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Reformulate some sentences
Change-Id: I4841aa8e8522008dd816261d9ad98e5fb8ad1758
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@@ -1152,8 +1152,7 @@ their shape graphically. More details can be found in
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Theory
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------
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Let us consider a problem with a single problem and a single parameter
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block.
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Let us consider a problem with a single parameter block.
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.. math::
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@@ -1171,8 +1170,8 @@ where the terms involving the second derivatives of :math:`f(x)` have
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been ignored. Note that :math:`H(x)` is indefinite if
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:math:`\rho''f(x)^\top f(x) + \frac{1}{2}\rho' < 0`. If this is not
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the case, then its possible to re-weight the residual and the Jacobian
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matrix such that the corresponding linear least squares problem for
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the robustified Gauss-Newton step.
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matrix such that the robustified Gauss-Newton step corresponds to an
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ordinary linear least squares problem.
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Let :math:`\alpha` be a root of
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@@ -1193,7 +1192,7 @@ In the case :math:`2 \rho''\left\|f(x)\right\|^2 + \rho' \lesssim 0`,
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we limit :math:`\alpha \le 1- \epsilon` for some small
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:math:`\epsilon`. For more details see [Triggs]_.
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With this simple rescaling, one can use any Jacobian based non-linear
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With this simple rescaling, one can apply any Jacobian based non-linear
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least squares algorithm to robustified non-linear least squares
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problems.
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