Image Segmentation Method

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The Multiresolution and Flooding Based RSST (MFRSST) Image ... a decimated image is partitioned into N regions by using the concepts of multiresolution ...
中華理工學刊 第一卷 第一期 第 9 至 16 頁 民國九十二年三月 Chung Hua Journal of Science and Engineering, Vol.1, No.1, pp.9-16 (2003)

The Multiresolution and Flooding Based RSST (MFRSST) Image Segmentation Method Chien-Hao Chen(陳建豪) and Cheng-Chang Lien1(連振昌) Computer Science and Information Engineering Department Chung Hua University Hsin-Chu, Taiwan, R.O.C.

關鍵字:遞迴最短路徑生成樹,多解析分解,區域擴散 摘要 影像分割技術為影像分析與影像識別的一項基礎技術。影像可以分割成許多相同之色彩、強度、或紋理 之區域。然而,傳統影像分割技術方法有一些問題造成分割處理之不精確,即無法保證區域的連接性, 精確地定義區域邊界,以及決定分割區域之數目。遞迴最短路徑生成樹(RSST)的方法被提出後,改進上 面所述問題,但是遞迴最短路徑生成樹演算法擁有過高計算量。緊接著,快速遞迴最短路徑生成樹演算 法(FRSST)被提出,藉著移除原有 RSST 之搜尋處理來降低計算複雜度,加快處理速度。然而 FRSST 依 舊無法有效應用於一些即將出現之視訊應用,例如視訊分割處理、區域視訊編碼、以及以視訊物件為基 礎之搜尋。本篇論文主要是應用多解析分解及分水嶺演算法區域擴散之概念,發展出多解析擴散遞迴最 短路徑生成樹(MFRSST)影像分割技術方法,用以提高處理速度並且保有與遞迴最短路徑生成樹演算法相 同的分割品質。在 MFRSST 之系統裡,利用多解析分解及分水嶺演算法區域擴散之方法先將一張消除縮 小之影像分割出 N 個區域,然後再利用區域邊界修正處理得到 M 個微小區域。 Keywords: recursive shortest spanning tree, multiresolution decomposition, flooding

Abstract Image segmentation is a fundamental technology in image processing and image understanding. Images are partitioned into many regions with the same color, intensity, or texture homogeneity. However, the conventional image segmentation methods have some problems that make the segmentation process inaccurate, i.e., they can’t ensure the region connectivity, define the region boundaries accurately, and partition image with an arbitrary number. The method of the recursive shortest spanning tree (RSST) is proposed to improve the above problems, but the computation complexity of RSST algorithm is high. In the following, the fast RSST (FRSST) algorithm is proposed to reduce the computation cost by removing the sorting process in the RSST method. However, the FRSST method is still too inefficient to meet the requirements for some new visual applications such as video segmentation, region-based video coding, and object-based video retrieval. In this paper, the concepts of multiresolution decomposition and flooding process in watershed algorithm are applied to develop the multiresolution and flooding based RSST (MFRSST) image segmentation method that can speed up the segmentation process and have the same partition quality as the RSST. In the MFRSST segmentation system, a decimated image is partitioned into N regions by using the concepts of multiresolution decomposition and flooding method, and then additional M high detailed regions are obtained by the boundary region refining process.

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to whom all the correspondence should be addressed, e-mail: [email protected].

