Abstract
We present a novel approach to measuring distances between objects in images, suitable for information-rich object representations which simultaneously capture several properties in each image pixel. Multiple spatial fuzzy sets on the image domain, unified in a vector-valued fuzzy set, are used to model such representations. Distance between such sets is based on a novel point-to-set distance suitable for vector-valued fuzzy representations. The proposed set distance may be applied in, e.g., template matching and object classification, with an advantage that a number of object features are simultaneously considered. The distance measure is of linear time complexity w.r.t. the number of pixels in the image. We evaluate the performance of the proposed measure in template matching in presence of noise, as well as in object detection and classification in low resolution Transmission Electron Microscopy images.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bloch, I.: On fuzzy distances and their use in image processing under imprecision. Pattern Recogn. 32, 1873–1895 (1999)
Bloch, I., Maître, H.: Fuzzy mathematical morphologies: a comparative study. Pattern Recogn. 28(9), 1341–1387 (1995)
Borgefors, G.: Distance transformations in digital images. Comput. Vis. Graph. Image Process. 34, 344–371 (1986)
Dražić, S., Sladoje, N., Lindblad, J.: Accurate estimation of feret’s diameter of a shape from pixel coverage digitization. Pattern Recogn. Lett. 80, 37–45 (2016)
Eiter, T., Mannila, H.: Distance measures for point sets and their computation. Acta Informatica 34(2), 103–133 (1997)
Lindblad, J., Ćurić, V., Sladoje, N.: On set distances and their application to image registration. In: Proceedings of the IEEE International Symposium Image Signal Processing and Analysis (ISPA), pp. 449–454 (2009)
Lindblad, J., Sladoje, N.: Linear time distances between fuzzy sets with applications to pattern matching and classification. IEEE Trans. Image Process. 23(1), 126–136 (2014)
Rosenfeld, A.: Fuzzy digital topology. Inf. Control 40, 76–87 (1979)
Rosenfeld, A.: The fuzzy geometry of image subsets. Pattern Recogn. Lett. 2, 311–317 (1984)
Saha, P.K., Udupa, J.K.: Relative fuzzy connectedness among multiple objects: theory, algorithms, and applications in image segmentation. Comput. Vis. Image Underst. 82(1), 42–56 (2001)
Saha, P.K., Wehrli, F.W., Gomberg, B.R.: Fuzzy distance transform: theory, algorithms, and applications. Comput. Vis. Image Underst. 86, 171–190 (2002)
Sladoje, N., Lindblad, J.: Estimation of moments of digitized objects with fuzzy borders. In: Roli, F., Vitulano, S. (eds.) ICIAP 2005. LNCS, vol. 3617, pp. 188–195. Springer, Heidelberg (2005). doi:10.1007/11553595_23
Sladoje, N., Lindblad, J.: High precision boundary length estimation by utilizing gray-level information. IEEE Trans. Pattern Anal. Mach. Intell. 31(2), 357–363 (2009)
Sladoje, N., Nyström, I., Saha, P.K.: Measurements of digitized objects with fuzzy borders in 2D and 3D. Image Vis. Comput. 23, 123–132 (2005)
Suveer, A., Sladoje, N., Lindblad, J., Dragomir, A., Sintorn, I.-M.: Automated detection of cilia in low magnification transmission electron microscopy images using template matching. In: Proceedings of IEEE International Symposium on Biomedical Imaging (ISBI), pp. 386–390 (2016)
Zadeh, L.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
Öfverstedt, J., Sladoje, N., Lindblad, J.: Distance between vector-valued fuzzy sets based on intersection decomposition with applications in object detection. In: Angulo, J., et al. (eds.) ISMM 2017. LNCS, vol. 10225, pp. 395–407. Springer, Cham (2017). doi:10.1007/978-3-319-57240-6_32
Acknowledgment
The authors acknowledge Amit Suveer, Anca Dragomir, and Ida-Maria Sintorn for acquired and annotated TEM images of Cilia. Ministry of Science of the Republic of Serbia is acknowledged for support through the Projects ON 174008 and III 44006 of MI-SANU. N. Sladoje is also supported by Swedish Governmental Agency for Innovation Systems (VINNOVA).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Sladoje, N., Lindblad, J. (2017). Distance Between Vector-Valued Representations of Objects in Images with Application in Object Detection and Classification. In: Brimkov, V., Barneva, R. (eds) Combinatorial Image Analysis. IWCIA 2017. Lecture Notes in Computer Science(), vol 10256. Springer, Cham. https://doi.org/10.1007/978-3-319-59108-7_19
Download citation
DOI: https://doi.org/10.1007/978-3-319-59108-7_19
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-59107-0
Online ISBN: 978-3-319-59108-7
eBook Packages: Computer ScienceComputer Science (R0)