This paper addresses the problem of simultaneous estimation of different linear deformations, resulting in a global non-linear transformation, between an original object and its broken fragments. A general framework is proposed without using correspondences, where the solution of a polynomial system of equations directly provides the parameters of the alignment. We quantitatively evaluate the proposed algorithm on a large synthetic dataset containing 2D and 3D images, where linear (rigid-body and affine) transformations are considered. We also conduct an exhaustive analysis of the robustness against segmentation errors and the numerical stability of the proposed method. Moreover, we present experiments on 2D real images as well as on volumetric medical images.

%B Pattern Analysis and Machine Intelligence, IEEE Transactions on %I IEEE %V pp %P 1 %8 June 2015 %G eng %N 99 %9 Journal article %R 10.1109/TPAMI.2015.2450726 %0 Journal Article %J IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE %D 2012 %T Nonlinear Shape Registration without Correspondences %A Csaba Domokos %A Jozsef Nemeth %A Zoltan Kato %X

In this paper, we propose a novel framework to estimate the parameters of a diffeomorphism that aligns a known shape and its distorted observation. Classical registration methods first establish correspondences between the shapes and then compute the transformation parameters from these landmarks. Herein, we trace back the problem to the solution of a system of nonlinear equations which directly gives the parameters of the aligning transformation. The proposed method provides a generic framework to recover any diffeomorphic deformation without established correspondences. It is easy to implement, not sensitive to the strength of the deformation, and robust against segmentation errors. The method has been applied to several commonly used transformation models. The performance of the proposed framework has been demonstrated on large synthetic data sets as well as in the context of various applications.

%B IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE %I IEEE %V 34 %P 943 - 958 %8 2012 %@ 0162-8828 %G eng %U http://www.inf.u-szeged.hu/~kato/papers/TPAMI-2010-03-0146.R2_Kato.pdf %N 5 %9 Journal article %M 12617610 %! IEEE T PATTERN ANAL %R 10.1109/TPAMI.2011.200 %0 Conference Paper %B International Conference on Pattern Recognition (ICPR) %D 2012 %T Simultaneous Affine Registration of Multiple Shapes %A Csaba Domokos %A Zoltan Kato %E Jan-Olof Eklundh %E Yuichi Ohta %E Steven Tanimoto %X

The problem of simultaneously estimating affine deformations between multiple objects occur in many applications. Herein, a direct method is proposed which provides the result as a solution of a linear system of equations without establishing correspondences between the objects. The key idea is to construct enough linearly independent equations using covariant functions, and then finding the solution simultaneously for all affine transformations. Quantitative evaluation confirms the performance of the method.

%B International Conference on Pattern Recognition (ICPR) %I IEEE %C Tsukuba, Japan %P 9 - 12 %8 Nov 2012 %@ 978-1-4673-2216-4 %G eng %9 Conference paper %M 13324478 %0 Conference Paper %B A Képfeldolgozók és Alakfelismerők Társaságának konferenciája - KÉPAF 2011 %D 2011 %T Affin Puzzle: Deformált objektumdarabok helyreállítása megfeleltetések nélkül %A Csaba Domokos %A Zoltan Kato %E Zoltan Kato %E Kálmán Palágyi %B A Képfeldolgozók és Alakfelismerők Társaságának konferenciája - KÉPAF 2011 %I NJSZT %C Szeged %P 206 - 220 %8 Jan 2011 %G eng %U http://www.inf.u-szeged.hu/kepaf2011/pdfs/S05_03.pdf %9 Conference paper %0 Generic %D 2011 %T Nonlinear Shape Registration without Correspondences %A Zoltán Kornél Török %A Csaba Domokos %A Jozsef Nemeth %A Zoltan Kato %X

This is the sample implementation and benchmark dataset of the nonlinear registration of 2D shapes described in the following papers: Csaba Domokos, Jozsef Nemeth, and Zoltan Kato. Nonlinear Shape Registration without Correspondences. IEEE Transactions on Pattern Analysis and Machine Intelligence, 34(5):943--958, May 2012. Note that the current demo program implements only planar homography deformations. Other deformations can be easily implemented based on the demo code.

%8 2011/// %G eng %U http://www.inf.u-szeged.hu/~kato/software/planarhombinregdemo.html %9 Software %0 Thesis %D 2011 %T Parametric Estimation of Affine Deformations without Correspondences %A Csaba Domokos %I University of Szeged %C Szeged, Hungary %G eng %9 PhD Thesis %0 Book Section %B European Conference on Computer Vision (ECCV) %D 2010 %T Affine puzzle: Realigning deformed object fragments without correspondences %A Csaba Domokos %A Zoltan Kato %E Kostas Daniilidis %E Petros Maragos %E Nikos Paragios %XThis paper is addressing the problem of realigning broken objects without correspondences. We consider linear transformations between the object fragments and present the method through 2D and 3D affine transformations. The basic idea is to construct and solve a polynomial system of equations which provides the unknown parameters of the alignment. We have quantitatively evaluated the proposed algorithm on a large synthetic dataset containing 2D and 3D images. The results show that the method performs well and robust against segmentation errors. We also present experiments on 2D real images as well as on volumetric medical images applied to surgical planning. © 2010 Springer-Verlag.

