Nikolas Lamb
Skip Abstract Section
Skip Supplemental Material SectionAbstract
We introduce DeepJoin, an automated approach to generate high-resolution repairs for fractured shapes using deep neural networks. Existing approaches to perform automated shape repair operate exclusively on symmetric objects, require a complete proxy shape, or predict restoration shapes using low-resolution voxels which are too coarse for physical repair. We generate a high-resolution restoration shape by inferring a corresponding complete shape and a break surface from an input fractured shape. We present a novel implicit shape representation for fractured shape repair that combines the occupancy function, signed distance function, and normal field. We demonstrate repairs using our approach for synthetically fractured objects from ShapeNet, 3D scans from the Google Scanned Objects dataset, objects in the style of ancient Greek pottery from the QP Cultural Heritage dataset, and real fractured objects. We outperform six baseline approaches in terms of chamfer distance and normal consistency. Unlike existing approaches and restorations generated using subtraction, DeepJoin restorations do not exhibit surface artifacts and join closely to the fractured region of the fractured shape. Our code is available at: https://github.com/Terascale-All-sensing-Research-Studio/DeepJoin.
Supplemental Material
- Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. 2018. Learning representations and generative models for 3d point clouds, In International conference on machine learning. International conference on machine learning 80, 35, 40--49.Google Scholar
- Kaja Antlej, Miran Eric, Mojca Savnik, Bernarda Zupanek, Janja Slabe, and B Borut Battestin. 2011. Combining 3D Technologies in the Field of Cultural Heritage: Three Case Studies.. In VAST (Short and Project Papers). The Eurographics Association, Geneve, Switzerland, 1--4.Google Scholar
- Aayush Bansal, Bryan Russell, and Abhinav Gupta. 2016. Marr revisited: 2d-3d alignment via surface normal prediction. In Proc. CVPR. IEEE, Piscataway, NJ, 5965--5974.Google ScholarCross Ref
- David E Breen, Sean Mauch, and Ross T Whitaker. 2000. 3d scan-conversion of CSG models into distance, closest-point and colour volumes. In Volume Graphics. Springer, London, UK, 135--158.Google ScholarCross Ref
- Andrew Brock, Theodore Lim, James M Ritchie, and Nick Weston. 2016. Generative and discriminative voxel modeling with convolutional neural networks. arXiv preprint arXiv:1608.04236 1, 1 (2016), 1--9.Google Scholar
- Rohan Chabra, Jan E Lenssen, Eddy Ilg, Tanner Schmidt, Julian Straub, Steven Lovegrove, and Richard Newcombe. 2020. Deep local shapes: Learning local sdf priors for detailed 3d reconstruction. In ECCV. Springer, Berlin, Germany, 608--625.Google Scholar
- Angel X. Chang, Thomas Funkhouser, Leonidas Guibas, Pat Hanrahan, Qixing Huang, Zimo Li, Silvio Savarese, Manolis Savva, Shuran Song, Hao Su, Jianxiong Xiao, Li Yi, and Fisher Yu. 2015. ShapeNet: An Information-Rich 3D Model Repository. Technical Report arXiv:1512.03012 [cs.GR]. Stanford University --- Princeton University --- Toyota Technological Institute at Chicago.Google Scholar
- Zhiqin Chen and Hao Zhang. 2019. Learning implicit fields for generative shape modeling. In Proc. CVPR. IEEE, Piscataway, NJ, 5939--5948.Google ScholarCross Ref
- Zhang Chen, Yinda Zhang, Kyle Genova, Sean Fanello, Sofien Bouaziz, Christian Häne, Ruofei Du, Cem Keskin, Thomas Funkhouser, and Danhang Tang. 2021. Multiresolution Deep Implicit Functions for 3D Shape Representation. In Proceedings of the IEEE/CVF International Conference on Computer Vision. IEEE, Piscataway, NJ, 13087--13096.Google ScholarCross Ref
- Julian Chibane, Thiemo Alldieck, and Gerard Pons-Moll. 2020a. Implicit functions in feature space for 3d shape reconstruction and completion. In Proc. CVPR. IEEE, Piscataway, NJ, 6970--6981.Google ScholarCross Ref
- Julian Chibane, Gerard Pons-Moll, et al. 2020b. Neural unsigned distance fields for implicit function learning. Advances in Neural Information Processing Systems 33 (2020), 21638--21652.Google Scholar
- Angela Dai, Christian Diller, and Matthias Nießner. 2020. Sg-nn: Sparse generative neural networks for self-supervised scene completion of rgb-d scans. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. IEEE, Piscataway, NJ, 849--858.Google ScholarCross Ref
- Angela Dai, Daniel Ritchie, Martin Bokeloh, Scott Reed, Jürgen Sturm, and Matthias Nießner. 2018. Scancomplete: Large-scale scene completion and semantic segmentation for 3d scans. In Proc. CVPR. IEEE, Piscataway, NJ, 4578--4587.Google ScholarCross Ref
- Angela Dai, Charles Ruizhongtai Qi, and Matthias Nießner. 2017. Shape completion using 3d-encoder-predictor cnns and shape synthesis. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. IEEE, Piscataway, NJ, 5868--5877.Google ScholarCross Ref
- Tien Do, Khiem Vuong, Stergios I Roumeliotis, and Hyun Soo Park. 2020. Surface normal estimation of tilted images via spatial rectifier. In ECCV. Springer, Springer, Berlin, Germany, 265--280.Google Scholar
- Tao Du, Jeevana Priya Inala, Yewen Pu, Andrew Spielberg, Adriana Schulz, Daniela Rus, Armando Solar-Lezama, and Wojciech Matusik. 2018. Inversecsg: Automatic conversion of 3d models to csg trees. ACM Transactions on Graphics (TOG) 37, 6 (2018), 1--16.Google ScholarDigital Library
- Yueqi Duan, Haidong Zhu, He Wang, Li Yi, Ram Nevatia, and Leonidas J Guibas. 2020. Curriculum deepsdf. In European Conference on Computer Vision. Springer, Berlin, Germany, 51--67.Google ScholarDigital Library
- Jean Duchon. 1977. Splines minimizing rotation-invariant semi-norms in Sobolev spaces. In Constructive theory of functions of several variables. Springer, Berlin, Germany, 85--100.Google Scholar
- Shivam Duggal, Zihao Wang, Wei-Chiu Ma, Sivabalan Manivasagam, Justin Liang, Shenlong Wang, and Raquel Urtasun. 2022. Mending Neural Implicit Modeling for 3D Vehicle Reconstruction in the Wild. In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision. IEEE, Piscataway, NJ, 1900--1909.Google ScholarCross Ref
- David Eigen and Rob Fergus. 2015. Predicting depth, surface normals and semantic labels with a common multi-scale convolutional architecture. In Proceedings of the IEEE International Conference on Computer Vision. IEEE, Piscataway, NJ, 2650--2658.Google ScholarDigital Library
- Jian Gao, Xin Chen, Oguzhan Yilmaz, and Nabil Gindy. 2008. An integrated adaptive repair solution for complex aerospace components through geometry reconstruction. The International Journal of Advanced Manufacturing Technology 36, 11--12 (2008), 1170--1179.Google ScholarCross Ref
- Kyle Genova, Forrester Cole, Avneesh Sud, Aaron Sarna, and Thomas Funkhouser. 2020. Local deep implicit functions for 3d shape. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. IEEE, Piscataway, NJ, 4857--4866.Google ScholarCross Ref
- GoogleResearch. 2022. Google Scanned Objects. Open Robotics. https://fuel.gazebosim.org/1.0/GoogleResearch/fuel/collections/Google%20Scanned%20ObjectsGoogle Scholar
- Robert Gregor, Ivan Sipiran, Georgios Papaioannou, Tobias Schreck, Anthousis Andreadis, and Pavlos Mavridis. 2014. Towards Automated 3D Reconstruction of Defective Cultural Heritage Objects.. In GCH. EUROGRAPHICS, Geneva, Switzerland, 135--144.Google Scholar