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中華理工學刊 第一卷 第一期 第 9 至 16 頁 民國九十二年三月 Chung Hua Journal of Science and Engineering, Vol.1, No.1, pp.9-16 (2003) watershed algorithm [16]. Instead of merging two vertices of the least weighted link, we merge all the neighboring vertices whose link weights are closed to the lowest weight concurrently. Such a merging process is similar to the flooding method in the watershed algorithm that fills up the image valleys. The second one is the concept of multiresolution decomposition. Performing the partition process in the low-resolution image can reduce the computation cost significantly. However, the reconstruction process may introduce the blocky effect in the boundary region. Therefore, the boundary refining process is developed to define the boundary region accurately. In this paper, the aforementioned concepts are applied to develop the multiresolution and flooding based RSST (MFRSST) image segmentation method that can speed up the segmentation process. In the MFRSST segmentation system, a low-resolution (decimated) image is partitioned into N regions by using the concepts of multiresolution decomposition and flooding method in watershed algorithm, and then additional M high detailed regions are obtained by the boundary region refining process. Furthermore, the RSST algorithm may generate many redundancy image regions, i.e., spark regions, and the separation of foreground and background is difficult when their colors are closed. In this paper, these problems are solved to obtain the better partition quality than the RSST. In Section 2, the RSST and fast RSST algorithms are reviewed. In Section 3, the MFRSST algorithm is described. Finally, the experimental results illustrate that MFRSST algorithm can partition the image very efficiently and outperform the conventional image segmentation methods.

1. Introduction Recently, with the great advance in computing and computer network, many new emerging multimedia applications, such as low bit rate video coding, video summarization, video indexing, and video query, enforce the development of new video coding standards: MPEG-4 [1] and MPEG-7 [2]. The objects in both the video coding systems are acquired by applying the image and video segmentation processes, which apply the image features such as color, intensity, motion, textures, and shapes to partition the regions of objects. Once the video objects are acquired, the aforementioned multimedia applications can be fulfilled. Hence, the quality and efficiency of image segmentation process determine the performance of the object-based video processing system. However, the conventional image segmentation methods, such as the histogram-based algorithms [3,4] and split-merge algorithms [5,6], have some problems that make the image segmentation process inaccurate. Firstly, the histogram-based segmentation methods can’t ensure the region connectivity. Secondly, the split-merge methods can’t define the region boundaries accurately. Finally, both methods are unable to partition the image with an arbitrary number. The method of recursive shortest spanning tree (RSST) [7] is proposed to solve these problems by using the global information and is widely adopted in many video segmentation systems [8-14]. Alatan et al. [10,11] develop the European COST 211 framework by utilizing the RSST algorithm to partition the regions with the same color or motion homogeneity. Tuncle et al. [12] utilize the RSST algorithm and affine motion model to develop their video object segmentation system. Doulamis et al. [13] propose an efficient RSST algorithm for non-sequential video content representation. Vlachos et al. [14] extend the RSST algorithm to partition the color image by introducing red-green-blue (RGB) components into the cost function. The high computation complexity is the main drawback of the RSST algorithm. The sorting procedure is required whenever two vertices of the least weighted link are merged. Kwork et al. [15] propose the fast RSST (FRSST) algorithm to reduce the computation cost of RSST by removing the sorting process and applying the region-growing method. However, the FRSST method is still too inefficient to meet the requirements for some new visual applications such as video segmentation, region-based video coding, and object-based video retrieval. In order to reduce the computation cost further, the concepts of two image processing methods are adopted to develop the new image segmentation algorithm. The first one is the flooding method in the

2. The Review of RSST and Fast RSST Image Segmentation Methods In this section, we will describe the principles of RSST and fast RSST algorithms. 2.1 The RSST algorithm The shortest spanning tree (SST) [7] segmentation method belongs to the graph-theoretic method. When an image is transformed into a weighted graph, the shortest spanning tree is the spanning tree that the sum of its link weights is minimum. The link weight can be defined by a specified monotonic function that depends upon the application of image processing. Here, the absolute difference value between adjacent pixels is defined as the link weight wi,j, i.e., wi,j = |vi - vj|, (1) where, vi and vj are the gray levels of the adjacent pixels.

