Morphological Active Contours for Image Segmentation

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1 Morphological Active Contours for Image Segmentation Juan Manuel Rendón Mancha 1, Vannary Meas-Yedid 2, Santiago Venegas Martínez 1, Jean-Christophe Olivo-Marin 2 and Georges Stamon 1 1 SIP Lab CRIP5 UFR de mathématiques et Informatique 45, rue des Saints-Pères Paris - FRANCE {rendon, venegas, stamon}@math-info.univ-paris5.fr 2 LAIQ - Institut Pasteur 25, rue du Docteur Roux Paris - FRANCE {vmeasyed, jcolivo}@pasteur.fr Abstract In this paper we introduce a new method of front propagation for image segmentation based on geodesic active contours. We propose a morphological active contour as another implementation of theory of curve evolution. This method uses a binary image morphology combined with substitutions of 3x3 pixel configurations, which represent an approximation of the curve evolution related to curvature, in order to overcome the difficulty and to reduce the computational cost of the Level Sets method. This method can be considered as a fast algorithm of curve evolution under anisotropic diffusion. Two kinds of images have been segmented and results are encouraging. The tests show the robustness of the algorithm. The proposed approach allows automatic topological changes and its implementation is very simple and can be extended to higher dimension. Keywords: Image segmentation, active contours, curve evolution, snakes, mathematical morphology, biological application. 1. Introduction Image segmentation is an important problem in low-level image processing, and many methods have been proposed. Among them, deformable models, first presented by Kass et al. [Kass, 1987], which are based on the paradigm that a method giving different possible answers depending on the choice of "energy" terms is better than a method with an unique answer. This paradigm explains the success of image segmentation based on active contours models [McInerney, 1996]. The model presented by Kass et al. is called snakes and is one example of the general technique of matching a deformable model to an image using energy minimisation. However, snakes present some drawbacks: because of the use of strictly information, they are sensitive to the initialisation step and as they are implemented with the Lagrangian approach, they can not deal with changes of topology. The geodesic active contour model [Caselles, 1995] was introduced as a geometric alternative for snakes and overcomes handicaps implied by snake model, in order to increase the convergence rate, and to deal with local minima the motion equation proposed in [Caselles, 1997] is:

2 where c 1 [ 0,1],c 2 [ 1,2] constant C t = g( I)c ( + c 1 2κ )N ( g( I ) N)N { } are positive constants. c 1 is a expanding/shrinking force and c 2 is the regularity Geodesic Active Contours based on Level Set methods [Sethian, 1999] handle topological change problems and allow straightforward extensions to higher dimensions. But their implementation is difficult and tedious and they are time consuming (because of reinitialisation of the distance function) even if some algorithms have been proposed to reduce this time [Paragios, 2000]. In order to perform a fast and robust segmentation we have developed a new method for front propagation. According to the theory of curve evolution and based on geodesic active contours, our algorithm propagates a front by performing morphological [Serra 1982] operations on a binary image instead of using a level sets implementation which works with a real 2D array. Our approach allows automatic topological changes and its implementation is very simple. In the next section, we present the developed methodology and we detail the algorithm and point out its forces and limits. In section 3, some results are shown. The first result is obtained on a noisy synthetic image and the second on a biological image. In the last section, we conclude and present some future works. 2. Methodology Three terms compose propagating speed: an expanding/shrinking term, a regularisation term and a term related to image. We handle separately two speed terms: the constant component (c 1 N) and the component related to the curvature (c 2 κn). The curve fit the border of a binary region. Our algorithm performs curve evolution with a constant speed using morphological erosions or dilations in the binary image (with a 4 neighbourhood mask). This is equivalent to an evolution under anisotropic diffusion. The curve evolution related to curvature is achieved by performing substitutions of 3x3 pixel patterns on the region boundary (central pixel must be black). These patterns represent all different configurations of the curve (with curvature values different from zero) for a specific point of the curve in the discrete domain. The substitutions simulate a curve evolution depending on its curvature. Figure 1 shows different patterns and their substitutions, where black pixels belong to region. The complete list can be created from all rotations and mirrors of shown patterns. 1) 2) 3) 4) 5) 6) 7) 8) Fig. 1: Configurations of different substitutions This configurations are not arbitrary selected, but represent the all possible configurations with central pixel belonging to region (black pixel).

