3D Correspondence by Breadth First Search Frontiers

This paper presents a novel, robust, and fast 3D shape correspondence algorithm applicable to the two snapshots of the same object in arbitrary deformation. Given two such frames as triangle meshes with fixed connectivity, our algorithm first classifies vertices into Breadth-First Search (BFS) frontiers according to their unweighted shortest path distance from a source vertex. This is followed by the rigid or non-rigid alignment of the corresponding frontiers of two meshes as the second and final step. This algorithm is flexible; high-resolution meshes are welcome. It is robust; results approved by human intuition as well as our own numerical correspondence error metric. It is fast; sequential running time turns out to be quadratic in number of vertices, whereas this upper bound can be pulled down as low as subquadratic O(V 1.5 ) once the second step is naturally and easily parallelized. Due to consistent frontier selection, second step does the optimal work of O(V 3 ) Hungarian assignment in less than a quadratic time.


3D Shape Correspondence Under Topological Noise
Genctav, Ash; Sahillioğlu, Yusuf; Tarı, Zehra Sibel (2016-05-19)
In this work, we present a new approach for the problem of 3D shape correspondence under topological noise. Topological noise can be easily encountered in 3D models acquired by various ways such as motion capture technology. In our proposed approach, the pair of 3D shapes is brought to comparable topology before doing matching. We remove the connections leading to topological changes by moving the shape surface inward along the surface normal with a velocity relative to the curvature at each point. We emplo...
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...
3D object representation using transform and scale invariant 3D features
AKAGÜNDÜZ, Erdem; Ulusoy, İlkay (2007-10-21)
An algorithm is proposed for 3D object representation using generic 3D features which are transformation and scale invariant. Descriptive 3D features and their relations are used to construct a graphical model for the object which is later trained and then used for detection purposes. Descriptive 3D features are the fundamental structures which are extracted from the surface of the 3D scanner output. This surface is described by mean and Gaussian curvature values at every data point at various scales and a ...
Part-based data-driven 3D shape interpolation
Aydinlilar, Melike; Sahillioğlu, Yusuf (2021-07-01)
An active problem in digital geometry processing is shape interpolation which aims to generate a continuous sequence of in-betweens for a given source and target shape. Unlike traditional approaches that interpolate source and target shapes in isolation, recent data-driven approaches utilize multiple interpolations through intermediate database shapes, and consequently perform better at the expense of a database requirement. In contrast to the existing data-driven approaches that consider intermediate shape...
Detail-Preserving Mesh Unfolding for Nonrigid Shape Retrieval
Sahillioğlu, Yusuf (2016-06-01)
We present a shape deformation algorithm that unfolds any given 3D shape into a canonical pose that is invariant to nonrigid transformations. Unlike classical approaches, such as least-squares multidimensional scaling, we preserve the geometric details of the input shape in the resulting shape, which in turn leads to a content-based nonrigid shape retrieval application with higher accuracy. Our optimization framework, fed with a triangular or a tetrahedral mesh in 3D, tries to move each vertex as far away f...
Citation Formats
Y. Sahillioğlu, “3D Correspondence by Breadth First Search Frontiers,” Las Vegas, Nevada, USA, 2009, p. 203, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/84211.