@TechReport{Zimmermann-TR-2005-23, IS = { zkontrolovano 26 Jan 2006 }, UPDATE = { 2005-12-15 }, author = {Zimmermann, Karel and Svoboda, Tom{\'a}{\v s}}, title = {Approximation of Euclidean Distance between Point from Ellipse}, institution = {Center for Machine Perception, K13133 FEE Czech Technical University}, address = {Prague, Czech Republic}, year = {2005}, month = {August}, type = {Research Report}, number = {{CTU--CMP--2005--23}}, issn = {1213-2365}, pages = {4}, authorship = {50-50}, annote = {Efficient computation of Euclidean distance between point and ellipse is needed in many computer vision problems. The true Euclidean distance requires solving of quartic equation which may have up to four solutions, requiring the one with the minimum distance to be determined. To avoid the complexity of evaluating the true Euclidean distance, we propose an approximation measure. We first find transformation projecting the ellipse to the unit circle. The point is projected by the same transformation. Distance of the point from the unit circle is simple to compute. Finally, distance is reprojected to original space.}, keywords = {computer vision, distance approximation}, project = { 1ET101210407, Dur IG2003-2 062, CONEX GZ 45.535 }, psurl = {[PDF] }, }