Given an image whose size is m×n pixels, we can generate an eight-connected graph shown in Fig. 1-(a). The corresponding SST graph may be obtained by using Kruskal’s algorithm [17] and is shown in Fig. 1-(b). After obtaining the shortest spanning 10

中華理工學刊 第一卷 第一期 第 9 至 16 頁 民國九十二年三月 Chung Hua Journal of Science and Engineering, Vol.1, No.1, pp.9-16 (2003) (1). Find the next least-weighted link.

tree, we can partition the image into N regions by cut the N-1 largest weighted links. The SST segmentation algorithm is described as follows. 1). Construct the weighted graph of the image. 2). Form the SST by using the Kruskal’s algorithm. 3). Cut the N-1 largest weighted links. 4). Map the regions onto a segmentation image. In the SST segmentation process, the image is partitioned into many homogenous regions hierarchically by cutting the next largest weighted link successively. For example, Fig. 1-(b) illustrates that two regions are separated by cutting the first costly weighted link and the third region is separated by cutting the second costly weighted link. However, the SST algorithm will generate sparks in a noisy or complex image because no global information is applied.

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(3). Merge two vertices into one vertex. (4). Recalculate the new vertex value and new adjacent link weights. (5). Remove the duplicated links. (6). Go to step (1) until only one vertex in the graph. 3. Cut the spanning tree at the N-1 most costly links. 4. Map the regions onto a segmentation image. Fig. 2-(a) shows the new spanning tree and Fig. 2-(b) shows that the image is partitioned into N regions by cut the spanning tree at the N-1 largest weighted links. It is obvious that computation cost of the RSST algorithm is high because the sorting process and link weight recalculation are required whenever the merging process takes place.

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(a) (b) Fig. 1. (a) An eight-connected weighted graph. (b) The shortest spanning tree of the weighted graph in (a). The image is partitioned into many regions hierarchically by cutting the next largest weighted link successively. The recursive shortest spanning tree (RSST) segmentation method [7] is proposed to improve spiky phenomenon by using the global information. It is considered as one of the most powerful method compared to other techniques [13], such as the pyramidal region growing, morphological watershed or color clustering. The region growing and color clustering methods can't define the boundary region accurately. Although the watershed algorithm [16] can define the boundary region accurately, its high computation cost makes it difficult to be applied to many image processing systems. The common drawback of the abovementioned algorithms is unable to partition the image with an arbitrary number. Starting from the least-weighted link, the RSST segmentation method merges the vertices of the least weighted link into one new vertex, and then save the link to a new spanning tree. The new vertex value is the mean of the two adjacent vertices. By searching the least-weighted link and perform the above process repeatedly; we can construct a spanning tree with the saved links. The RSST segmentation algorithm for partitioning N regions is described as follows. 1. Construct the weighted graph for an image. 2. Form a spanning tree by the following steps

2.2 The FRSST method In order to reduce the computation cost of the RSST algorithm, Kwork et al. [15] propose a new method called the fast recursive shortest spanning tree (FRSST). In the FRSST algorithm, the sorting process is removed and the region growing method is applied to the merging process. Based on these modifications, the spanning tree can be constructed more efficiently. The flowchart of FRSST method is shown in Fig. 3.

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中華理工學刊 第一卷 第一期 第 9 至 16 頁 民國九十二年三月 Chung Hua Journal of Science and Engineering, Vol.1, No.1, pp.9-16 (2003) using the concepts of multiresolution decomposition and flooding method, and then additional M high detailed regions are obtained by the boundary region refining process. The block diagram of the MFRSST is illustrated in Fig. 4.

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3.1 The Segmentation using the Improved FRSST for the Low-Resolution Image The reason why the FRSST method can improve the efficiency of the RSST algorithm is applying the merging process in forming the new spanning tree. Instead of merging the two vertices of the least weighted link, it merges all the neighboring vertices whose link weights are closed to the lowest link weight concurrently. Fig. 5 illustrates such a merging process. The adjacent vertices are merged into a new single vertex when the difference of the corresponding weighted links below a specified threshold and then the new weighted links are recalculated. The merging process in FRSST algorithm is similar to the flooding process in the watershed algorithm that fills up the image valleys concurrently. However, the FRSST method is still too inefficient to meet the requirements for some new visual applications such as video segmentation, region-based video coding, and object-based video retrieval. In this paper, the concept of multiresolution decomposition is used to reduce the computation cost of the FRSST algorithm further. In [7], three methods are proposed to modify the SST segmentation algorithm by incorporating global information into the segmentation method. The three methods are recursive SST (RSST), minimax SST, and local averaging SST. Applying the FRSST algorithm to segment the decimated image has the effect of combining the RSST and local averaging SST methods. Furthermore, segmentation in the decimated image may reduce the computation cost significantly. However, applying the FRSST method to partition the decimated image still may generate some spark regions and the separation of foreground and background is difficult when their colors are closed. Hence, we improve the FRSST method by fusing the smaller regions into their neighboring regions such that the spark regions are removed. The fusion process is illustrated in Fig. 6. If the number of vertices in a region is lower than a specified threshold value, the region is fused into its neighboring region.

