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Title
Abstract
Figures
Introduction
Comparisons with the Normalized Cut Method [2]
Conclusions
References
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Computer Science
Computer Graphics

A Graph-Based Approach for Image Segmentation

Profile image of Thang LeThang LeProfile image of Casimir A KulikowskiCasimir A Kulikowski

2008, Lecture Notes in Computer Science

https://doi.org/10.1007/978-3-540-89639-5_27
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Abstract

We present a novel graph-based approach to image segmentation. The objective is to partition images such that nearby pixels with similar colors or grayscale intensities belong to the same segment. A graph representing an image is derived from the similarity between the pixels and partitioned by a computationally efficient graph clustering method, which identifies representative nodes for each cluster and then expands them to obtain complete clusters of the graph. Experiments with synthetic and natural images are presented. A comparison with the well known graph clustering method of normalized cuts shows that our approach is faster and produces segmentations that are in better agreement with visual assessment on original images.

Figures (6)
Fig. 1. (a) is a grayscale image. (b), (c), and (d) show core pixels when B = 3, 5 = 90%, 96%, and 99%, respectively. The segmentation result (e) is the same for any settings Since the number of nodes is finite, there are a limited number of possible settings for B and 6. Parameter B is an integer with the role of eliminating noisy pixels in the set of pixels of high decreasing rates of D values. Usually we set B value to 3 or 4. The main parameter of the clustering method is 6, changing 6 can result in increas- ing or decreasing the number of segments. In (b), (c), and (d) of Fig. 1, we illustrate the effect of 5 on the set of core pixels. The cores of segments shrink if we increase 6, and they are enlarged if 5 is decreased. In general, we set 5 to a value greater than 90% because for noisy images, setting 5 too low may produce core pixels which are not very reliable. For images that contain a mixture of segments with different sizes, by increasing or decreasing 5, we can obtain a coarse or fine-grained segmentation. In Fig. 2, (a) shows a grayscale image, (b), (c), and (d) show segmentation results of (a) with different values of 6. Higher 6 produces coarser segmentation while lower 5 yields finer segmentation. This demonstrates the point that core pixels are arranged in an order such that the pixels having higher rates of decrease in their D values belong to the cores of stronger segments.
Fig. 1. (a) is a grayscale image. (b), (c), and (d) show core pixels when B = 3, 5 = 90%, 96%, and 99%, respectively. The segmentation result (e) is the same for any settings Since the number of nodes is finite, there are a limited number of possible settings for B and 6. Parameter B is an integer with the role of eliminating noisy pixels in the set of pixels of high decreasing rates of D values. Usually we set B value to 3 or 4. The main parameter of the clustering method is 6, changing 6 can result in increas- ing or decreasing the number of segments. In (b), (c), and (d) of Fig. 1, we illustrate the effect of 5 on the set of core pixels. The cores of segments shrink if we increase 6, and they are enlarged if 5 is decreased. In general, we set 5 to a value greater than 90% because for noisy images, setting 5 too low may produce core pixels which are not very reliable. For images that contain a mixture of segments with different sizes, by increasing or decreasing 5, we can obtain a coarse or fine-grained segmentation. In Fig. 2, (a) shows a grayscale image, (b), (c), and (d) show segmentation results of (a) with different values of 6. Higher 6 produces coarser segmentation while lower 5 yields finer segmentation. This demonstrates the point that core pixels are arranged in an order such that the pixels having higher rates of decrease in their D values belong to the cores of stronger segments.
Fig. 3, (b) shows the segmentation of the image in (a) by a two-way normalized cut The cut partitions the image into two segments similar in size. It fails to find the central oval as one segment because of the disparity between the number of pixel: inside and outside the oval. In Fig. 4, (g), (h), (i), G), (x), and (1) show the segmenta- tions for image (a) by normalized cuts with k = 2, 3, 4, 5, 6 and 7, respectively Clearly, for any k, the image is partitioned into segments of roughly similar sizes. Moreover, varying parameter k dramatically changes the segmentation result.
Fig. 3, (b) shows the segmentation of the image in (a) by a two-way normalized cut The cut partitions the image into two segments similar in size. It fails to find the central oval as one segment because of the disparity between the number of pixel: inside and outside the oval. In Fig. 4, (g), (h), (i), G), (x), and (1) show the segmenta- tions for image (a) by normalized cuts with k = 2, 3, 4, 5, 6 and 7, respectively Clearly, for any k, the image is partitioned into segments of roughly similar sizes. Moreover, varying parameter k dramatically changes the segmentation result.