%B European Conference on Computer Vision (ECCV) %S Lecture Notes in Computer Science %I Springer %C Crete, Greece %P 777 - 790 %8 Sep 2010 %@ 978-3-642-15551-2 %G eng %9 Conference paper %! LNCS %R 10.1007/978-3-642-15552-9_56 %0 Journal Article %J PATTERN RECOGNITION %D 2010 %T Parametric estimation of affine deformations of planar shapes %A Csaba Domokos %A Zoltan Kato %B PATTERN RECOGNITION %V 43 %P 569 - 578 %8 March 2010 %@ 0031-3203 %G eng %N 3 %9 Journal article %! PATTERN RECOGN %R 10.1016/j.patcog.2009.08.013 %0 Book Section %B 16th IEEE International Conference on Image Processing (ICIP), 2009 %D 2009 %T Affine alignment of compound objects: A direct approach %A Csaba Domokos %A Zoltan Kato %XA direct approach for parametric estimation of 2D affine deformations between compound shapes is proposed. It provides the result as a least-square solution of a linear system of equations. The basic idea is to fit Gaussian densities over the objects yielding covariant functions, which preserves the effect of the unknown transformation. Based on these functions, linear equations are constructed by integrating nonlinear functions over appropriate domains. The main advantages are: linear complexity, easy implementation, works without any time consuming optimization or established correspondences. Comparative tests show that it outperforms state-of-the-art methods both in terms of precision, robustness and complexity. ©2009 IEEE.

%B 16th IEEE International Conference on Image Processing (ICIP), 2009 %I IEEE %C Cairo, Egypt %P 169 - 172 %8 Nov 2009 %@ 978-1-4244-5653-6 %G eng %9 Conference paper %M 11150920 %R 10.1109/ICIP.2009.5414195 %0 Generic %D 2009 %T Affine Registration of Planar Shapes %A Zsolt Katona %A Csaba Domokos %A Zoltan Kato %XThis is the sample implementation and benchmark dataset of the binary image registration algorithm described in the following paper: Csaba Domokos and Zoltan Kato. Parametric Estimation of Affine Deformations of Planar Shapes. Pattern Recognition, 43(3):569--578, March 2010.

%8 2009/// %G eng %U http://www.inf.u-szeged.hu/~kato/software/affbinregdemo.html %0 Conference Paper %B 16th IEEE International Conference on Image Processing (ICIP) %D 2009 %T Nonlinear registration of binary shapes %A Jozsef Nemeth %A Csaba Domokos %A Zoltan Kato %XA novel approach is proposed to estimate the parameters of a diffeomorphism that aligns two binary images. Classical approaches usually define a cost function based on a similarity metric and then find the solution via optimization. Herein, we trace back the problem to the solution of a system of non-linear equations which directly provides the parameters of the aligning transformation. The proposed method works without any time consuming optimization step or established correspondences. The advantage of our algorithm is that it is easy to implement, less sensitive to the strength of the deformation, and robust against segmentation errors. The efficiency of the proposed approach has been demonstrated on a large synthetic dataset as well as in the context of an industrial application. ©2009 IEEE.

%B 16th IEEE International Conference on Image Processing (ICIP) %I IEEE %C Cairo, Egypt %P 1101 - 1104 %8 Nov 2009 %@ 978-1-4244-5653-6 %G eng %9 Conference paper %R 10.1109/ICIP.2009.5413468 %0 Book Section %B Image Analysis %D 2009 %T Recovering affine deformations of fuzzy shapes %A Attila Tanacs %A Csaba Domokos %A Nataša Sladoje %A Joakim Lindblad %A Zoltan Kato %E Arnt-Borre Salberg %E Jon Yngve Hardeberg %E Robert Jenssen %XFuzzy sets and fuzzy techniques are attracting increasing attention nowadays in the field of image processing and analysis. It has been shown that the information preserved by using fuzzy representation based on area coverage may be successfully utilized to improve precision and accuracy of several shape descriptors; geometric moments of a shape are among them. We propose to extend an existing binary shape matching method to take advantage of fuzzy object representation. The result of a synthetic test show that fuzzy representation yields smaller registration errors in average. A segmentation method is also presented to generate fuzzy segmentations of real images. The applicability of the proposed methods is demonstrated on real X-ray images of hip replacement implants. © 2009 Springer Berlin Heidelberg.