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The flowchart of the FRSST algorithm.

The FRSST algorithm is described as follows. (1) Construct the spanning tree in a region growing fashion instead of a single link. (2) Remove the sorting algorithm from the construction process. (3) Evaluate the link weight function in order to maintain best possible output quality.

3. The Multiresolution and Flooding Based RSST Segmentation Method Here, we propose a new image segmentation method to improve the efficiency of the fast RSST method and obtain better partition quality than the RSST algorithm. Two concepts of image processing methods are adopted to develop the new image segmentation algorithm. The first one is the flooding method in the watershed algorithm [16]. Instead of merging the two vertices of the least weighted link, we merge all the neighboring vertices whose link weights are closed to the lowest weight concurrently. Such a merging process is similar to the flooding method in the watershed algorithm that fills up the image valleys. The second one is the concept of multiresolution decomposition. Performing the partition process in the decimated image can reduce the computation cost significantly. However, the reconstruction process may introduce the blocky effect in the boundary region. Therefore, the boundary refining process is developed to define the boundary region accurately. In the MFRSST segmentation system, a decimated image is partitioned into N regions by

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3.2 The Boundary Region Refining Process The objectives of the boundary region refining process are partitioning the high detailed region (boundary region) carefully and removing the blocky effect for the reconstruction process. In Section 3.1, the decimated image is partitioned into N regions and then the boundary region will be partitioned into the additional M detailed regions by applying the boundary region refining process. The boundary region refining process shown in Fig. 7 consists of two procedures. Firstly, the boundary region on the segmented decimated image is detected by using a 3×3 mask. If the pixels in the mask have different labels, then the central pixel in the mask is regarded as the boundary pixel. Fig. 7-(a) illustrates the boundary detection process. Secondly, we apply the interpolation process to the decimated image to reconstruct the segmented image. Here, the direct mapping is used for the interpolation process shown in Fig. 7-(b). However, the direct mapping will introduce the serious blocky effect. Hence, we make the pixels in the boundary region blank in the interpolation process shown in Fig. 7-(c) and apply the boundary region refining process to remove the blocky effect. The blank regions (boundary regions) in the interpolated image are similar to the watersheds in the segmented image. After the interpolation process, each reconstructed region is regarded as a single node, the pixels in the boundary region are replaced by the original image pixels, and then a new weighted graph may be constructed shown in Fig. 7-(c). By applying the SST algorithm and cutting the most costly M-1 links in the boundary region, we may partition the boundary region into M high detailed regions. It is important that we must maintain the original N regions that are segmented in the decimated image, such that there are totally N+M regions partitioned in the image. The number of M may be determined by the user. With larger value of M, better quality of segmented image may be acquired. The boundary refining process is illustrated in Fig. 8.

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(a) (b) Fig. 5. (a) The eight-connected weighted graph. (b) The adjacent vertices are merged into a new single vertex when the difference of the neighboring link weight below a specified threshold and the new link weights are recalculated.

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Fig. 6. (a) The image is partitioned into three regions and the region #1 is the spark region. (b) The regions #1 and #2 are merged into a new region. Here, the decimated image is obtained by utilizing the wavelet decomposition. Once the decimated image is partitioned, we may apply the interpolation process to reconstruct the segmented image. However, the interpolation process will introduce the blocky effect in the region boundaries. Hence, the boundary region refining process is required to define the boundary region accurately.

