@conference {16847,
	title = {Indexing Point Triples Via Triangle Geometry},
	booktitle = {Data Engineering, 2007. ICDE 2007. IEEE 23rd International Conference on},
	year = {2007},
	month = {2007/04//},
	pages = {936 - 945},
	abstract = {Database search for images containing icons with specific mutual spatial relationships can be facilitated by an appropriately structured index. For the case of images containing subsets each of which consist of three icons, the one-to-one correspondence between (distinct) point triples and triangles allows the use of such triangle attributes as position, size, orientation, and "shape" in constructing a point-based index, in which each triangle maps to a single point in a resulting hyperdimensional index space. Size (based on the triangle perimeter) can be represented by a single linear dimension. The abstract "shape" of a triangle induces a space that is inherently two-dimensional, and a number of alternative definitions of a basis for this space are examined. Within a plane, orientation reduces to rotation, and (after assignment of a reference direction for the triangle) can be represented by a single, spatially closed dimension. However, assignment of a reference direction for triangles possessing a k-fold rotational symmetry presents a significant challenge. Methods are described for characterizing shape and orientation of triangles, and for mapping these attributes onto a set of linear axes to form a combined index. The shape attribute is independent of size, orientation, and position, and the characterization of shape and orientation is stable with respect to small variations in the indexed triangles.},
	keywords = {database, databases;, dimension;spatial, geometry;database, hyperdimensional, index, index;single, index;triangle, indexing;query, linear, point;k-fold, processing;visual, relationships;structured, rotational, search;indexing, space;image, symmetry;point-based},
	doi = {10.1109/ICDE.2007.367939},
	author = {Cranston,C.B. and Samet, Hanan}
}
@conference {13188,
	title = {Detecting rotational symmetries},
	booktitle = {Computer Vision, 2005. ICCV 2005. Tenth IEEE International Conference on},
	volume = {2},
	year = {2005},
	month = {2005/10//},
	pages = {954 - 961 Vol. 2 - 954 - 961 Vol. 2},
	abstract = {We present an algorithm for detecting multiple rotational symmetries in natural images. Given an image, its gradient magnitude field is computed, and information from the gradients is spread using a diffusion process in the form of a gradient vector flow (GVF) field. We construct a graph whose nodes correspond to pixels in tire image, connecting points that are likely to be rotated versions of one another The n-cycles present in tire graph are made to vote for C<sub>n</sub> symmetries, their votes being weighted by the errors in transformation between GVF in the neighborhood of the voting points, and the irregularity of the n-sided polygons formed by the voters. The votes are accumulated at tire centroids of possible rotational symmetries, generating a confidence map for each order of symmetry. We tested the method with several natural images.},
	keywords = {axial, computational, detection;, field;, flow;, geometry;, gradient, graph, graph;, image, image;, magnitude, methods;, multiple, n-sided, object, polygons;, recognition;, rotational, symmetries;, symmetry;, theory;, tire, tyres;, vector},
	doi = {10.1109/ICCV.2005.71},
	author = {Shiv Naga Prasad,V. and Davis, Larry S.}
}
@conference {12725,
	title = {Shape and motion driven particle filtering for human body tracking},
	booktitle = {Multimedia and Expo, 2003. ICME {\textquoteright}03. Proceedings. 2003 International Conference on},
	volume = {3},
	year = {2003},
	month = {2003/07//},
	pages = {III - 61-4 vol.3 - III - 61-4 vol.3},
	abstract = {In this paper, we propose a method to recover 3D human body motion from a video acquired by a single static camera. In order to estimate the complex state distribution of a human body, we adopt the particle filtering framework. We present the human body using several layers of representation and compose the whole body step by step. In this way, more effective particles are generated and ineffective particles are removed as we process each layer. In order to deal with the rotational motion, the frequency of rotation is obtained using a preprocessing operation. In the preprocessing step, the variance of the motion field at each image is computed, and the frequency of rotation is estimated. The estimated frequency is used for the state update in the algorithm. We successfully track the movement of figure skaters in TV broadcast image sequence, and recover the 3D shape and motion of the skater.},
	keywords = {3D, body, broadcast, camera;, cameras;, estimation;, Filtering, framework;, human, image, MOTION, motion;, particle, processing;, rotational, sequence;, sequences;, signal, single, static, theory;, tracking;, TV, video},
	doi = {10.1109/ICME.2003.1221248},
	author = {Yamamoto, T. and Chellapa, Rama}
}