- Thibault Groueix, Matthew Fisher, Vladimir G Kim, Bryan C Russell, and Mathieu Aubry. 2018. A papier-mâché approach to learning 3d surface generation. In Proc. CVPR. IEEE, Piscataway, NJ, 216--224.Google ScholarCross Ref
- Madan M Gupta and J11043360726 Qi. 1991. Theory of T-norms and fuzzy inference methods. Fuzzy sets and systems 40, 3 (1991), 431--450.Google Scholar
- Xiaoguang Han, Zhen Li, Haibin Huang, Evangelos Kalogerakis, and Yizhou Yu. 2017. High-resolution shape completion using deep neural networks for global structure and local geometry inference. In Proceedings of the IEEE international conference on computer vision. IEEE, Piscataway, NJ, 85--93.Google ScholarCross Ref
- Zekun Hao, Hadar Averbuch-Elor, Noah Snavely, and Serge Belongie. 2020. Dualsdf: Semantic shape manipulation using a two-level representation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. IEEE, Piscataway, NJ, 7631--7641.Google ScholarCross Ref
- Ola LA Harrysson, Yasser A Hosni, and Jamal F Nayfeh. 2007. Custom-designed orthopedic implants evaluated using finite element analysis of patient-specific computed tomography data: femoral-component case study. BMC musculoskeletal disorders 8, 1 (2007), 1--10.Google Scholar
- Renato Hermoza and Ivan Sipiran. 2018. 3D reconstruction of incomplete archaeological objects using a generative adversarial network. In Proceedings of Computer Graphics International. ACM, New York, NY, 5--11.Google ScholarDigital Library
- Steven Hickson, Karthik Raveendran, Alireza Fathi, Kevin Murphy, and Irfan Essa. 2019. Floors are flat: Leveraging semantics for real-time surface normal prediction. In Proceedings of the IEEE/CVF International Conference on Computer Vision Workshops. IEEE, Piscataway, NJ, 0--0.Google ScholarCross Ref
- Jingwei Huang, Yichao Zhou, Thomas Funkhouser, and Leonidas J Guibas. 2019. Framenet: Learning local canonical frames of 3d surfaces from a single rgb image. In Proceedings of the IEEE International Conference on Computer Vision. IEEE, Piscataway, NJ, 8638--8647.Google ScholarCross Ref
- Meng Jia and Matthew Kyan. 2020. Learning Occupancy Function from Point Clouds for Surface Reconstruction. arXiv preprint arXiv:2010.11378 1 (2020), 1--11.Google Scholar
- Kacper Kania, Maciej Zieba, and Tomasz Kajdanowicz. 2020. UCSG-NET-unsupervised discovering of constructive solid geometry tree. Advances in Neural Information Processing Systems 33 (2020), 8776--8786.Google Scholar
- Diederik P Kingma and Jimmy Ba. 2014. Adam: A method for stochastic optimization. In Proc. ICLR. International Conference on Representation Learning, La Jolla, CA, 1--15.Google Scholar
- Anestis Koutsoudis, George Pavlidis, Fotis Arnaoutoglou, Despina Tsiafakis, and Christodoulos Chamzas. 2009. Qp: A tool for generating 3D models of ancient Greek pottery. Journal of Cultural Heritage 10, 2 (2009), 281--295.Google ScholarCross Ref
- Nikolas Lamb, Sean Banerjee, and Natasha Kholgade Banerjee. 2019. Automated reconstruction of smoothly joining 3D printed restorations to fix broken objects. In Proc. SCF. ACM, New York, NY, 1--12.Google ScholarDigital Library
- Nikolas Lamb, Noah Wiederhold, Benjamin Lamb, Sean Banerjee, and Natasha Kholgade Banerjee. 2021. Using Learned Visual and Geometric Features to Retrieve Complete 3D Proxies for Broken Objects. In Proc. SCF. ACM, New York, NY, 1--15.Google ScholarDigital Library
- Jan Eric Lenssen, Christian Osendorfer, and Jonathan Masci. 2020. Deep iterative surface normal estimation. In Proc. CVPR. IEEE, Piscataway, NJ, 11247--11256.Google ScholarCross Ref