3 Substitutions are inspired by evolution of continued curve driven by curvature (see figure 2). Fig. 2: Two examples of discretisation of curve evolution driven by curvature for a 3x3 window Details of implementation: To manage all these configurations, we can of course compute a Research Table. Instead of programming a Research Table, as the central pixel is always black (it belongs to region) so only eight pixels are considered. These pixels with binary values will form the address of a 256 bytes large vector containing substitutions (figure 3). In this way the complexity of the algorithm is reduced from O(n) to O(1). Computational cost can be reduced by working only with a variable-size window containing the region evolving instead of whole image. Fig. 3: Direct addressing. The 8 pixels (black or white, 0 or 1) are the address of each configuration. The configurations not listed in figure 1 are left unchanged. This way, the reader can observe that all vertical, horizontal and diagonal lines are preserved. Lines whose angles are different from 0, 90 and 45 are unchanged by the combination of the two last patterns (Fig. 1 n 7 and 8), called 'convex' and 'concave'. The other five patterns are referred to as 'of priority 1' because they may belong to a part of the curve with a high curvature. See Figure 4. Fig. 4. Straight lines are preserved. For horizontal, vertical and diagonal lines, no changes are made (Left and middle), so there is no configuration in our list for these cases. Right, marked pixels are removed by configuration 7 and then recovered by configuration 8. If all substitutions are performed at the same time, it could generate curve instability. To overcome this problem, a 4 steps algorithm is proposed: 1. Substitutions of Priority 1 Patterns 2. Substitutions of Concave Patterns 3. Substitutions of Priority 1 Patterns (again) 4. Substitutions of Convex Patterns These four steps constitute the evolution depending on curvature. One iteration of a complete evolution, including both speed terms is composed as follow: 1. Substitutions of Priority 1 Patterns 2. Substitutions of Concave Patterns

4 3. Substitutions of Priority 1 Patterns 4. Substitutions of Convex Patterns 5. Substitutions of Priority 1 Patterns 6. Erosion or Dilation Noise points (points which satisfy stopping criterion but do not belong to an edge) are simply eliminated in traditional Active Contours and Level Set approaches. With our method these points are detected and isolated as little regions. An additional removed algorithm can be used or preferably, we can add a single pixel pattern to our configuration list, which will remove noise consisting of an isolated pixel (figure 5). Fig. 5: Configuration of the substitution to remove isolated pixels. Let us now mention some drawbacks. A limitation of our method is apparent from fig. 6, which shows a curve evolution driven only by its local curvature. When a certain curvature value is reached, the repetition of the 4 steps does not produce any change in the curve. This limitation is due to our choice of the 3x3 window size. In edge detection applications, active contours approaches give closed contours, even if the object boundaries exhibit discontinuities, such as subjective contour illusion [Kass, 1987]. The limitation mentioned above restricts the applicability of our method to images whose discontinuities are smaller than 8 pixels. Fig 6: An example of curve evolution driven by local curvature. After the last image no change occurs.

5 3. Results We present different results of experimental tests performed on synthetic images and microscopic images. Figure 7 exhibits an edge detection performed by morphological active contours in a noisy synthetic image. The image test has been first, created by drawing grey patterns on white background. And then 50% of random noise was added. Fig 7. Edge detection in a noisy synthetic image. One of every ten iterations (120 iterations in total). Image size: 256 x 256, computational cost: 1.45 seconds including initialisation (PIII 450Mhz, 128Mb RAM). Biological application Entamoeba histolytica is a unicellular parasite that causes amoebic dysentery to humans. The amoeba s mechanisms of virulence are not yet understood, but they depend critically on its movement and morphology properties, which control the cell s ability to phagocyte and penetrate host tissue. In order to study these properties, biologists perform videomicroscopy observations of amoeba in vitro, using different mutants and various concentrations of signalling molecules. For these studies, it is essential to quantify and compare the motion and shape characteristics of the cells under various experimental conditions. This information is used to characterise the effect of potential drugs against the pathogenecity of the parasite. This task requires a precise knowledge of the cell contours at each instant. Our aim of in this context is to automatically detect cell contours and track their evolution in time throughout the sequences. Because of the highly deformable character of the cells and the good temporal resolution of the data, active contours seem particularly suited to this problem.

