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.

1 aDomokos, Csaba1 aNemeth, Jozsef1 aKato, Zoltan uhttp://www.inf.u-szeged.hu/~kato/papers/TPAMI-2010-03-0146.R2_Kato.pdf01252nas a2200181 4500008004100000020002300041245005600064210005600120260003500176300001100211520065300222100001900875700001700894700002200911700001700933700002100950856009900971 2012 eng d a978-1-4673-2216-4 00aSimultaneous Affine Registration of Multiple Shapes0 aSimultaneous Affine Registration of Multiple Shapes aTsukuba, JapanbIEEEcNov 2012 a9 - 123 a

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.

1 aDomokos, Csaba1 aKato, Zoltan1 aEklundh, Jan-Olof1 aOhta, Yuichi1 aTanimoto, Steven uhttps://www.inf.u-szeged.hu/en/publication/simultaneous-affine-registration-of-multiple-shapes00524nas a2200145 4500008004100000245008900041210007300130260002800203300001400231100001900245700001700264700001700281700002300298856005700321 2011 eng d00aAffin Puzzle: Deformált objektumdarabok helyreállítása megfeleltetések nélkül0 aAffin Puzzle Deformált objektumdarabok helyreállítása megfelelte aSzegedbNJSZTcJan 2011 a206 - 2201 aDomokos, Csaba1 aKato, Zoltan1 aKato, Zoltan1 aPalágyi, Kálmán uhttp://www.inf.u-szeged.hu/kepaf2011/pdfs/S05_03.pdf00956nas a2200145 4500008004100000245005700041210005700098260001200155520048800167100002900655700001900684700001900703700001700722856007100739 2011 eng d00aNonlinear Shape Registration without Correspondences0 aNonlinear Shape Registration without Correspondences c2011///3 a

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.

1 aTörök, Zoltán Kornél1 aDomokos, Csaba1 aNemeth, Jozsef1 aKato, Zoltan uhttp://www.inf.u-szeged.hu/~kato/software/planarhombinregdemo.html01396nas a2200193 4500008004100000020002200041022001400063245008000077210006900157260003800226300001400264520070300278100001900981700001701000700002301017700002001040700002001060856012201080 2010 eng d a978-3-642-15551-2 a0302-974300aAffine puzzle: Realigning deformed object fragments without correspondences0 aAffine puzzle Realigning deformed object fragments without corre aCrete, GreecebSpringercSep 2010 a777 - 7903 aThis 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.

1 aDomokos, Csaba1 aKato, Zoltan1 aDaniilidis, Kostas1 aMaragos, Petros1 aParagios, Nikos uhttps://www.inf.u-szeged.hu/en/publication/affine-puzzle-realigning-deformed-object-fragments-without-correspondences00514nas a2200145 4500008004100000020001400041245006600055210006600121260001500187300001400202490000700216100001900223700001700242856010900259 2010 eng d a0031-320300aParametric estimation of affine deformations of planar shapes0 aParametric estimation of affine deformations of planar shapes cMarch 2010 a569 - 5780 v431 aDomokos, Csaba1 aKato, Zoltan uhttps://www.inf.u-szeged.hu/en/publication/parametric-estimation-of-affine-deformations-of-planar-shapes01290nas a2200157 4500008004100000020002300041022001500064245006000079210005900139260003300198300001400231520074900245100001900994700001701013856010201030 2009 eng d a978-1-4244-5653-6 a1522-4880 00aAffine alignment of compound objects: A direct approach0 aAffine alignment of compound objects A direct approach aCairo, EgyptbIEEEcNov 2009 a169 - 1723 aA 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.

1 aDomokos, Csaba1 aKato, Zoltan uhttps://www.inf.u-szeged.hu/en/publication/affine-alignment-of-compound-objects-a-direct-approach00675nas a2200133 4500008004100000245004100041210004100082260001200123520028700135100001800422700001900440700001700459856006500476 2009 eng d00aAffine Registration of Planar Shapes0 aAffine Registration of Planar Shapes c2009///3 aThis 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.