%B Image Analysis %S Lecture Notes in Computer Science %I Springer-Verlag %C Oslo, Norway %P 735 - 744 %8 June 2009 %G eng %9 Conference paper %! LNCS %R 10.1007/978-3-642-02230-2_75 %0 Book Section %B 12th International Conference on Computer Vision, ICCV 2009 %D 2009 %T Recovering planar homographies between 2D shapes %XImages taken from different views of a planar object are related by planar homography. Recovering the parameters of such transformations is a fundamental problem in computer vision with various applications. This paper proposes a novel method to estimate the parameters of a homography that aligns two binary images. It is obtained by solving a system of nonlinear equations generated by integrating linearly independent functions over the domains determined by the shapes. The advantage of the proposed solution is that it is easy to implement, less sensitive to the strength of the deformation, works without established correspondences and robust against segmentation errors. The method has been tested on synthetic as well as on real images and its efficiency has been demonstrated in the context of two different applications: alignment of hip prosthesis X-ray images and matching of traffic signs. ©2009 IEEE.

%B 12th International Conference on Computer Vision, ICCV 2009 %I IEEE %P 2170 - 2176 %8 2009/// %G eng %0 Conference Paper %B A Képfeldolgozók és Alakfelismerők Társaságának konferenciája - KÉPAF 2009 %D 2009 %T Síkbeli alakzatok regisztrációja kovariáns függvények felhasználásával %B A Képfeldolgozók és Alakfelismerők Társaságának konferenciája - KÉPAF 2009 %I Akaprint %C Budapest %P 1 - 8 %8 Jan 2009 %G eng %9 Conference papers %0 Conference Paper %B A Képfeldolgozók és Alakfelismerők Társaságának konferenciája - KÉPAF 2009 %D 2009 %T Síkhomográfia paramétereinek becslése bináris képeken %B A Képfeldolgozók és Alakfelismerők Társaságának konferenciája - KÉPAF 2009 %I Akaprint %C Budapest %P 1 - 8 %8 Jan 2009 %G eng %9 Conference paper %0 Book Section %B Image Analysis and Recognition %D 2008 %T Binary image registration using covariant gaussian densities %A Csaba Domokos %A Zoltan Kato %E Aurélio Campilho %XWe consider the estimation of 2D affine transformations aligning a known binary shape and its distorted observation. The classical way to solve this registration problem is to find correspondences between the two images and then compute the transformation parameters from these landmarks. In this paper, we propose a novel approach where the exact transformation is obtained as a least-squares solution of a linear system. The basic idea is to fit a Gaussian density to the shapes which preserves the effect of the unknown transformation. It can also be regarded as a consistent coloring of the shapes yielding two rich functions defined over the two shapes to be matched. The advantage of the proposed solution is that it is fast, easy to implement, works without established correspondences and provides a unique and exact solution regardless of the magnitude of transformation. © 2008 Springer-Verlag Berlin Heidelberg.

%B Image Analysis and Recognition %S Lecture Notes in Computer Science %I Springer %C Póvoa de Varzim, Portugal %P 455 - 464 %8 June 2008 %@ 978-3-540-69811-1 %G eng %9 Conference paper %! LNCS %R 10.1007/978-3-540-69812-8_45 %0 Book Section %B Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) %D 2008 %T Parametric estimation of affine deformations of binary images %A Csaba Domokos %A Zoltan Kato %A Joseph M Francos %XWe consider the problem of planar object registration on binary images where the aligning transformation is restricted to the group of affine transformations. Previous approaches usually require established correspondences or the solution of nonlinear optimization problems. Herein we show that it is possible to formulate the problem as the solution of a system of up to third order polynomial equations. These equations are constructed in a simple way using some basic geometric information of binary images. It does not need established correspondences nor the solution of complex optimization problems. The resulting algorithm is fast and provides a direct solution regardless of the magnitude of transformation. ©2008 IEEE.

%B Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) %I IEEE %C Las Vegas, NV, USA %P 889 - 892 %8 March 2008 %@ 978-1-4244-1483-3 %G eng %9 Conference paper %M 9973096 %R 10.1109/ICASSP.2008.4517753 %0 Conference Paper %B A Képfeldolgozók és Alakfelismerők Társaságának konferenciája - KÉPAF 2007 %D 2007 %T Parametric Estimation of Two-Dimensional Affine Transformations of Binary Images %B A Képfeldolgozók és Alakfelismerők Társaságának konferenciája - KÉPAF 2007 %I Képfeldolgozók és Alakfelismerők Társasága %C Debrecen %P 257 - 265 %8 Jan 2007 %G eng %9 Conference paper