- Yiyi Liao, Simon Donne, and Andreas Geiger. 2018. Deep marching cubes: Learning explicit surface representations. In Proc. CVPR. IEEE, Piscataway, NJ, 2916--2925.Google ScholarCross Ref
- Chen-Hsuan Lin, Chaoyang Wang, and Simon Lucey. 2020. SDF-SRN: Learning Signed Distance 3D Object Reconstruction from Static Images. arXiv preprint arXiv:2010.10505 1, 1 (2020), 1--17.Google Scholar
- Stefan Lionar, Daniil Emtsev, Dusan Svilarkovic, and Songyou Peng. 2021. Dynamic Plane Convolutional Occupancy Networks. In Proc.WACV. IEEE, Piscataway, NJ, 1829--1838.Google ScholarCross Ref
- Minghua Liu, Lu Sheng, Sheng Yang, Jing Shao, and Shi-Min Hu. 2020. Morphing and sampling network for dense point cloud completion. In Proceedings of the AAAI Conference on Artificial Intelligence, Vol. 34. AAAI, Menlo Park, CA, 11596--11603.Google ScholarCross Ref
- William E Lorensen and Harvey E Cline. 1987. Marching cubes: A high resolution 3D surface construction algorithm. ACM SIGGRAPH Computer Graphics 21, 4 (1987), 163--169.Google ScholarDigital Library
- Baorui Ma, Zhizhong Han, Yu-Shen Liu, and Matthias Zwicker. 2020. Neural-Pull: Learning Signed Distance Functions from Point Clouds by Learning to Pull Space onto Surfaces. arXiv preprint arXiv:2011.13495 1, 1 (2020), 1--12.Google Scholar
- Lars Mescheder, Michael Oechsle, Michael Niemeyer, Sebastian Nowozin, and Andreas Geiger. 2019. Occupancy networks: Learning 3d reconstruction in function space. In Proc. CVPR. IEEE, Piscataway, NJ, 4460--4470.Google ScholarCross Ref
- Liang Pan, Xinyi Chen, Zhongang Cai, Junzhe Zhang, Haiyu Zhao, Shuai Yi, and Ziwei Liu. 2021. Variational relational point completion network. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. IEEE, Piscataway, NJ, 8524--8533.Google ScholarCross Ref
- Georgios Papaioannou, Tobias Schreck, Anthousis Andreadis, Pavlos Mavridis, Robert Gregor, Ivan Sipiran, and Konstantinos Vardis. 2017. From reassembly to object completion: A complete systems pipeline. Journal on Computing and Cultural Heritage 10, 2 (2017), 1--22.Google ScholarDigital Library
- Jeong Joon Park, Peter Florence, Julian Straub, Richard Newcombe, and Steven Lovegrove. 2019. Deepsdf: Learning continuous signed distance functions for shape representation. In Proc. CVPR. IEEE, Piscataway, NJ, 165--174.Google ScholarCross Ref
- Songyou Peng, Michael Niemeyer, Lars Mescheder, Marc Pollefeys, and Andreas Geiger. 2020. Convolutional occupancy networks. In Computer Vision-ECCV 2020: 16th European Conference, Glasgow, UK, August 23--28, 2020, Proceedings, Part III 16. Springer, Berlin, Germany, 523--540.Google Scholar
- Les Piegl and Wayne Tiller. 1996. The NURBS book. Springer Science & Business Media, Berlin, Germany.Google Scholar
- Omid Poursaeed, Matthew Fisher, Noam Aigerman, and Vladimir G Kim. 2020. Coupling explicit and implicit surface representations for generative 3d modeling. In European Conference on Computer Vision. Springer, Berlin, Germany, 667--683.Google ScholarDigital Library
- Charles Ruizhongtai Qi, Li Yi, Hao Su, and Leonidas J Guibas. 2017. Pointnet++: Deep hierarchical feature learning on point sets in a metric space. Advances in neural information processing systems 30 (2017), 1--10.Google Scholar
- Fabian Rengier, Amit Mehndiratta, Hendrik Von Tengg-Kobligk, Christian M Zechmann, Roland Unterhinninghofen, H-U Kauczor, and Frederik L Giesel. 2010. 3D printing based on imaging data: review of medical applications. International journal of computer assisted radiology and surgery 5, 4 (2010), 335--341.Google Scholar
- Muhammad Sarmad, Hyunjoo Jenny Lee, and Young Min Kim. 2019. Rl-gan-net: A reinforcement learning agent controlled gan network for real-time point cloud shape completion. In Proc. CVPR. IEEE, Piscataway, NJ, 5898--5907.Google ScholarCross Ref
