Coloring 3D symmetry set: perceptual meaning and significance in 3D

A computational implementation for assigning perceptual meaning and significance to the points in the symmetry is presented. The coloring scheme allows recovery of the features of interest such as the shape skeletons from the complicated symmetry representation. The method is applicable to arbitrary data including color and multi-modality images. On the computational side, for a 256 × 256 binary image, two minutes on a low-end Pentium machine is enough to compute both the distance function and the colored nested symmetries at four scales.
Visual Information Processing VIII Conference


On equivelar triangulations of surfaces
Adıgüzel, Ebru; Pamuk, Semra; Department of Mathematics (2018)
Persistent homology is an algebraic method for understanding topological features of discrete objects or data (finite set of points with metric defined on it). In algebraic topology, the Mayer Vietoris sequence is a powerful tool which allows one to study the homology groups of a given space in terms of simpler homology groups of its subspaces. In this thesis, we study to what extent does persistent homology benefit from Mayer Vietoris sequence.
Shape models based on elliptic PDES, associated energies, and their applications in 2D and 3D
Gençtav, Aslı; Tarı, Zehra Sibel; Can, Tolga; Department of Computer Engineering (2018)
By using an elliptic PDE or its modifications, we develop implicit shape representations and demonstrate their two- and three-dimensional applications. In the first part of the thesis, we present a novel shape characterization field that provides a local measure of roundness at each shape point. The field is computed by comparing the solution of the elliptic PDE on the shape domain and the solution of the same PDE on the reference disk. We demonstrate its potential via illustrative applications including gl...
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 ...
Simultaneous segmentation of images and shapes
Tarı, Zehra Sibel (1997-01-01)
A novel method for simultaneous image segmentation and shape decomposition is presented. The method may be applied directly to grayscale images. The method is based on the analysis of the level curves of an ''edge-strength'' function which is a measure of boundaryness of the image at each point.
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...
Citation Formats
Z. S. Tarı, “Coloring 3D symmetry set: perceptual meaning and significance in 3D,” Orlando, FL, 1999, vol. 3716, Accessed: 00, 2020. [Online]. Available: