User:Moderately Sized Greg/sandbox: Difference between revisions

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== Estimation ==
 
Sequences of ordered images allow the estimation of motion as either instantaneous image velocities or discrete image displacements.<ref name="S. S. Beauchemin, J. L. Barron 1995" /> David J. Fleet and Yair Weiss provide a tutorial introduction to gradient based optical flow.<ref>{{Cite book |title=Handbook of Mathematical Models in Computer Vision |last1=Fleet |first1=David J. |last2=Weiss |first2=Yair |publisher=Springer |year=2006 |isbn=978-0-387-26371-7 |editor-last=Paragios |editor-first=Nikos |pages=237–257 |chapter=Optical Flow Estimation |editor-last2=Chen |editor-first2=Yunmei |editor-last3=Faugeras |editor-first3=Olivier D. |chapter-url=http://www.cs.toronto.edu/~fleet/research/Papers/flowChapter05.pdf}}</ref>
Fleet, along with John L. Barron, David J. Fleet, and Steven Beauchemin, also provideprovides a performance analysis of a number of optical flow techniques. It, emphasizesemphasizing the accuracy and density of measurements.<ref>{{Cite journal |last1=Barron |first1=John L. |last2=Fleet |first2=David J. |last3=Beauchemin |first3=Steven |name-list-style=amp |year=1994 |title=Performance of optical flow techniques |url=http://www.cs.toronto.edu/~fleet/research/Papers/ijcv-94.pdf |journal=International Journal of Computer Vision |volume=12 |pages=43–77 |citeseerx=10.1.1.173.481 |doi=10.1007/bf01420984|s2cid=1290100 }}</ref>
 
The optical flow methods try to calculate the motion between two image frames which are taken at times <math>t</math> and <math>t+\Delta t</math> at every [[voxel]] position. These methods are called differential since they are based on local [[Taylor series]] approximations of the image signal; that is, they use partial derivatives with respect to the spatial and temporal coordinates.