Application of the Fundamental Solution Method to object recognition in the pictures


  • Tomasz Klekiel


Recognition of objects in pictures and movies requires the use of techniques, such as filtering, segmentation and classification. Image filtering is required to remove all artifacts that hinder the unequivocal identification and sharpen interesting objects. Segmentation refers to finding areas of images respected to individual objects. For the selected areas corresponding to objects in the selected picture, the classification of objects finally gives information about the type of object which orientation is made. This paper presents a method for the classification of objects from drawings as a bitmap using the method of fundamental solutions (MFS). The MFS was tested on the selected bitmap depicting simple geometric shapes. The correlations between errors occurring on the boundary for particular shapes are used for the selection of geometric shape figures. Due to this correlation, it is possible to recognize the shape of the image appearing on the drawing by an analysis consisting of the comparison of recognized points describing the shape of contour to a database containing solutions of boundary value problems for the selected shape. In one way, the comparison of the pattern can determine which shape from database it is most similar to in terms of contour. This article appear that this approach is very simple and clearly. In result, this method can be used to recognition of the objects in the systems of real-time processing.


Akgül, C. B., Sankur, B., Yemez, Y., Schmitt, F. (2006, September). A framework for histograminduced 3D descriptors. In Signal Processing Conference, 2006 14th European (pp. 1-5). IEEE

Anvaripour, M., Ebrahimnezhad, H. (2015). Accurate object detection using local shape descriptors. Pattern Analysis and Applications, 18(2), 277-295

Bertalmio, M., Sapiro, G., Caselles, V., Ballester, C. (2000, July). Image inpainting. In Proceedings of the 27th annual conference on Computer graphics and interactive techniques (pp. 417-424). ACM Press/Addison-Wesley Publishing Co.

Chanda, B., Kundu, M. K., Padmaja, Y. V. (1998). A multi-scale morphologic edge detector. Pattern Recognition, 31(10), 1469-1478

Deng, H., Chan, K. L., Liu, J. (2003). The Poisson equation for image texture modelling. Pattern recognition letters, 24(9-10), 1571-1582

Fairweather, G., Karageorghis, A. (1998). The method of fundamental solutions for elliptic boundary value problems. Advances in Computational Mathematics, 9(1-2), 69

Gokaramaiah, T., Viswanath, P., Reddy, B. E. (2011). A shape representation scheme for 2D images using distributions of centroid contour distances and their local variations. In Computational Intelligence and Information Technology1 (pp. 489-493). Springer, Berlin, Heidelberg

Gorelick, L., Basri, R. (2009). Shape based detection and top-down delineation using image segments. International journal of computer vision, 83(3), 211-

Gorzelanczyk, P., Kołodziej, J. A. (2008). Some remarks concerning the shape of the source contour with application of the method of fundamental solutions to elastic torsion of prismatic rods. ngineering Analysis with Boundary Elements, 32(1), 64-75

Grady, L. (2008, October). A lattice-preserving multigrid method for solving the inhomogeneous poisson equations used in image analysis. In European Conference on Computer Vision (pp. 252-264). Springer, Berlin, Heidelberg

Hornegger, J., Niemann, H., Risack, R. (2000). Appearance-based object recognition using optimal feature transforms. Pattern Recognition, 33(2), 209-224

Hui, L., Pei-jun, D.U., Chang-sheng, Z.H.A.O., Ning, S.H.U. (2004). Edge detection method of remote sensing images based on mathematical morphology of multi-structure elements. Chinese Geographical Science, 14(3), 263

Kang, C. C., Wang, W. J. (2007). A novel edge detection method based on the maximizing objective function. Pattern Recognition, 40(2), 609-618

Kang, D. J., Kweon, I. S. (2001). An edge-based algorithm for discontinuity adaptive color image smoothing. Pattern Recognition, 34(2), 333-342

Mahoor, M. H., Abdel-Mottaleb, M. (2009). Face recognition based on 3D ridge images obtained from range data. Pattern Recognition, 42(3), 445-451

Mainberger, M., Bruhn, A., Weickert, J., Forchhammer, S. (2011). Edge-based compression of cartoonlike images with homogeneous diffusion. Pattern Recognition, 44(9), 1859-1873

Morel, J.M., Petro, A. B., Sbert, C. (2012). Fourier implementation of Poisson image editing. Pattern Recognition Letters, 33(3), 342-348

Nayak, N. M., Zhu, Y., Roy-Chowdhury, A. K. (2013). Vector field analysis for multi-object behavior modeling. Image and Vision Computing, 31(6-7), 460-472

Pan, X., You, Q., Liu, Z., Chen, Q. H. (2011). 3D shape retrieval by Poisson histogram. Pattern Recognition Letters, 32(6), 787-794

Shafiq, M. S., Tümer, S. T., Güler, H. C. (2001). Marker detection and trajectory generation algorithms for a multicamera based gait analysis system.

Mechatronics, 11(4), 409-437

Shen, J., Jin, X., Zhou, C., Wang, C. C. (2007). Gradient based image completion by solving the Poisson equation. Computers & Graphics, 31(1), 119-126

Smyrlis, Y. S., Karageorghis, A. (2001, September). Rotation of the Sources and Normalization of

the Fundamental Solutions in the MFS. In International Conference on Parallel Processing and Applied Mathematics (pp. 762-769). Springer, Berlin, Heidelberg

Sun, J., Yuan, L., Jia, J., Shum, H. Y. (2005, July). Image completion with structure propagation. In ACM Transactions on Graphics (ToG) (Vol. 24, No. 3, pp. 861-868). ACM

Toivanen, P. J., Ansamäki, J., Parkkinen, J. P. S., Mielikäinen, J. (2003). Edge detection in multispectral images using the self-organizing map. Pattern Recognition Letters, 24(16), 2987-2994

Tsai, P., Chang, C. C., Hu, Y. C. (2002). An adaptive two-stage edge detection scheme for digital color images. Real-Time Imaging, 8(4), 329-343

Yu, Y. H., Chang, C. C. (2006). A new edge detection approach based on image context nalysis. Image and Vision Computing, 24(10), 1090-1102