@conference {12650,
	title = {An algebraic approach to surface reconstruction from gradient fields},
	booktitle = {Computer Vision, 2005. ICCV 2005. Tenth IEEE International Conference on},
	volume = {1},
	year = {2005},
	month = {2005/10//},
	pages = {174 - 181 Vol. 1 - 174 - 181 Vol. 1},
	abstract = {Several important problems in computer vision such as shape from shading (SFS) and photometric stereo (PS) require reconstructing a surface from an estimated gradient field, which is usually non-integrable, i.e. have non-zero curl. We propose a purely algebraic approach to enforce integrability in discrete domain. We first show that enforcing integrability can be formulated as solving a single linear system Ax =b over the image. In general, this system is under-determined. We show conditions under which the system can be solved and a method to get to those conditions based on graph theory. The proposed approach is non-iterative, has the important property of local error confinement and can be applied to several problems. Results on SFS and PS demonstrate the applicability of our method.},
	keywords = {algebra;, algebraic, approach;, Computer, confinement;, discrete, domain, error, field;, from, gradient, graph, image, integrability;, linear, local, methods;, photometric, reconstruction;, shading;, SHAPE, stereo;, surface, system;, theory;, vision;},
	doi = {10.1109/ICCV.2005.31},
	author = {Agrawal,A. and Chellapa, Rama and Raskar, R.}
}
@article {17809,
	title = {Temporal probabilistic object bases},
	journal = {Knowledge and Data Engineering, IEEE Transactions on},
	volume = {15},
	year = {2003},
	month = {2003/08//july},
	pages = {921 - 939},
	abstract = {There are numerous applications where we have to deal with temporal uncertainty associated with objects. The ability to automatically store and manipulate time, probabilities, and objects is important. We propose a data model and algebra for temporal probabilistic object bases (TPOBs), which allows us to specify the probability with which an event occurs at a given time point. In explicit TPOB-instances, the sets of time points along with their probability intervals are explicitly enumerated. In implicit TPOB-instances, sets of time points are expressed by constraints and their probability intervals by probability distribution functions. Thus, implicit object base instances are succinct representations of explicit ones; they allow for an efficient implementation of algebraic operations, while their explicit counterparts make defining algebraic operations easy. We extend the relational algebra to both explicit and implicit instances and prove that the operations on implicit instances correctly implement their counterpart on explicit instances.},
	keywords = {algebra;, algebraic, bases;, constraints;, data, database, database;, databases;, distribution, explicit, functions;, handling;, implicit, instances;, integrity;, intervals;, management;, model;, models;, object, object-oriented, operations;, probabilistic, probability, probability;, relational, temporal, theory;, Uncertainty, uncertainty;},
	isbn = {1041-4347},
	doi = {10.1109/TKDE.2003.1209009},
	author = {Biazzo,V. and Giugno,R. and Lukasiewicz,T. and V.S. Subrahmanian}
}
