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1 TEMPORAL STABILITY IN SEQUENCE SEGMENTATION USING THE WATERSHED ALGORITHM FERRAN MARQU ES Dept. of Signal Theory and Communications Universitat Politecnica de Catalunya Campus Nord - Modulo D5 C/ Gran Capita, Barcelona, Spain Tel: (343) , Fax: (343) ferran@gps.tsc.upc.es Abstract. The necessity of temporal stability in partition sequences for segmentation-based video coding techniques is stated. A time recursive segmentation approach is analyzed under this scope. The structure of this approach has ve main steps: Partition projection, Image modeling, Image simplication, Marker extraction and Decision. New techniques are proposed to improve the Partition projection in order to enable better temporal stability. Such techniques involve the denition of a new cost function for the watershed algorithm that accounts for the relative position between initial markers and candidate pixels. Key words: segmentation-based image coding, watershed algorithm, motion estimation. 1. Introduction Among the dierent coding approaches grouped under the name of second generation coding techniques [3], there is an increasing interest in segmentation-based image sequence coding approaches. This interest is mainly due to two reasons: Segmentation-based coding approaches give the possibility of reaching higher compression ratios. The segmentation procedure should yield partitions whose regions are homogeneous in some sense (e.g.: gray level, color or motion). Due to this homogeneity, the information of each region can be separately coded in a very ecient manner. This homogeneity has to be ensured since, with respect to classical coding techniques, segmentation-based approaches must code an additional information which is the image partition [11]. Segmentation-based coding approaches open the door to new functionalities within the coding scheme. Coding schemes with embedded functionalities such as content-based scalability or content-based manipulation are a very active eld of research [2]. These functionalities require a description of the image sequence in terms of objects. A natural way to describe objects in the scene is by detecting and tracking their boundaries; that is, by segmenting the image sequence. This work has been partially supported by the RACE Project 2072 (MAVT) of the European Union and the TIC C05-05 of the Spanish Government

2 2 FERRAN MARQUES However, image segmentation is an ill-posed problem [1]. In order to regularize the segmentation problem, constraints related to the specic application should be introduced. Thus, the segmentation procedure has to be goal-oriented. In the framework of image coding, the main goals for segmentation are to improve the coding eciency and to allow functionalities. Both goals require a very stable segmentation through the time domain. If a region has a coherent motion, its shape and position can be easily predicted and, as a consequence, they can be easily coded. In addition, in order to correctly track an object through the sequence, the region(s) describing this object should be stable since the object shape is assumed to change very little from frame to frame. Towards this goal, two main segmentation approaches have been proposed in the literature. The principal dierence between these approaches is the relative importance they assign to the spatial or the motion information. Spatial segmentation of sequences is of paramount importance in the context of coding [6]. Among this kind of methods, the so-called Time recursive techniques [5, 7, 9] lead to the best results in terms of coherence in time, random uctuations of the partitions, possible regulation of the bit rate and time delay [6]. In this paper, new methods for improving the motion stability of Time recursive image sequence segmentations are presented. These improvements are developed in the framework of the segmentation algorithm presented in [9]. Therefore, this algorithm is briey outlined in Section 2 and its main drawbacks are analyzed in Section 3. Section 4 is devoted to new techniques for improving the previous segmentation approach. Finally, some conclusions are presented in Section 5 and the current research in this framework is outlined. 2. The starting algorithm: A time recursive segmentation approach The basic structure of this Time recursive algorithm is an extension of the structure presented in [10]. It involves ve basic steps: Partition projection, Image modeling, Image simplication, Marker extraction and Decision. This general structure is presented in Figure 1. Partition projection: It accommodates the partition of image k? 1 to the data of image k. That is, it gives a rst approximation of the nal partition of image k. Since it is based on the previous partition, new regions cannot be introduced in the partition at this step. Image modeling: Each projected region is actually coded. The dierence between the coded and the original images is then computed. This image is refered to as the modeling residue. It concentrates all the information about the areas in the image which are poorly coded using the projected partition. Image simplication: The modeling residue is simplied in order to make it easier to segment. The simplication controls the amount and nature of the information that is kept.

3 TEMPORAL STABILITY IN SEQUENCE SEGMENTATION 3 Marker extraction: It detects, in the simplied modeling residue, the presence of relevant regions. For each relevant region, a marker is obtained. Markers are connected components with a specic label identifying the presence of homogeneous regions. Decision: Markers are extended in order to correctly cover the uncertainty areas. The precise shape of every region is obtained. Image #k-1 Partition #k-1 PROJECTION MODELING Image #k + SIMPLIFICATION MARKER EXTRACTION DECISION Image #k Partition #k Fig. 1. Block diagram of the basic segmentation structure In this structure, the step that deals with the temporal stability of regions is the Partition projection. The implementation of this step in the algorithm presented in [9] is further detailed in the sequel in order to analyze its performance Partition projection The rst frame in a sequence is segmented by means of a hierarchical algorithm that relies on size and contrast criteria [10]. In order to segment a generic frame Ik, the partition obtained in the previous one Pk?1 is used. The regions obtained in the segmentation of frame Ik?1 are used as markers and propagated in the following frame Ik in order to obtain its nal partition Pk. To solve the problem of the possible lack of connectivity between regions related to objects with rapid motion, motion information has to be included in the seg-

