121 lines
1.9 KiB
Plaintext
121 lines
1.9 KiB
Plaintext
#LyX 2.0 created this file. For more info see http://www.lyx.org/
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\lyxformat 413
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\begin_document
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\begin_header
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\textclass article
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\use_default_options true
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\maintain_unincluded_children false
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\language english
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\language_package default
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\papersize default
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\use_geometry true
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\use_amsmath 1
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\use_esint 1
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\cite_engine basic
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\use_bibtopic false
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\use_indices false
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\paperorientation portrait
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\suppress_date false
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\use_refstyle 1
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\index Index
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\shortcut idx
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\color #008000
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\end_index
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\leftmargin 1in
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\topmargin 1in
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\rightmargin 1in
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\bottommargin 1in
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\secnumdepth 3
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\tocdepth 3
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\end_header
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\begin_body
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\begin_layout Standard
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Derivative of EssentialMatrix epipolar error.
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\end_layout
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\begin_layout Standard
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With respect to orientation:
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\begin_inset Formula
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\[
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e(\omega)=a^{T}[t]_{\times}Re^{\omega}b=a^{T}Ee^{\omega}b
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\]
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\end_inset
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\begin_inset Formula
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\[
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\frac{\partial e(\omega)}{\partial v}=a^{T}E[b]_{\times}
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\]
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\end_inset
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\end_layout
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\begin_layout Standard
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With respect to tangent to sphere:
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\begin_inset Formula
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\[
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e(v)=a^{T}(Bv\times Rb)
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\]
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\end_inset
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\begin_inset Formula
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\[
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\frac{\partial e(v)}{\partial v}=a^{T}\frac{\partial(Bv\times Rb)}{\partial v}=a^{T}[-Rb]_{\times}B=a^{T}R[-b]_{\times}RB
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\]
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\end_inset
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\begin_inset Formula
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\[
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(1*3)(3*3)(3*2)
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\]
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\end_inset
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\end_layout
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\end_body
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\end_document
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