SMS - The supervised color image segmentation method
Image segmentation is one of the most important tools in computer vision and image understanding. Its use can be extended to different application areas, such as medical imaging, robot navigation, aerospace industry, security control and many others. Among the most popular image segmentation concepts are the variational models, more specifically the Mumford-Shah model [MumfordShah89]. This model uses low-level vision to segment a domain of an image I into segments. The basic idea is merging the regions on which the signal I is homogeneous and is delimited by a system of regular discontinuities K, in order to make visible the objects on the scene.
In this work a novel region-merging image segmentation approach is presented. This approach is based on a two-step procedure: a distance metric is learned from some features on the image, then a piecewise approximation function for the Mumford-Shah model is optimized by this metric. The global optimum of the approximation function is inductively achieved under high polynomial terms of the Mahalanobis distance [Grudic06], extracting the nonlinear features of the pattern distributions into topological maps. The penalizer terms of the Mumford-Shah equation are based on new similarity criteria, computed from the topological maps and the class label information.
Figure 1 - merging evolution #1
Figure 2 - merging evolution #2
Besides providing the image results obtained with our method, we aim to
objectively compare its quality with other state-of-art algorithms. For this
goal, we have selected four distance measures developed for image segmentation
evaluation. These measures -- Rand [Rand71], Fowlkes-Mallows [Fowlkes83], Jacard
[Jacard02] and Dongen [Dongen00] -- result in float values are in the [0,1] interval,
where the closest to 0 the better the segmentation is.
All these evaluation techniques are ground-truth based evaluation methods. So, every image set selected has to have a group of ground-truth images available for the evaluation of the experiments. For this reason, we selected our test sets from the Berkeley Segmentation Dataset and Benchmark
For this purpose, we selected 60 images from the Berkeley Image Dataset, where the following experiments were performed:
1- A merging evolution experiment in order to verify the influence of this approximation function to the Mumford-Shah model;
2- A direct comparison against the conventional Mumford-Shah model using the vector norm as discrimination function;
3- A comparison among different image segmentation approaches using the aforementioned evaluation indexes. In this experiment we used the methods:
* (S-MS) - The proposed supervised image segmentation approach (Computer Vision and Image Understanding - 2011).
* (MS) - The conventional Mumford-Shah Model [Megawave10].
* (CSC) - Color Structure Code [RehrmannPriese98].
* (EDISON) - the edge detection and image segmentation system [ComaniciuMeer02].
* (WS) - the classical Watershed algorithm [VincentSoille91].
* (JSEG) - the unsupervised color image segmentation method [DengManjunath01].
* (RHSEG) - a hierarquical image segmentation [Tilton06].
* (GNM and GNM2) - two versions of a Gradient Network Method previously published. This method is a post-processing segmentation, which can be combined with other methods. [Wangenheim09].
The results we obtained show a better discrimination of object boundaries and the location of regions when compared against the conventional Mumford-Shah and the state-of-the-art algorithms, as presented in our results page.
You also can download the evaluation tables, objective evaluation sources and the segmentation results we obtained.
Figure 3 - Comparison among other image segmentation methods: (a) original image, (b) ground-truth, (c) S-MS, (d) MS+gnm2, (e) CSC+gnm2,
(f) MS, (g) MS+gnm, (h) CSC+gnm,
(i) Edison, (j) CSC, (k) JSEG, (l) WS and in (m) RHSEG
[MumfordShah89] D. Mumford, J. Shah, Optimal approximations by piecewise smooth functions and associated variational problems, Commun. Pure Appl. Math. 42 (1989) 577-684.
[Grudic06] G. Grudic. J. Mulligan, Outdoor path labeling using polynomial Mahalanobis distance, Robotics: Sci- ence and Systems II Conference. 2006.
[Rand71] W. M. Rand, Objective criteria for the evaluation of clustering methods, Journal of American Statistical Association 66 (1971) 846-850.
[Fowlkes83] E. B. Fowlkes, C. L. Mallows, A method for comparing two hierarchical clusterings, Journal of the American Statistical Association 78 (383) (1983) 553-569. URL http://www.jstor.org/stable/2288117
[Jacard02] A. Ben-Hur, A. Elissee, I. Guyon, A stability based method for discovering structure in clustered data, in: Pacific Symposium on Biocomputing, 2002, pp. 6-17.
[Dongen00] S. Dongen, Performance criteria for graph clustering and markov cluster experiments, Tech. rep., Am- sterdam, The Netherlands, The Netherlands (2000).
[Martin01] Martin, D., Fowlkes, C., Tal, D., Malik, J. A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In: Proc. 8th Int'l Conf. Computer Vision. vol. 2; 2001. p. 416-423.
[Rehrmann98] Rehrmann, V. and Priese, L. Fast and Robust Segmentation of Natural Color Scenes. ACCV (1), 1998: 598-606.
[Wangenheim09] Wangenheim, A. V., Bertoldi, R. F., Abdala, D. D., Sobieranski, A., Coser, L., Jiang, X., Richter, M. M., Priese, L., and Schmitt, F. 2009. Color image segmentation using an enhanced Gradient Network Method. Pattern Recogn. Lett. 30, 15 (Nov. 2009), 1404-1412. DOI= http://dx.doi.org/10.1016/j.patrec.2009.07.005
[Megawave10] http://megawave.cmla.ens-cachan.fr/. Access in: 17 may 2010.
[ComaniciuMeer02] D. Comaniciu, P. Meer. Mean Shift: A Robust Approach Toward Feature Space Analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence; 2002; 24 (5); 603-619.
[VincentSoille91] L. Vincent and P. Soille. Watersheds in digital spaces: An efficient algorithm based on immersion simulations. In Transactions on Pattern Analysis and Machine Inteligence, volume 9, pages 735-744. IEEE, 1991.
[DengManjunath01] Deng, Y., Manjunath B.S. Unsupervised segmentation of color-texture regions in images and video. IEEE Transactions on Pattern Analysis and Machine Intelligence; 2001; 23(8):800-810.
[Tilton06] Tilton, J.C. D-dimensional formulation and implementation of recursive hierarchical segmentation, Disclosure of Invention and New Technology: NASA Case No. GSC 15199-1, May 26, 2006.