Partial 3-D Correspondence from Shape Extremities

We present a 3-D correspondence method to match the geometric extremities of two shapes which are partially isometric. We consider the most general setting of the isometric partial shape correspondence problem, in which shapes to be matched may have multiple common parts at arbitrary scales as well as parts that are not similar. Our rank-and-vote-and-combine algorithm identifies and ranks potentially correct matches by exploring the space of all possible partial maps between coarsely sampled extremities. The qualified top-ranked matchings are then subjected to a more detailed analysis at a denser resolution and assigned with confidence values that accumulate into a vote matrix. A minimum weight perfect matching algorithm is finally iterated to combine the accumulated votes into an optimal (partial) mapping between shape extremities, which can further be extended to a denser map. We test the performance of our method on several data sets and benchmarks in comparison with state of the art.


3D Shape Correspondence by Isometry Driven Greedy Optimization
Sahillioğlu, Yusuf (null; 2010-06-01)
We present an automatic method that establishes 3D correspondence between isometric shapes. Our goal is to find an optimal correspondence between two given (nearly) isometric shapes, that minimizes the amount of deviation from isometry. We cast the problem as a complete surface correspondence problem. Our method first divides the given shapes to be matched into surface patches of equal area and then seeks for a mapping between the patch centers which we refer to as base vertices. Hence the correspondence is...
Coarse-to-Fine Isometric Shape Correspondence by Tracking Symmetric Flips
Sahillioğlu, Yusuf; Yemez, Y. (2013-02-01)
We address the symmetric flip problem that is inherent to multi-resolution isometric shape matching algorithms. To this effect, we extend our previous work which handles the dense isometric correspondence problem in the original 3D Euclidean space via coarse-to-fine combinatorial matching. The key idea is based on keeping track of all optimal solutions, which may be more than one due to symmetry especially at coarse levels, throughout denser levels of the shape matching process. We compare the resulting den...
A general representation for classical detection theory with Euclidean geometry Klasik tespit kurami için Öklid geometrisi ile genel bir gösterim
Bayramog̃lu, Muhammet Fatih; Yılmaz, Ali Özgür (2010-12-01)
A general geometric representation for the classical detection theory which is compatible with Euclidean geometry is proposed. The proposed representation is so generic that can be employed to almost all communication problems. The a posteriori probability of a symbol given an observation occurred decreases exponentially with the square of the Eclidean distance between vectors in R N that the symbol and the observation are mapped onto.
3B Izometrik Şekil Eşleme
Sahillioğlu, Yusuf (2010-06-01)
3B izometrik şekiller arasındaki eşleme problemini ele alıyoruz. Önerdiğimiz yöntem, verilen iki izometrik şekil arasındaki izometrik sapmayı enküçülten optimal eşlemeyi otomatik olarak bulabilmektedir.İzometri hatasını iki adımda eniyiliyoruz. İlk adımda, şekil yüzeylerinden örneklenmiş bir örnek 3B noktalar kesel ilginlik bilgisine dayanarak spektral uzaya aktarılır.İlk eşleme spektral uzayda tam iki kısımlı bir çizge eşleştirme yöntemi kullanarak izometri hatasının polinom zamanda enküçültülmesiyle eld...
Coarse-to-Fine Combinatorial Matching for Dense Isometric Shape Correspondence
Sahillioğlu, Yusuf; Yemez, Y. (2011-08-01)
We present a dense correspondence method for isometric shapes, which is accurate yet computationally efficient. We minimize the isometric distortion directly in the 3D Euclidean space, i.e., in the domain where isometry is originally defined, by using a coarse-to-fine sampling and combinatorial matching algorithm. Our method does not require any initialization and aims to find an accurate solution in the minimum-distortion sense for perfectly isometric shapes. We demonstrate the performance of our method on...
Citation Formats
Y. Sahillioğlu and Y. Yemez, “Partial 3-D Correspondence from Shape Extremities,” COMPUTER GRAPHICS FORUM, vol. 33, no. 6, pp. 63–76, 2014, Accessed: 00, 2022. [Online]. Available: