OH 45701 USA {mm186500, celenk, limma}@ohio.edu

Abstract In this paper, we present a method that detects lesions in two-dimensional (2D) cross-sectional brain images. Use of the morphological watershed segmentation technique localizes shape variation in the gray level distribution of brain images and, in turn, identifies the regions with abnormal shape and/or texture structure. The detected brain areas are then subjected to a model-based inverse filtering to determine their physiological characteristics whether they are lesions or other types of anomalies. The proposed algorithm was tested on different images of “The Whole Brain Atlas” database [13]. The experimental results have produced 90% classification accuracy in processing 10 arbitrary images, representing different kinds of brain lesion. Keywords: Brain images, lesion detection, morphological watershed segmentation, model-based inverse filtering

1. Introduction Detection of abnormal, anatomical brain structures with their location and orientation is an extremely important task in the diagnosis stage and in the planning and analysis of various treatments including radiation therapy and surgery [1], [3], [4]. Because of this importance, accurate lesion diagnosis is a highly active study area. In recent years, significant research effort has been devoted to the development of medicalimaging systems for an early detection of brain anomalies. For example, in [1] the authors utilize statistical analysis to track the changes of brain lesions across the temporal dimension to assess treatment outcomes. A deformable model is employed in [3] to accurately segment volumetric heart data to aid in

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visualization. In [4], the authors use maximal likelihood estimation in conjunction with deformable models to accurately segment tumors in functional images of mice. Detecting lesions in brain images is usually driven by such low-level image processing operations as smoothing and segmentation [9]. Image segmentation is carried out using the morphological watershed approach [10], [11], [12]. In this work, we use a priori information about the shape of different lesions to guide the segmentation algorithm so as to improve its image partitioning accuracy. An adaptive deformation model is devised in such a way that it captures the interrelation among the region of interest (ROI) and background with the inclusion of a blurring function and additive noise in the analytical model [2], [4], [5], [6]. The results show that the proposed approach achieves more accurate segmentation results than the use of morphological watershed segmentation as a stand alone processing tool The remaining part of this paper is organized as follows. In section 2, a description of the overall approach is presented in detail. Section 3 is devoted to experimental results and performance assessment of the approach developed in this research. Conclusions and further research topics are given at the end.

2. Description of the Overall Approach The overall approach taken for lesion detection is illustrated by a flow-diagram given in Figure 1. Upon receiving an input slice to be analyzed, the algorithm requires several normal (i.e., healthy) images to compute the spectral composition of the background. Currently, these are manually chosen and fed to the algorithm as input. In our later work [7], the algorithm is able to analyze the slice to determine its most probable orientation and exploit known information about brain images to compute the required

background spectral properties. An image is considered normal if it does not exhibit any significant anomalies or deformations due to disease, physical causes of impaired development, or physiological and/or neurological disorder. Once the spectral characteristics of the background and the observed signal (i.e., the slice to be analyzed) have been computed, frequency domain subtraction is employed to estimate the desired signal, that is, the spectrum of the lesions and/or other abnormalities. The spectrally estimated 2D signal is then converted to the spatial domain to find the abnormalities present in the brain. Sections 2.1 and 2.2 provide further discussion on this process. Next, the morphological watershed partitioning is employed on the newly computed image. The resulting segments, or regions, include all abnormalities, normal areas, and additional regions as described in section 2.3 in detail. Segmentation results, the original image, and our a priori knowledge of the types of lesions detected are used to compute a ‘lesion metric’ for each of the resultant segments to determine the probability for each candidate region being a lesion or other abnormality. This is the final stage of the algorithm. Future development will aim to extend the method with units that take these segments determined to be abnormal and then classify them based on a number of characteristics such as intensity distribution, texture, and shape. Section 2.4 includes further discussion.

ellipsoid type analytical expression. It is allowed to deform in an arbitrary way with penalties associated with random motion. Blurring is taken into account and Gaussian white noise is added to the deformable template to aid in matching. The region is labeled appropriately depending on which model provides the lowest cost match based on warping to fit the object. The model adopted herein can be defined analytically by [2] f(s,t) = [v(s,t) + b(s,t)]*g(s,t) + n(s,t)

(1)

Here, f(s,t) is the observed image, v(s,t) is the deformable model, b(s,t) is the background, g(s,t) is the known blurring point-spread function, n(s,t) is the additive Gaussian white noise, s is the 2D spatial domain variable (x,y)-coordinates of a point, and t denotes cross-sectional slice index in the 3D space.