1 aKatona, Zsolt1 aDomokos, Csaba1 aKato, Zoltan uhttp://www.inf.u-szeged.hu/~kato/software/affbinregdemo.html01320nas a2200157 4500008004100000020002300041245004400064210004400108260003300152300001600185520081900201100001901020700001901039700001701058856008701075 2009 eng d a978-1-4244-5653-6 00aNonlinear registration of binary shapes0 aNonlinear registration of binary shapes aCairo, EgyptbIEEEcNov 2009 a1101 - 11043 aA 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.

1 aNemeth, Jozsef1 aDomokos, Csaba1 aKato, Zoltan uhttps://www.inf.u-szeged.hu/en/publication/nonlinear-registration-of-binary-shapes01497nas a2200205 4500008004100000245005100041210005100092260004500143300001400188520082800202100001901030700001901049700002101068700002101089700001701110700002401127700002601151700002001177856009401197 2009 eng d00aRecovering affine deformations of fuzzy shapes0 aRecovering affine deformations of fuzzy shapes aOslo, NorwaybSpringer-VerlagcJune 2009 a735 - 7443 aFuzzy 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.

1 aTanacs, Attila1 aDomokos, Csaba1 aSladoje, Nataša1 aLindblad, Joakim1 aKato, Zoltan1 aSalberg, Arnt-Borre1 aHardeberg, Jon, Yngve1 aJenssen, Robert uhttps://www.inf.u-szeged.hu/en/publication/recovering-affine-deformations-of-fuzzy-shapes01264nas a2200109 4500008004100000245005300041210005300094260001800147300001600165520092800181856004501109 2009 eng d00aRecovering planar homographies between 2D shapes0 aRecovering planar homographies between 2D shapes bIEEEc2009/// a2170 - 21763 aImages 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.

uhttps://www.inf.u-szeged.hu/en/node/122800387nas a2200097 4500008004100000245008400041210007600125260003300201300001000234856004500244 2009 eng d00aSíkbeli alakzatok regisztrációja kovariáns függvények felhasználásával0 aSíkbeli alakzatok regisztrációja kovariáns függvények felhasznál aBudapestbAkaprintcJan 2009 a1 - 8 uhttps://www.inf.u-szeged.hu/en/node/129100355nas a2200097 4500008004100000245006400041210006400105260003300169300001000202856004500212 2009 eng d00aSíkhomográfia paramétereinek becslése bináris képeken0 aSíkhomográfia paramétereinek becslése bináris képeken aBudapestbAkaprintcJan 2009 a1 - 8 uhttps://www.inf.u-szeged.hu/en/node/129201519nas a2200157 4500008004100000020002200041245006500063210006500128260005200193300001400245520093500259100001901194700001701213700002301230856010801253 2008 eng d a978-3-540-69811-100aBinary image registration using covariant gaussian densities0 aBinary image registration using covariant gaussian densities aPóvoa de Varzim, PortugalbSpringercJune 2008 a455 - 4643 aWe 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.

1 aDomokos, Csaba1 aKato, Zoltan1 aCampilho, Aurélio uhttps://www.inf.u-szeged.hu/en/publication/binary-image-registration-using-covariant-gaussian-densities01344nas a2200169 4500008004100000020002300041022001500064245006600079210006600145260004100211300001400252520074100266100001901007700001701026700002201043856010901065 2008 eng d a978-1-4244-1483-3 a1520-6149 00aParametric estimation of affine deformations of binary images0 aParametric estimation of affine deformations of binary images aLas Vegas, NV, USAbIEEEcMarch 2008 a889 - 8923 aWe 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.

1 aDomokos, Csaba1 aKato, Zoltan1 aFrancos, Joseph M uhttps://www.inf.u-szeged.hu/en/publication/parametric-estimation-of-affine-deformations-of-binary-images00425nas a2200097 4500008004100000245008500041210006900126260007300195300001400268856004500282 2007 eng d00aParametric Estimation of Two-Dimensional Affine Transformations of Binary Images0 aParametric Estimation of TwoDimensional Affine Transformations o aDebrecenbKépfeldolgozók és Alakfelismerők TársaságacJan 2007 a257 - 265 uhttps://www.inf.u-szeged.hu/en/node/1293