annmarie kuzel geometric nets video

We review the recent progress in the design of efficient algorithms for various problems in geometric optimization. We present several techniques used to attack these problems, such as parametric searching, geometric alternatives to parametric searching, prune-and-search techniques for linear programming and related problems, and LP-type problems and their efficient solution. We then describe a wide range of applications of these and other techniques to numerous problems in geometric optimization, including facility location, proximity problems, statistical estimators and metrology, placement and intersection of polygons and polyhedra, and ray shooting and other query-type problems.

We first investigate the meaning of "statistical methods" for geometric inference based on image feature points. Tracing back the origin of feature uncertainty to image processing operations, we discuss the implications of asymptotic analysis in reference to "geometric fitting" and "geometric model selection" and point out that a correspondence exists between the standard statistical analysis and the geometric inference problem. Then, we derive the "geometric AIC" and the "geometric MDL" as counterparts of Akaike's AIC and Rissanen's MDL. We show by experiments that the two criteria have contrasting characteristics in detecting degeneracy