2.2 Spectral Subtraction Method To solve for the target ROI v(s,t) in Equation (1), we take the Fourier transform of f(s,t). This results in F(w,t) = [V(w,t) + B(w,t)] · G(w,t) + N(w,t)

(2)

where, F(w,t), V(w,t), B(w,t), G(w,t), and N(w,t) are the 2D spatial-domain Fourier transforms of f(s,t), v(s,t), b(s,t), g(s,t), and n(s,t), and w is the frequency domain variable (wx,wy) corresponding to the variations in the (x,y)-spatial plane coordinates, respectively. After some arithmetic manipulation, we arrive at the inverse filtering relation of the form V(w,t) = {[F(w,t)–N(w,t)] /G(w,t)}–B(w,t)

(3)

If there is no blurring (i.e., G(w,t) = 1) and noise has already been eliminated (i.e., N(w,t) = 0) via Weiner or Gaussian filtering, we are left with the simplified, yet powerful, formulation which is given by V(w,t) = F(w,t) – B(w,t)

Figure 1. Block diagram representation of the lesion detection system.

(4)

This lends itself directly to the spectral subtraction method that is widely used to reduce undesired portions in speech or other audio signals [8].

2.1 Adaptive Deformation Modeling

2.3 Morphological Watershed Segmentation

Once regions of interest (ROI) are delineated, an adaptive deformation modeling algorithm is driven to find the contour and size of each lesion. In 2D cross sectional representation, our deformable model is essentially a flat planar region of the volumetric lesion whose boundary can be described by a circular or

Morphological watershed analysis segments an image into different regions by interpreting the image as a topographic surface. Each color (or gray level or texture) value is given a different height and ‘flooding’ is started. During the flooding stage, the water level slowly rises, covering an increasing amount of the

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image. The assumption being made here is that regions of similar characteristics will have a lower height than those of the boundaries. In order to make this constraint applicable, the image on which the segmentation routine works is often the gradient of the original one. By using the gradient magnitude, areas of relatively low variation will be mapped to very low heights whereas areas with transitions will be mapped to higher elevations. As the flooding occurs, local maxima are quickly overflooded and, thus, considered to be a part of the larger partition. When the water reaches a certain level, it then tries to over-flood a large height so as to merge two or more basins (i.e., contiguous flooded areas). This is prevented by building a dam which is a thin line that has a height greater than the highest point in the image and is positioned in such a way that it prevents the multiple basins from merging. This is continued until the water has reached the maximum height in the image and the remaining visible platform and obstacle above the waterline are the dams themselves. These dams are the boundaries of the different segments. Note that every point is either in a segment or is a boundary point. Also, no point is assigned to more than one region. In order to avoid excess segmentation [11], [12], the image is first processed with an edge-enhancing filter [2]. The gradient magnitude of the image is then taken as the input of the segmentation algorithm after it is processed to eliminate small local minima. Quadregions which are only 30 units different than their neighbors are considered superfluous and are reassigned to the mean value of the neighbors. This process greatly reduces the number of local minima leading to a reasonable number of distinct segments.

2.4 Lesion Metric Computation After isolating regions of interest from v(s,t), a metric (not in the strict mathematical sense as it is only a unary operator) is computed for each resultant segment. Since a lesion is by nature an anomaly in the brain, its presence is often accompanied with an abrupt change of intensity values near its boundaries. Thus, regions with a high Laplacian magnitude on the boundary points are given positive weight. Another property exploited in the computation of the metric is that of solidity (or circularity). Because lesions start from a small set of seed points and grow from there, the image of the lesion is much more likely to fill its bounding box (or circumscribing circle). Regions with a higher degree of solidity are therefore given positive weight. Once the metric has been computed for all the regions of interest, those surpassing a preset threshold

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value will be considered to be a part of the lesion(s) contained in the image and passed on to the diagnostic stage.