- René Schilling, Benjamin Jastram, Oliver Wings, Daniela Schwarz-Wings, and Ahi Sema Issever. 2014. Reviving the dinosaur: virtual reconstruction and three-dimensional printing of a dinosaur vertebra. Radiology 270, 3 (2014), 864--871.Google ScholarCross Ref
- Roberto Scopigno, Marco Callieri, Paolo Cignoni, Massimiliano Corsini, Matteo Dellepiane, Federico Ponchio, and Guido Ranzuglia. 2011. 3D models for cultural heritage: Beyond plain visualization. Computer 44, 7 (2011), 48--55.Google ScholarDigital Library
- Maria Luiza Seixas, Paulo Santos Assis, João Cura D'Ars Figueiredo, Maria Aparecida Pinto, and Daniella Gualberto Caldeira Paula. 2018. The use of rapid prototyping in the joining of fractured historical silver object. Rapid Prototyping Journal 24 (2018), 532--538.Google ScholarCross Ref
- Abhishek Sharma, Oliver Grau, and Mario Fritz. 2016. Vconv-dae: Deep volumetric shape learning without object labels. In ECCV. Springer, Berlin, Germany, 236--250.Google Scholar
- Gopal Sharma, Rishabh Goyal, Difan Liu, Evangelos Kalogerakis, and Subhransu Maji. 2018. Csgnet: Neural shape parser for constructive solid geometry. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. IEEE, Piscataway, NJ, 5515--5523.Google ScholarCross Ref
- Vincent Sitzmann, Eric R Chan, Richard Tucker, Noah Snavely, and Gordon Wetzstein. 2020. Metasdf: Meta-learning signed distance functions. arXiv preprint arXiv:2006.09662 1, 1 (2020), 1--17.Google Scholar
- Edward J Smith and David Meger. 2017. Improved adversarial systems for 3d object generation and reconstruction. In Conference on Robot Learning. PMLR, Cambridge, UK, 87--96.Google Scholar
- Hyeontae Son and Young Min Kim. 2020. SAUM: Symmetry-Aware Upsampling Module for Consistent Point Cloud Completion. In Proc. ACCV. Springer, Berlin, Germany, 1--17.Google Scholar
- Shuran Song, Fisher Yu, Andy Zeng, Angel X Chang, Manolis Savva, and Thomas Funkhouser. 2017. Semantic scene completion from a single depth image. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. IEEE, Piscataway, NJ, 1746--1754.Google ScholarCross Ref
- David Stutz and Andreas Geiger. 2020. Learning 3d shape completion under weak supervision. International Journal of Computer Vision 128, 5 (2020), 1162--1181.Google ScholarDigital Library
- Raphael Sulzer, Loic Landrieu, Alexandre Boulch, Renaud Marlet, and Bruno Vallet. 2022. Deep Surface Reconstruction from Point Clouds with Visibility Information. arXiv preprint arXiv:2202.01810 1, 1 (2022), 1--13.Google Scholar
- Jiapeng Tang, Jiabao Lei, Dan Xu, Feiying Ma, Kui Jia, and Lei Zhang. 2021. Sign-Agnostic CONet: Learning Implicit Surface Reconstructions by Sign-Agnostic Optimization of Convolutional Occupancy Networks. arXiv preprint arXiv:2105.03582 1, 1 (2021), 1--16.Google Scholar
- Edgar Tretschk, Ayush Tewari, Vladislav Golyanik, Michael Zollhöfer, Carsten Stoll, and Christian Theobalt. 2020. PatchNets: Patch-based generalizable deep implicit 3D shape representations. In Proc. ECCV. Springer, Berlin, Germany, 293--309.Google Scholar
- Rahul Venkatesh, Sarthak Sharma, Aurobrata Ghosh, Laszlo Jeni, and Maneesh Singh. 2020. DUDE: Deep Unsigned Distance Embeddings for Hi-Fidelity Representation of Complex 3D Surfaces. arXiv preprint arXiv:2011.02570 1, 1 (2020), 1--9.Google Scholar
- Lukasz Witek, Kimberly S Khouri, Paulo G Coelho, and Roberto L Flores. 2016. Patient-specific 3D models for autogenous ear reconstruction. Plastic and Reconstructive Surgery-Global Open 4, 10 (2016), e1093.Google ScholarCross Ref