6 In another work, the GVF approach [Meas-Yedid, 2000] combined with a topological snake [Zimmer, 2001] has been implemented to segment the sequence images and the results are quite good but some problems still persist. In particular, the initialisation and topology problems are not well handled. The initialisation of the first image is done crudely by polygons drawn manually around each cell. For the following images, the detected contours of the previous image are used as initialisation of the contour deformation. But with this method, new objects appearing in the focal plane can not be automatically detected. The presented method could overcome this problem (see figure 8), and even with a rectangle over the whole image (720x540) as curve initialisation, the algorithm is fast. Fig 8. Original image and output of a Canny edge filter Figure 9 shows some preliminary results, where all groups of objects are correctly detected. The detected curves can be used as the initialisation for parametric active contour methods. To distinguish two amoeba in aggregation, a dilation should be performed instead of an erosion.

7 Fig 9. Curve evolution on the amoeba image, the stopping criterion is defined from the thresholding of a Canny image. 300 iterations have been performed. Image size: 720x540. Results show that the topology change is automatically handled by our algorithm and that this method is fast and robust against noise. 4. Conclusion and Future Work This paper introduces a new method of curve evolution in 2D which is simple, fast and robust. This method uses morphological operators to propagate a front and makes an approximation of a curvature motion by the way of successive substitutions of predetermined patterns. A possible drawback is pixelic resolution of the final curve (in comparison with level sets method), and the weight of speed curvature component of the curve is not adjustable. For tracking problem, the algorithm should be adapted to manage both directions simultaneously of the curve evolution (erosion, dilation) by introducing a region-based criterion which helps to decide whether dilation or erosion should be performed. Another development is a multiscale approach in order to reduce the computational cost. A Gaussian pyramid of images is built upon the full resolution image and similar morphologic active contours problems are defined across the different levels. This multiresolution structure can be used according to a coarse-to-fine strategy. An order-zero extrapolation is sufficient to go through different resolution levels. We have developed a 3D version of the algorithm and we are currently testing it. Results with 3D image segmentation and 3D reconstruction will be presented later.

8 5 Acknowledgements This work was partially founded by an Institut Pasteur's PTR grant. Juan M. Rendón M. and Santiago Venegas M. would like to acknowledge the financial support of CONACYT, Mexican Council of Science and Technology. 6 References [Adalsteinsson, 1995] D. Adalsteinsson and J. A. Sethian. A fast level set method for propagating interfaces. Journal Of Computational Physics, 120: , [Caselles, 1995] V. Caselles, R. Kimmel and G. Sapiro. Geodesic active contours. In IEEE International Conference en Computer Vision, Boston, USA, [Caselles, 1997] V. Caselles, R. Kimmel and G. Sapiro. Geodesic active contours. International Journal of Computer Vision, 22:61-79, [Deriche, 1995] Rachid Deriche et Oliver Faugeras. Les EDP en Traitement des Images et Vision par Ordinateur. Rapport de recherche INRIA Sophia-Antipolis. Nov [Kass, 1987] M Kass, A. Witking, & D. Terzopoulos, (1987) Snakes : Active contour models, Int. J. Comput. Vis. Vol 1, pp [McInerney, 1996] T. Mc.Inerney and D. Terzopoulos, Deformable models in medical image analysis: a survey, Medical mage Analysis, 1996, 1(2): [Meas-Yedid, 2000] V. Meas-Yedid, J.-C. Olivo-Marin, "Active contours for biological motility analysis", ICIP 2000, Vancouver, sept [Paragios, 2000] N. Paragios and R. Deriche. Geodesic Active Contours and Level Sets for the Detection and Tracking of Moving Objects. N. IEEE Trans. On Pattern Analysis and Machine Intelligence, 22(3) : , March [Serra, 1982] Serra, Image Analysis and Mathematical Morphology. Academic Press, London, [Sethian, 1999] J. A. Sethian. Level Set Methods and Fast Marching Methods. Cambridge University Press, [Zhu, 1996] S. C. Zhu and A. Yuille. Region Competition: Unifying Snakes, Region Growing, and Bayes/MDL for Multiband Image Segmentation. IEEE Trans. On Pattern Analysis and Machine Intelligence, 18(9) : , [Zimmer, 2001] C. Zimmer, V. Meas-Yedid, E. Glory, E. Labruyere, N. Guillen, J-C Olivo-Marin, Active contours applied to the shape and motion analysis of amoeba, SPIE International Symposium on Optical Science and Technology, 29 July-3 August, San Diego