Algorithm for Calculating the Similarity between Histograms for Texture Segmentation
DOI:
https://doi.org/10.15407/intechsys.2025.01.003Keywords:
Image processing, Similarity of histograms, Texture features, Texture segmentationAbstract
Introduction. An algorithm for calculating the similarity degree between multidimensional histograms is presented. The proposed algorithm was intended for texture segmentation of images using histograms as texture features. The need to develop such a special algorithm is justified by the fact that the methods for estimating the similarity/difference measure between multidimensional vectors described in the literature provide such measures that are not very suitable for solving the texture segmentation task. The main peculiarity of the proposed algorithm is that when calculating the similarity value, it considers not only the corresponding histogram components, but also takes into account their nearest neighboring components. Due to this, the algorithm more adequately evaluates the similarity of histograms. The proposed algorithm was implemented as a computer program as an integral part of the image segmentation model. The effectiveness of the histogram comparison algorithm was indirectly confirmed by the results of texture segmentation of the image segmentation model in experiments on processing various images, including natural landscapes.
Methods. The task of calculating the similarity between histograms is considered. A special algorithm is proposed because the analogical methods described in the literature are not very suitable for solving the texture segmentation task. The main peculiarity of the algorithm is that it takes into account as the corresponding histogram components as their
nearest neighboring components. Due to this, the algorithm more adequately evaluates the similarity of histograms. The algorithm was implemented as a computer program. The effectiveness of the algorithm is indirectly confirmed by the results of texture segmentation of the image segmentation model in experiments on processing various images, including natural landscapes.
Purpose. The goal of this work is to develop an efficient algorithm for assessing the similarity of histograms, such as brightness histograms and orientation histograms of the texture windows. The algorithm is based on the idea of taking into account not only the corresponding components of both histograms, but also the components of their immediate environment.
Results. The main advantage of the proposed algorithm, compared to popular methods of calculating similarity/difference between objects (vectors), is that the range of similarity between the compared histograms (from complete similarity to complete difference) is 100%, while popular methods can offer several times smaller ranges of similarity percentage.
Conclusion. The proposed algorithm provides a wide range of similarity between the compared histograms which is 100% (from complete similarity to complete difference), while popular methods can offer several times smaller ranges of similarity percentage. The algorithm was implemented as a computer program as a component of a model that solves the problem of segmenting a visual image into homogeneous texture areas. It is worth noting that the proposed histogram comparison algorithm calculates the similarity measure between histograms very quickly, since it uses only simple operations.
The effectiveness of the algorithm for texture segmentation of images into homogeneous texture areas is confirmed by the results in the experiments on natural image processing. The results obtained in the experiments demonstrate the effectiveness of the algorithm and show that the algorithm performs correct (from a human point of view) texture segmentation of a wide range of images. Thus, the effectiveness of the key operation of the segmentation algorithm, the histogram comparison algorithm, is indirectly confirmed.
References
Kussul E.M., Rachkovskij D.A., Baidyk T.N. On image texture recognition by associativeprojective neurocomputer. ANNIE’91 Conf., Intelligent Engineering Systems through Artificial Neural Networks, St. Louis, 1991, 453–458.
Kussul E.M., Baidyk T.N., Lukovitch V.V., Rachkovskij D.A. Adaptive neural network classifier with multifloat input coding. 6th Int. Conf. “Neuro-Ni mes 93”, Nimes, 1993, 209–216.
Kussul E.M, Baidyk T.N., Wunsch D.C. Neural Networks and Micro Mechanics. Springer, New York, 2010, 210 p. https://doi.org/10.1007/978-3-642-02535-8
Goltsev A. An assembly neural network for texture segmentation. Neural Networks, 1996, Vol. 9 (4), 643–653. https://doi.org/10.1016/0893-6080(95)00136-0
Goltsev A., Wunsch D.C. Inhibitory connections in the assembly neural network for texture segmentation. Neural Networks, 1998, Vol. 11 (5), 951–962. https://doi.org/10.1016/S0893-6080(98)00053-7
Goltsev A.D. Neural networks with the assembly organization. Naukova Dumka, Kyiv, 2005, 200 p. [In Russian]
Melendez J., Puig D., Garcia M.A. Multi-level pixel-based texture classificati on through efficient prototype selection via normalized cut. Pattern Recognition, 2010, Vol. 43 (12), 4113–4123. https://doi.org/10.1016/j.patcog.2010.06.014