- Jiajun Wu, Chengkai Zhang, Tianfan Xue, William T Freeman, and Joshua B Tenenbaum. 2016. Learning a probabilistic latent space of object shapes via 3d generative-adversarial modeling. In Proc. NeurIPS. Neural Information Processing Systems, San Diego, CA, 82--90.Google Scholar
- Yifan Xu, Tianqi Fan, Yi Yuan, and Gurprit Singh. 2020. Ladybird: Quasi-monte carlo sampling for deep implicit field based 3d reconstruction with symmetry. In European Conference on Computer Vision. Springer, Berlin, Germany, 248--263.Google ScholarDigital Library
- Siming Yan, Zhenpei Yang, Haoxiang Li, Li Guan, Hao Kang, Gang Hua, and Qixing Huang. 2022b. Implicit Autoencoder for Point Cloud Self-supervised Representation Learning. arXiv preprint arXiv:2201.00785 1, 1 (2022), 1--24.Google Scholar
- Xingguang Yan, Liqiang Lin, Niloy J Mitra, Dani Lischinski, Daniel Cohen-Or, and Hui Huang. 2022a. Shapeformer: Transformer-based shape completion via sparse representation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. IEEE, Piscataway, NJ, 6239--6249.Google ScholarCross Ref
- Mingyue Yang, Yuxin Wen, Weikai Chen, Yongwei Chen, and Kui Jia. 2021. Deep optimized priors for 3d shape modeling and reconstruction. In Proc. CVPR. IEEE, Piscataway, NJ, 3269--3278.Google ScholarCross Ref
- Li Yi, Boqing Gong, and Thomas Funkhouser. 2021. Complete & label: A domain adaptation approach to semantic segmentation of lidar point clouds. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. IEEE, Piscataway, NJ, 15363--15373.Google ScholarCross Ref
- Qian Yu, Chengzhuan Yang, and Hui Wei. 2022. Part-Wise AtlasNet for 3D point cloud reconstruction from a single image. Knowledge-Based Systems 242 (2022), 108395.Google ScholarDigital Library
- Wentao Yuan, Tejas Khot, David Held, Christoph Mertz, and Martial Hebert. 2018. Pcn: Point completion network. In 2018 International Conference on 3D Vision (3DV). IEEE, Piscataway, NJ, 728--737.Google ScholarCross Ref
- Jiahui Zhang, Hao Zhao, Anbang Yao, Yurong Chen, Li Zhang, and Hongen Liao. 2018. Efficient semantic scene completion network with spatial group convolution. In Proceedings of the European Conference on Computer Vision (ECCV). Springer, Berlin, Germany, 733--749.Google ScholarDigital Library
- Jianming Zheng, Zhongguo Li, and Xi Chen. 2006. Worn area modeling for automating the repair of turbine blades. The International Journal of Advanced Manufacturing Technology 29, 9 (2006), 1062--1067.Google ScholarCross Ref
- Zerong Zheng, Tao Yu, Qionghai Dai, and Yebin Liu. 2021. Deep implicit templates for 3D shape representation. In Proc. CVPR. IEEE, Piscataway, NJ, 1429--1439.Google ScholarCross Ref
Index Terms
- DeepJoin: Learning a Joint Occupancy, Signed Distance, and Normal Field Function for Shape Repair
Recommendations
DeepMend: Learning Occupancy Functions to Represent Shape for Repair
Computer Vision – ECCV 2022AbstractWe present DeepMend, a novel approach to reconstruct resto- rations to fractured shapes using learned occupancy functions. Existing shape repair approaches predict low-resolution voxelized restorations or smooth restorations, or require symmetries ...
Ricci Flow for 3D Shape Analysis
Ricci flow is a powerful curvature flow method, which is invariant to rigid motion, scaling, isometric, and conformal deformations. We present the first application of surface Ricci flow in computer vision. Previous methods based on conformal geometry, ...
2D-Shape Analysis Using Conformal Mapping
The study of 2D shapes and their similarities is a central problem in the field of vision. It arises in particular from the task of classifying and recognizing objects from their observed silhouette. Defining natural distances between 2D shapes creates ...
Comments