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\contentsline {chapter}{\tocchapter {Chapter}{1}{Background}}{3}
\contentsline {section}{\tocsection {}{1}{Optical Flow}}{3}
\contentsline {subsection}{\tocsubsection {}{1.1}{Mutual Information}}{5}
\contentsline {subsection}{\tocsubsection {}{1.2}{Correlation Ratio}}{5}
\contentsline {subsection}{\tocsubsection {}{1.3}{Cross Correlation}}{6}
\contentsline {section}{\tocsection {}{2}{Setup of the camera rig}}{6}
\contentsline {section}{\tocsection {}{3}{Image Fusion}}{6}
\contentsline {section}{\tocsection {}{4}{Lie Groups and the Noether Theorem}}{8}
\contentsline {subsection}{\tocsubsection {}{4.1}{Motivation}}{8}
\contentsline {subsection}{\tocsubsection {}{4.2}{Lie Groups}}{9}
\contentsline {subsection}{\tocsubsection {}{4.3}{Noether's Theorem}}{11}
\contentsline {subsubsection}{\tocsubsubsection {}{4.3.1}{Motivation}}{11}
\contentsline {subsubsection}{\tocsubsubsection {}{4.3.2}{Noethers First Theorem}}{12}
\contentsline {subsubsection}{\tocsubsubsection {}{4.3.3}{Kepler's Two Body Problem}}{13}
\contentsline {section}{\tocsection {}{5}{Total Variation}}{13}
\contentsline {subsection}{\tocsubsection {}{5.1}{The Mean Curvature of Total Variation}}{15}
\contentsline {subsection}{\tocsubsection {}{5.2}{Image Denoising}}{15}
\contentsline {chapter}{\tocchapter {Chapter}{2}{Geometrical Prior}}{17}
\contentsline {section}{\tocsection {}{1}{The Generalized Structure Tensor}}{18}
\contentsline {subsection}{\tocsubsection {}{}{The Group $O\left (2\right )$}}{18}
\contentsline {subsection}{\tocsubsection {}{1.1}{The Transformation Properties of the GST}}{19}
\contentsline {section}{\tocsection {}{2}{Structure Tensor Based Prior}}{20}
\contentsline {subsection}{\tocsubsection {}{2.1}{Analysis of the Eigenvalues of the Rotation Dilation Group}}{21}
\contentsline {chapter}{\tocchapter {Chapter}{3}{Geometrical Optical Flow Model}}{23}
\contentsline {section}{\tocsection {}{1}{Disparity}}{23}
\contentsline {section}{\tocsection {}{2}{Localization}}{24}
\contentsline {section}{\tocsection {}{3}{The solution algorithm}}{26}
\contentsline {chapter}{\tocchapter {Chapter}{4}{Results}}{27}
\contentsline {section}{\tocsection {}{1}{Uni-Modal Data}}{27}
\contentsline {subsection}{\tocsubsection {}{1.1}{Middleburry Dataset}}{27}
\contentsline {section}{\tocsection {}{2}{Eigenvalue analysis and the stabilization parameter $\lambda _2$}}{29}
\contentsline {chapter}{\tocchapter {Chapter}{5}{Multimodal Optical Flow}}{37}
\contentsline {section}{\tocsection {}{1}{Estimation of the resolution parameter $\sigma $}}{37}
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