Freixenet J., Munoz X., Raba D., Marti J., Cuff X. Yet another survey on image segmentation. 7th European Conf. on Computer Vision (ECCV), Copenhagen, 2002, 408–422. https://doi.org/10.1007/3-540-47977-5_27
Rousson M., Brox T., Deriche R. Active unsupervised texture segmentation on a diffusion based feature space. IEEE Conf. on Computer Vision and Pattern Recognition (CVPR’03): June 16 — June 22 2003, Madison, 2003, Vol. 2, 699–704. https://doi.org/10.1109/CVPR.2003.1211535
Clausi D.A., Deng H. Design-based texture feature fusion using Gabor filters and cooccurrence probabilities. IEEE Transactions on Image Processing, 2005, Vol. 14 (7), 925–936. https://doi.org/10.1109/TIP.2005.849319
Wei H, Bartels M. Unsupervised segmentation using Gabor wavelets and statistical features in LIDAR data analysis. 18th Int. Conf. on Pattern Recognition (ICPR’06): August 20 –August 24 2006, Hong Kong, 2006, Vol. 1, 667–670. https://doi.org/10.1109/ICPR.2006.1145
Yang A.Y., Wright J., Ma Y., Sastry S.S. Unsupervised segmentation of natural images via lossy data compression. Computer Vision and Image Understanding, 2008, Vol. 110 (2), 212–225. https://doi.org/10.1016/j.cviu.2007.07.005
Sebe N., Lew M.S. Texture features for content-based retrieval. In: M.S. Lew (Ed.), Principles of Visual Information Retrieval. Advances in Computer Vision and Pattern Recognition: Springer, 2001, 51–85. https://doi.org/10.1007/978-1-4471-3702-3_3
Hafner J.L., Sawhney H.S., Equitz W., Flickner M., Niblack W. Efficient color histogram indexing for quadratic form distance functions. IEEE Trans. PAMI, 1995, Vol. 17 (7), 729–736. https://doi.org/10.1109/34.391417
Goltsev A., Gritsenko V. Algorithm of sequential finding the characteristic features of homogeneous texture regions for the problem of image segmentation. Cybernetics and Computer Engineering, 2013, Vol. 173, 25–34. [In Russian]
Goltsev A., Gritsenko V., Kussul E., Baidyk T. Finding the texture features characterizing the most homogeneous texture segment in the image. Lecture Notes in Computer Science, Springer, 2015, Vol. 9094, Part I, 287–300. https://doi.org/10.1007/978-3-319-19258-1_25
Goltsev A., Gritsenko V., Husek D. Extraction of homogeneous fine-grained texture segments in visual images. Neural Network World, 2017, Vol. 27, 447–477. https://doi.org/10.14311/NNW.2017.27.024
Goltsev A., Gritsenko I.V., Husek D. Segmentation of visual images by sequential extracting homogeneous texture areas. Journal of Signal and Information Processing, 2020, Vol. 11, 75–102. https://doi.org/10.4236/jsip.2020.114005
Fan J.P., Zeng G.H., Body M., Hacid M.S. Seeded region growing: an extensive and comparative study. Pattern Recognition Letters, 2005, Vol. 26, 1139–1156. https://doi.org/10.1016/j.patrec.2004.10.010
Kamdi S., Krishna, R.K. Image segmentation and region growing algorithm. International Journal of Computer Technology and Electronics Engineering, 2012, Vol. 2, 103–107.
Peng Q. An image segmentation algorithm research based on region growth. Journal of Software Engineering, 2015, Vol. 9, 673–679. https://doi.org/10.3923/jse.2015.673.679
Cleary J.G. Analysis of an algorithm for finding nearest neighbors in Euclidean space. ACM Trans. on Math. Softw., 1979, Vol. 5 (2), 183–192. https://doi.org/10.1145/355826.355832
Rubner Y., Tomasi C., Guibas L.J. The earth mover’s distance as a metric for image retrieval. Int. J. Comput. Vision., 2000, Vol. 40 (2), 99–121.
Deza M., Deza E. Encyclopedia of Distances. Berlin, Heidelberg, Springer, 2014, 733 p. https://doi.org/10.1007/978-3-662-44342-2
Rachkovskij D.A. Introduction to Fast Similarity Search. Kyiv, Interservice, 2019, 294 p. [In Russian]
Gricenko V.I., Rachkovskij D.A. Methods of Vector Representation of Objects for Fast Similarity Assessment. Naukova Dumka, Kyiv, 2019, 312 p. [In Russian]
Rachkovskij D.A. Codevectors: Sparse Binary Distributed Representations of Numerical Data. Interservice, Kyiv, 2019, 200 p. [In Russian]
Rachkovskij D.A. Representation of spatial objects by shift-equivariant similarity-preserving hypervectors. Neural Computing and Applications, 2022, Vol. 34 (24), 22387–22403. https://doi.org/10.1007/s00521-022-07619-1
Goltsev A., Holtsev O. An algorithm for measuring the similarity of histograms for texture image segmentation. WSEAS Transactions on Information Science and Applications, 2024, Vol. 21, 107–115. https://doi.org/10.37394/23209.2024.21.11
Jahne B., Scharr H., Korkel S. Principles of Filter Design. In: B. Jahne, H. Scharr, S. Korkel, B. Jahne, H. Haussecker, P. Geissler (Eds.), Handbook of Computer Vision and Applications, Vol. 2: Signal Processing and Pattern Recognition, Academic Press, San Diego, 2000, 125–152.
Ruiz-Del-Solar J. Neural-based architectures for the segmentation of textures. Proceedings of the 15th International Conference on Pattern Recognition, Barcelona, Spain, 2000, Vol. 3, 1080–1083. https://doi.org/10.1109/ICPR.2000.903733
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Information Technologies and Systems
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
The paper is an Open Access under the CC BY-NC-ND 4.0 license - Attribution-NonCommercial-NoDerivatives 4.0 International.