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(c) Fig. 7. The description of boundary region refining process. (a) The 2-D interpolation process. (b) Boundary region detection. (c) Each reconstructed region is regarded as a single node, the pixels in the boundary region are replaced by the original image pixels, and then a new weighted graph may be constructed.

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image may be partitioned with a given number N including the segmented regions in the decimated image and the reconstructed boundary regions. The MFRSST segmentation algorithm is described as follows. 1. Perform the wavelet transform to obtain the decimated image. 2. Apply the FRSST method to partition the decimated image into N regions. 3. Apply the fusion process to remove the spark regions. 4. Reconstruct the segmented regions by interpolating the segmented decimated image according to the following rules: (1) If the pixel is located at the boundary region Interpolate it by an empty block with size of 2L×2L.(L is the level of wavelet decomposition). (2) Else Interpolate the segmented decimated image by 2L factor. 4. Regard each reconstructed region as a single

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(a) (b) Fig. 8. (a) The number of segmented regions after reconstruction process is five. (b) The number of segmented regions after boundary region refining process is nine. 3.3 The MFRSST Algorithm The MFRSST algorithm is designed to meet three crucial requirements. The first one is that the boundary region should be defined accurately. The second one is that the computation cost has to be less than the FRSST algorithm. The third one is that the 14

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node and then construct the new weighted graph. Form the SST. Cut the N links to maintain the N regions in the decimated image. Cut the other most costly M-1 links to partition the M high detailed regions. Map the regions onto a segmentation image.

The experimental results show that the three algorithms may define the boundary region accurately.

4. Experimental Results In this section, the quality of segmentation and the computation complexity are compared for the RSST, FRSST, and MFRSST algorithms. Both the gray level image and color image are used for the three segmentation methods.

(a)Lena (b)Boy Fig. 10. (a) Lena and (b) Boy images.

4.1 The Experimental Results of MFRSST Segmentation Algorithm Fig. 9 illustrates the experimental results of MFRSST segmentation algorithm. Fig. 9(a) illustrates original image with size 128× 128 pixels. The segmented regions in decimated image is shown in Fig. 9(b) and the watershed-like image after 2-D interpolation process is shown in Fig. 9(c). Fig. 9(d) illustrates the segmented regions after boundary refining process.

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Fig. 11. The Lena image is partitioned into 300 regions using (a) RSST, (b) FRSST, and (c) MFRSST algorithms.

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Fig. 12. The Boy image is partitioned into 300 regions using (a) RSST, (b) FRSST, and (c) MFRSST algorithms. (a)

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4.3 The Efficiency Analysis of RSST, FRSST, and MFRSST Algorithms In this section, the efficiency analysis of the three segmentation methods is given. The computation time of the three methods for partitioning various size of image is shown in Fig. 13. The experimental results show that the MFRSST is the faster than the other algorithms. The reason why the MFRSST method may improve the efficiency of the FRSST algorithm is the partition process performed in the decimated image.

Fig. 9. (a) The original image with size 128×128 pixels, (b) 98 regions are partitioned in the decimated image with size 64× 64 pixels, (c) The reconstructed image for the boundary refining process, and (d) 200 regions are partitioned after the boundary refining process. 4.2 The Quality Analysis of RSST, FRSST, and MFRSST Segmentation Algorithms Fig. 10 illustrates the original images with size 128×128 pixels. Fig. 10 and 11 illustrate that the Lean and Boy images are partitioned into 300 regions using the RSST, FRSST, and MFRSST algorithms. 15