4 4 FERRAN MARQUES mentation. This is done by, before segmenting the current frame Ik, estimating the motion between both frames. This estimation is done using a block matching algorithm and a backward approach. For each block in Ik, a search is conducted within a conned window in the previous image Ik?1 to locate the best matching block. The previous segmentation Pk?1 is used to constrain the block matching technique. If the best matching block contains pixels belonging to more than one region, the block is split into smaller blocks. Once the motion between the previous frame Ik?1 and the current one Ik is estimated, it is utilized to compensate both the previous partition Pk?1 and the previous frame Ik?1. The compensated partition and frame are denoted by ~ P k and ~ I k, respectively. Given the block-based nature of the motion estimation, the compensation of the partition can produce disconnected components with the same label. A procedure to regularize the compensated partition is implemented by keeping only the largest connected component for each label. Therefore, the compensated partition ~Pk does not dene a real partition since some parts of it may not be assigned to any label. Nevertheless, there is a marker in the compensated partition for each region in the previous image and these markers are propagated both in the compensated image ~ I k and in the current image Ik in order to build the current partition. These propagation is carried out by means of a watershed algorithm [8]. The cost function of this watershed algorithm combines the complexity of both the gray levels and the contours of the nal regions. 3. Main drawbacks of the Partition projection The above Partition projection step, although performing correctly for coding purposes, still rises some problems. Such problems result in a lack of coherence between regions in two consecutive partitions. The main reasons for this lack of motion coherence in the previous segmentation algorithm are three. 1. A basic block-matching motion estimation approach does not yield good enough motion parameters. This problem is emphasized by the fact that, in the framework of image sequence coding, a usual approach to reduce the information to be sent is to code only a subset of the total amount of frames. In the receiver side, frames which have not been sent are interpolated from the transmitted information. In this case, the motion estimation for segmentation is to be carried out between two frames which are not consecutive, Ik?p and Ik. Therefore, a straighforward block matching may not be reliable enough. 2. Given that the motion parameters do not perfectly describe the motion between frames Ik?p and Ik (even when p = 1), images are not perfectly compensated. Therefore, the propagation of the markers of ~ P k on both images ~ I k and Ik may present some problems. For instance, markers may propagate through the compensated image ~ I k covering areas with gray level values that do not correspond to the real ones. Afterwards, these propagated markers may connect areas of the current image Ik that should not be connected.

5 TEMPORAL STABILITY IN SEQUENCE SEGMENTATION 5 3. A watershed algorithm relying only on gray level information does not ensure the temporal coherence of the nal segmentation. This problem has been parcially solved by combining contour complexity and texture information in the distance used in the watershed algorithm. However, some problems still remain. This is the case of areas of the image that, due to their gray level values, may be part of two dierent neighbor regions. A watershed algorithm that utilizes a cost function relying only on gray level and contour complexity information may assign such areas to any of these neighbor regions. This may result in an oscillation of the label of such areas which in consecutive segmented frames may have dierent labels. In Figure 2 an example illustrating the eect of the above commented drawbacks is presented. In this example, two frames of the sequence Foreman have been segmented with the technique presented in [9]. The rst row presents the original frames whereas the second row contains the labelled images resulting from the segmentation procedure. The lack of temporal stability can be seen in the evolution of the regions forming the face of the man. Note that, even in this case where there is not a large motion between both frames, the projection of the rst partition does not yield stable results. Due to this lack of stability, the coding cost of these partitions is very high. Fig. 2. Example of the erratic evolution of some regions

6 6 FERRAN MARQUES 4. Improving the temporal coherence The dierent problems commented in the previous Section have been addressed in this work. For each one of the problems, a possible solution is presented Motion estimation In order to improve the motion estimation, several methods can be used. A possible solution is to use motion models more complex than the simple traslation used in [9]. An extension of this model can be achieved assuming an ane model for the motion. In this sense, ane motion parameters can be computed directly from the original images [12] or in a recursive way interleaving the motion estimation with the segmentation itself [9]. In both cases, the computational load is highly increased. Another possibility is to carry out the motion estimation frame by frame and to related the information in image Ik with that of image Ik?p through the p? 1 intermediate images (Ik+1 Ik?p?1) [4]. The motion estimation and the segmentation are computed at two dierent rates, being the block matching algorithm applied for each single pair of consecutive images. With this technique, images can be better compensated without increasing too much the global computational load. There are dierent ways to implement this algorithm. The solution adopted in this work uses, for each block, the vector obtained between images Ik and Ik?1 to locate the search area in the image Ik?2. In this area, the best matching block is found using blocks from images Ik and Ik?2. This procedure is iterated up to reaching Ik?p? Marker propagation Even though the above technique improves the motion representation, some areas of the compensated image ~ I k do not correctly correspond with the original image Ik. Therefore, the propagation of the markers of ~ P k in both images (~ I k and Ik) should be constrained. This is done by preventing the markers to propagate through the compensated image ~ I k. The compensated image ~ I k is only used to compare its gray level information with the gray level of new pixels to be labeled, belonging to the new image Ik. In this way, the markers in the image ~ P k only propagate to the image to be segmented Ik Cost function In order to improve the temporal coherence of the segmented sequences, the cost function used in the watershed algorithm has been modied to take into account the information about the position of every pixel within the image. That is, the cost function accounts for the relative position between a candidate pixel and the original marker. The larger the distant from a marker to a candidate pixel, the less likely this pixel will get the label of the marker. In this way, markers are prevented to grow far from their original location and labels of areas between markers will less likely oscilate. Therefore, the cost of assigning a pixel pi to a region rj uses three dierent types of information: Cost(pi; rj) = 1distt(pi; rj) + 2distc(pi; rj) + 3distp(pi; rj) (1)