3. Experimental Results Because the standard mode of 3D medical image acquisition is that of obtaining many 2D slices and combining these into a 3D volume, particular 2D slices were examined in this study. The algorithm was run on sample images of the database “The Whole Brain Atlas” [13]. A set of cross-sectional 2D slices from this database is shown in Figure 2. They are obtained from the axial plane.

Figure 2. A sample set of brain cross-sectional slices from the axial plane (from [13]).

As can be seen from Figure 3, the devised approach possesses a significant improvement over the traditional morphological watershed method. The estimated background which was computed from only 6 separate slices is shown in Figure 4. The final segmentations for two example images are shown in Figure 5. The presented results show the pixels classified as belonging to a lesion using a different intensity.

Figure 3. Segmentation results for left brain image in Fig. 5 using morphological watershed (left) and spectral-subtraction (right) methods.

present. As an extension to the computation of ‘lesion metric’, a probabilistic model of background will be compared to the input image the resulting belief matrix will be an aide in decision making process.

the the and the

References [1] D. Rey, et al., “A spatio-temporal model-based statistical approach to detect evolving multiple sclerosis lesions,” Proc. IEEE Workshop on Mathematical Methods in Biomedical Image Analysis, Kauai, Hawaii, Dec. 2001, pp. 105-112 Figure 4. Image created by the spectrum of the estimated background signal.

[2] J. S. Lim, Two-Dimensional Signal and Image Processing. Prentice Hall, 1990 [3] L. Zhukov, et al., “Dynamic deformable models for 3D MRI heart segmentation,” Medical Imaging 2002, Proc. SPIE Vol. 4681, pp. 1398-1405, 26-27 Feb. 2002, San Diego, CA [4] M. Celenk, et al., “Tumor detection in vivo NIRF images,” Medical Imaging 2004, Proc. SPIE Vol. 5370, pp. 2122-2129, 16-19 Feb. 2004, San Diego, CA [5] M. Lee and S. Ranganath, “Pose-invariant face recognition using a 3D deformable model,” Pattern Recognition 36, 2003, pp. 1835-1846 [6] C. Xu and J. Prince, “Active contours, deformable models, and vector flow,” Image Analysis and Communications Lab, Johns Hopkins University,

Figure 5. Lesion detection results (bottom) from crosssectional brain images (top) depicted in the outlining brain boundary.

From the segmented image pairs of Figure 5, average pixel classification accuracy was measured to be 97%. A pixel was considered accurate if it was marked as a lesion in the ground truth segmentation.

4. Conclusions and Discussion The presented method appears to be capable of finding brain lesions in the 2D brain image dataset utilized in this research. The high accuracy achieved shows that it is an important step towards the reliable segmentation and classification that are necessary in many clinical settings. Further improvement of the algorithm will focus on extending it to 3D brain imaging. We anticipate that the accurate volumetric characterization of background and lesion in conjunction with the 3D model will also be possible. Other future work is in the classification of the resulting regions of interest based on their intensity and texture probabilities. This will be especially useful for images where multiple lesions of differing types are

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[7] M. Macenko, R. Luo, M. Celenk, L. Ma, and Q. Zhou, “Lesion detection and extraction using symmetry-driven background estimation and Gabor-based saliency field mapping,” International Workshop on Medical Imaging and Augmented Reality 2006, 17-18 Aug. 2006, Shanghai, China (submitted) [8] M. K. Mandal, Multimedia Signals and Systems. Kluwer, 2004 [9] G. Taubin and T. Watson, “Curve and surface smoothing without shrinkage,” Proc. ICCV’95, pp. 852-859 [10] R. C. Gonzalez and R. E. Woods, Digital Image Processing. Prentice Hall, 2002 [11] L. Najman and M Schmitt, “Geodesic saliency of watershed contours and hierarchical segmentation,” IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 18, Issue 12, 1996, pp. 1163-1173 [12] J. Sijbers, et al., “Watershed-based segmentation of 3D MR data for volume quantization,” Magnetic Resonance Imaging, Vol. 15, No. 6, 1997, pp. 679-688 [13] K. A. Johnson and J. A. Becker, The Whole Brain Atlas.