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[8] M. M. Chang, A. M Tekalp, and M. I. Sezan, "Simultaneous motion estimation and segmentation," IEEE Transaction. Image Processing, vol. 6, pp. 1326-1333, Sept. 1997. [9] G. D. Borshukov, G. Bozdagi, Y. Altunbasak, and A. M. Tekalp, "Motion segmentation by multistage affine classification," IEEE Transaction. Image Processing, vol. 6, pp. 1591-1594, Nov. 1997. [10] A. A. Alatan, E. Tuncel, and L. Onural, "A rule-based method for object segmentation in video sequences," in Proc. 1997 IEEE Int. Conf. Image Processing ICIP 97, vol. II, pp. 522-525, Oct. 1997. [11] A. A. Alatan, L. Onural, M. Wollborn, R. Mech, E. Tuncel, and T. Sikora, “Image sequence analysis for emerging interactive multimedia services-the european cost 211 framework,” IEEE Transactions. Circuit and System for Video Technology, Vol. 8, No. 7, Nov. 1998. [12] Ertem Tuncel and Levent Onural, “Utilization of the recursive shortest spanning tree algorithm for video-object segmentation by 2-D affine motion modeling,” IEEE Transactions. Circuit and System for Video Technology, vol. 10, no.5, Aug. 2000. [13] Anastasios D. Doulamis, Nikolaos Doulamis and Stefanos Kollias, “Non-sequential video content representation using temporal variation of feature vectors,” IEEE Transactions on Consumer Electronics, vol. 46, no. 3, AUG. 2000. [14] T. Vlachos and A. G. Constantinides, “A graph-theoretic approach to color image segmentation and contour classification,” in Proc. 4th. Int. Conf. Image Processing and Its Applications, Maastrict, Netherlands, Apr. 1992. [15] S. H. Kwok and A. G. Constantinides, “A fast recursive shortest spanning tree for image segmentation and edge detection,” IEEE Transactions on Image Processing, vol. 6, no. 2, FEB. 1997. [16] L. Vincent and P. Soille, “Watersheds in digital spaces: An efficient algorithm based on immersion simulations,” IEEE Transactions. Pattern Analysis and Machine Intelligence, vol. 13, no. 6, June 1991. [17] J. B. KRUSKAL, “On the shortest spanning subtree of a graph and the traveling salesman problem,” Proc. Am. Mach. Soc., vol. 7, pp.48-50, 1956.

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Fig. 13. The efficiency analysis of the RSST, FRSST, and MFRSST algorithms. 5. Conclusion In this paper, the concepts of multiresolution decomposition and flooding method in the watershed algorithms are applied to develop the multiresolution and flooding based RSST (MFRSST) image segmentation method that can speed up the segmentation process and have the same partition quality as the RSST. The experimental results show that the MFRSST algorithm can partition the image very efficiently and outperform the conventional image segmentation methods. In the future, we will apply the MFRSST algorithm to develop the video segmentation system for many new visual applications such as region-based video coding and object-based video retrieval. REFERENCES [1] MPEG, MPEG-4: Applications document, Tech. Rep. ISO/IEC/JTC1/SC29/WG11/w2724, MPEG, Seoul, Korea, Mar. 1999. [2] MPEG, MPEG-7: Applications document, Tech. Rep. ISO/IEC/JTC1/SC29/WG11/w2860, MPEG, Vancouver, Canada, July 1999. [3] R. M. HARALICK, and L.G. SHAPIRO, “Image segmentation technique,” Computer Vision, Graphics & Image Processing, vol. 29, pp.100-132, 1985. [4] R. OHLANDER, K. PRICE, and D. R. REDDY, “Picture segmentation using a recursive region splitting method,” Computer Graphics & Image Process., vol. 8, pp.313-333, 1978. [5] S. L. HOROWITZ, and T. PAVLIDS, “Picture segmentation by a tree traversal algorithm,” J. Assoc. Computer Machine, vol. 23, pp.368-388, 1976. [6] Patrice Willemin, Todd R. Reed, and Murat Kunt, “Image Sequence Coding by Split and Merge,” IEEE Transactions on Communications, vol. 39, no. 12, DEC. 1991. [7] O. J. Morris, M. J. Lee, and A. G Constantinides, "Graph theory for image analysis: an approach base on the shortest spanning tree," Proc. Inst. Elect. Eng., vol. 133, pp. 146-152, Apr. 1986. 16