7 TEMPORAL STABILITY IN SEQUENCE SEGMENTATION 7 The three functions distt, distc and distp are the distances related to the texture, contour complexity and position information, respectively. The exact computation of distp between all the possible candidate pixels and markers demands a large amount of either memory or computational time. Therefore, an approximation of this distance is calculated. This approximation is done recursively and relying on the pixels previously assign to a marker. All the pixels belonging to the initial marker of a region have assigned distp = 0. From this state, a pixel pn that is neighbor of a pixel pm already labelled as belonging to the region rj has assign a distp value: distp(pn; rj) = distp(pm; rj) + 1 (2) The use of the term related to the position prevents markers to overgrow, as it is shown in Figure 3. In this example, three frames from the sequence Carccett are segmented using the cost function proposed in [9] as well as that of (1). Fig. 3. Improvement using the position information. In the rst row, the original frames are presented whereas the second row contains the labelled images obtained using the cost function proposed in [9]. Note that the

8 8 FERRAN MARQUES evolution of the bright region that initially is related to the background extends up to covering a large area of the gate. In the third row, the result achieved using the cost function of (1) is presented. In this case, the regions remain very stable and, therefore, they can more easily be coded. 5. Conclusions and current work In this paper, new techniques for improving the temporal stability of the Partition projection step proposed in [9] have been presented. These techniques allow the regularization of the evolution of the regions in the partition. The main idea is to minize the errors introduced by the motion compensation of the previous image and the markers from the previous partition as well as to prevent the overgrowing of the markers in the current partition. With these improvements, the set of projected markers already denes correctly the position of the regions in the current image. Therefore, the current work aims at using the projected markers directly as markers in the current image. This approach avoids the use of the compensated image ~ I n wich may introduce errors in the segmentation procedure. Methods for ensuring that all regions can be projected in the current image as well as to allow some regions to disappear in the projection step are currently under development. References 1. M. Bertero, T. A. Poggio, and V. Torre. Ill-posed problems in early vision. Proceedings of the IEEE, 76:869{887, ISO/IEC JTC1/SC29/WG11. MPEG-4 Proposal Package Description (PPD). July M. Kunt, A. Ikonomopoulos, and M. Kocher. Second generation image coding techniques. Proceedings of the IEEE, 73(4):549{575, April B. Marcotegui. Segmentation de sequences d'images en vue de codage. PhD thesis, Ecole des Mines de Paris, France, B. Marcotegui and F. Meyer. Morphological segmentation of image sequences. In J. Serra and P. Soille, editors, Mathematical morphology and its applications to image processing, pages 101{108. Kluwer Academic Publishers, F. Marques, M. Pardas, and P. Salembier. Coding-oriented segmentation of video sequences. In L. Torres and M. Kunt, editors, Video Coding: The second generation approach, pages 79{124. Kluwer Academic Publishers, F. Marques, V. Vera, and A. Gasull. A hierarchical image sequence model for segmentation: Application to object-based sequence coding. In Proc. SPIE Visual Communication and Signal Processing-94 Conference, pages 554{563, Oct F. Meyer and S. Beucher. Morphological segmentation. Journal of Visual Communication and Image Representation, 1(1):21{46, September M. Pardas and P. Salembier. 3D morphological segmentation and motion estimation for image sequences. EURASIP Signal Processing, 38(1):31{43, September P. Salembier. Morphological multiscale segmentation for image coding. EURASIP Signal Processing, 38(3):359{386, September P. Salembier, F. Marques, and A. Gasull. Coding of partition sequences. In L. Torres and M. Kunt, editors, Video Coding: The second generation approach, pages 125{170. Kluwer Academic Publishers, H. Sanson. Joint estimation and segmentation of motion video coding at very low bitrates. In Proc. COST 211ter European Workshop on New Techniques for Coding of Video Signals at Very Low Bitrates, pages 2.2.1{2.2.8, Dec 1993.

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