Robust non-rigid registration of 2D and 3D graphs

We present a new approach to matching graphs embedded in ℝ2 or ℝ3. Unlike earlier methods, our approach does not rely on the similarity of local appearance features, does not require an initial alignment, can handle partial matches, and can cope with non-linear deformations and topological differences. To handle arbitrary non-linear deformations, we represent them as Gaussian Processes. In the absence of appearance information, we iteratively establish correspondences between graph nodes, update the structure accordingly, and use the current mapping estimate to find the most likely correspondences that will be used in the next iteration. This makes the computation tractable. We demonstrate the effectiveness of our approach first on synthetic cases and then on angiography data, retinal fundus images, and microscopy image stacks acquired at very different resolutions.

[1]  Martial Hebert,et al.  An Integer Projected Fixed Point Method for Graph Matching and MAP Inference , 2009, NIPS.

[2]  Ieee Xplore,et al.  IEEE Transactions on Pattern Analysis and Machine Intelligence Information for Authors , 2022, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[3]  Hao Li,et al.  Global Correspondence Optimization for Non‐Rigid Registration of Depth Scans , 2008, Comput. Graph. Forum.

[4]  Jiri Matas,et al.  Matching with PROSAC - progressive sample consensus , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[5]  Minsu Cho,et al.  Reweighted Random Walks for Graph Matching , 2010, ECCV.

[6]  Max A. Viergever,et al.  Mutual-information-based registration of medical images: a survey , 2003, IEEE Transactions on Medical Imaging.

[7]  Paul Suetens,et al.  Robust matching of 3D lung vessel trees , 2010 .

[8]  Fredrik Kahl,et al.  Optimal correspondences from pairwise constraints , 2009, 2009 IEEE 12th International Conference on Computer Vision.

[9]  Andriy Myronenko,et al.  Point Set Registration: Coherent Point Drift , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[10]  Francesc Moreno-Noguer,et al.  Simultaneous pose, correspondence and non-rigid shape , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[11]  Vincent Lepetit,et al.  Pose Priors for Simultaneously Solving Alignment and Correspondence , 2008, ECCV.

[12]  Sami Romdhani,et al.  Optimal Step Nonrigid ICP Algorithms for Surface Registration , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[13]  Martial Hebert,et al.  A spectral technique for correspondence problems using pairwise constraints , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[14]  Jan Flusser,et al.  Image registration methods: a survey , 2003, Image Vis. Comput..

[15]  Vincent Lepetit,et al.  Combining Geometric and Appearance Priors for Robust Homography Estimation , 2010, ECCV.

[16]  Robert C. Bolles,et al.  Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography , 1981, CACM.

[17]  Francesc Moreno-Noguer,et al.  Robust elastic 2D/3D geometric graph matching , 2012, Medical Imaging.

[18]  Steven Gold,et al.  A Graduated Assignment Algorithm for Graph Matching , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[19]  Paul J. Besl,et al.  A Method for Registration of 3-D Shapes , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[20]  J. Munkres.  ALGORITHMS FOR THE ASSIGNMENT AND TRANSIORTATION tROBLEMS* , 1957 .

[21]  Vladimir Kolmogorov,et al.  Feature Correspondence Via Graph Matching: Models and Global Optimization , 2008, ECCV.

[22]  Francesc Moreno-Noguer,et al.  Simultaneous correspondence and non-rigid 3D reconstruction of the coronary tree from single X-ray images , 2011, 2011 International Conference on Computer Vision.

[23]  Katsushi Ikeuchi,et al.  Locally rigid globally non-rigid surface registration , 2011, 2011 International Conference on Computer Vision.

[24]  Nikos Paragios,et al.  Non-rigid registration using distance functions , 2003, Comput. Vis. Image Underst..

[25]  Xing Zhang,et al.  Retinal Fundus Image Registration via Vascular Structure Graph Matching , 2010, Int. J. Biomed. Imaging.

[26]  Eric Mjolsness,et al.  New Algorithms for 2D and 3D Point Matching: Pose Estimation and Correspondence , 1998, NIPS.

[27]  Ghassan Hamarneh,et al.  VascuSynth: Vascular Tree Synthesis Software , 2011 .