Fig. 4. Effects of parameters on segmentation results. (a) is a grayscale image from the Berke- ley dataset. (b), (c), (d), (e), and (f) show segmentations by our method with 6 = 99%, 97%, 95%, 93%, and 90%, respectively. (g), (h), (i), (j), (k), and (1) show segmentations of the normalized cut method on the same proximity graph with k = 2, 3, 4, 5, 6 and 7, respectively Based on the same proximity graphs, our algorithm produces better results. In Fig. 4, (b), (c), (d), (e), and (f) are our segmentations for image (a) with B = 3 and 6 = 99%, 97%, 95%, 93%, and 90%, respectively. Note that lowering 6 yields finer seg- mentation and the results are very consistent in their sensitivity to perturbations of the different parameter settings. In terms of speed, our implementation has a total time complexity of O(|E| + |V| log |V|). Experiments show that it runs much faster than the normalized cut method on the same proximity graphs. In Tab. 1, we show the execution times on different proximity graphs of the two methods using a PC with a CPU of Core 2 Duo 2.4GHz and 2GB RAM. It can be seen that the running time of the coring method is roughly linear to the number of edges of the proximity graphs. The running times of the normalized cut are the average time for partition- ing the graph into 2, 3, and 4 segments. For the cases that the graphs contain more than 105*10° nodes and 18*10° edges, the normalized cut method fails to execute because of an ‘Out of memory’ error. In addition, an advantage of the coring method is that we can change B or 6 and quickly obtain a new result by re-executing fast steps 3, 4 and 5 of the method. In contrast, for the normalized cut method, changing k will result in having to re-compute the cut from scratch.
Fig. 4. Effects of parameters on segmentation results. (a) is a grayscale image from the Berke- ley dataset. (b), (c), (d), (e), and (f) show segmentations by our method with 6 = 99%, 97%, 95%, 93%, and 90%, respectively. (g), (h), (i), (j), (k), and (1) show segmentations of the normalized cut method on the same proximity graph with k = 2, 3, 4, 5, 6 and 7, respectively Based on the same proximity graphs, our algorithm produces better results. In Fig. 4, (b), (c), (d), (e), and (f) are our segmentations for image (a) with B = 3 and 6 = 99%, 97%, 95%, 93%, and 90%, respectively. Note that lowering 6 yields finer seg- mentation and the results are very consistent in their sensitivity to perturbations of the different parameter settings. In terms of speed, our implementation has a total time complexity of O(|E| + |V| log |V|). Experiments show that it runs much faster than the normalized cut method on the same proximity graphs. In Tab. 1, we show the execution times on different proximity graphs of the two methods using a PC with a CPU of Core 2 Duo 2.4GHz and 2GB RAM. It can be seen that the running time of the coring method is roughly linear to the number of edges of the proximity graphs. The running times of the normalized cut are the average time for partition- ing the graph into 2, 3, and 4 segments. For the cases that the graphs contain more than 105*10° nodes and 18*10° edges, the normalized cut method fails to execute because of an ‘Out of memory’ error. In addition, an advantage of the coring method is that we can change B or 6 and quickly obtain a new result by re-executing fast steps 3, 4 and 5 of the method. In contrast, for the normalized cut method, changing k will result in having to re-compute the cut from scratch.
Table 1. Execution times of the normalized cut and coring methods for clustering graphs
Table 1. Execution times of the normalized cut and coring methods for clustering graphs
Fig. 5. Segmentations and derived boundaries on images from the Berkeley dataset. The same parameter settings B = 3, 6 = 97% are used for all the images (e), the segmentations of these noisy images shown in (d) and (f) remain stable. In addition to speed and robustness, an advantage is that parameters can be adjusted to yield a range of results from a coarse to fine-grained segmentation. The current weight functions (1) and (2) do not take into account texture information. It is possi- ble to apply the method to texture segmentation by additionally incorporating statis- tical texture information around each image pixel into the weight functions. This should help refine the segmentation results for images that have texture.
Fig. 5. Segmentations and derived boundaries on images from the Berkeley dataset. The same parameter settings B = 3, 6 = 97% are used for all the images (e), the segmentations of these noisy images shown in (d) and (f) remain stable. In addition to speed and robustness, an advantage is that parameters can be adjusted to yield a range of results from a coarse to fine-grained segmentation. The current weight functions (1) and (2) do not take into account texture information. It is possi- ble to apply the method to texture segmentation by additionally incorporating statis- tical texture information around each image pixel into the weight functions. This should help refine the segmentation results for images that have texture.

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References (8)

  1. Le, T., Kulikowski, C., Muchnik, I.: Coring method for clustering a graph. Proceedings of the 19th International Conference on Pattern Recognition (2008)
  2. Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Trans. on Pattern Analy- sis and Machine Intelligence (2000) 888-905
  3. Charikar, M.: Greedy approximation algorithms for finding dense components in a graph. Volume 1913 of Lecture Notes in Computer Science, Springer-Verlag (2000) 84-95
  4. Berkeley segmentation dataset, http://www.cs.berkeley.edu/projects/vision/bsds/
  5. Martin, D., Fowlkes, C., Tal, D., Malik, J.: A database of human segmented natural im- ages and its application to evaluating segmentation algorithms and measuring ecological statistics. Proc. of the 8th International Conference on Computer Vision (2001) 416-423
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  8. Fig. 5. Segmentations and derived boundaries on images from the Berkeley dataset. The same parameter settings b = 3, d = 97% are used for all the images

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