ICP Docs #2964
ICP Docs #2964
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DumDereDum
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category: documentation
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Why is this documentation added to the rgbd module? I can see that ICP algorithm is implemented in the surface_matching module: https://docs.opencv.org/master/dc/d9b/classcv_1_1ppf__match__3d_1_1ICP.html I propose extracting this section to separate page and referring it in the rgbd and ICP descriptions. In order to do it you have to add a page to the |
modules/rgbd/doc/kinfu_icp.markdown
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| The Iterative closest point (ICP) function minimizes the PointToPlane Distance (PPD) between the corresponding points in two clouds of points and normals. | ||
| Specifically, it is the distance from the point ***P*** to the plane with the normal ***N*** in which the point ***Q*** located | ||
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| The main equetion, which it needs to minimize: |
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*equation
Need to add the notion about projective correspondence:
"Two points P and Q are considered correspondent if given current camera pose they are projected in the same pixel"
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*which needs to be minimized
modules/rgbd/doc/kinfu_icp.markdown
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| ***q*** - i'th point in the old cloud of points | ||
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| ***n*** - i'th normal in the old cloud of normals |
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*i'th normal in the point Q in the old point cloud
modules/rgbd/doc/kinfu_icp.markdown
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| ***ppd(...)***- is the distance ergo its formula is the dot product of (difference between ***p*** and ***q***) and (***n***): | ||
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| <img src="https://render.githubusercontent.com/render/math?math=dot(T_{p2q}(p)-q, n)=dot((R\cdot p+t)-q,n)=[(R\cdot p+t)-q]^{T}\cdot n"> |
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plus sign is not rendered here
modules/rgbd/doc/kinfu_icp.markdown
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| Where ***R*** - rotation, ***t*** - translation. | ||
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| We use the Gauss-Newton method for the minimization of function. | ||
| In the beginning, we will perform some mathematical operations: |
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It's better to say something like "Here's a formula we're going to minimize by changing R and t:"
modules/rgbd/doc/kinfu_icp.markdown
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| ***n*** - i'th normal in the old cloud of normals | ||
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| ***ppd(...)***- is the distance ergo its formula is the dot product of (difference between ***p*** and ***q***) and (***n***): |
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*is the point-to-plane distance ergo ...
| In the beginning, we will perform some mathematical operations: | ||
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| <img src="https://render.githubusercontent.com/render/math?math=E=\sum\left\|[(R\cdot p %2B t)-q]^{T}\cdot n\right\|_{2}"> | ||
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It's better to add something like this:
In Gauss-Newton method we do sequential steps by changing R and t in the direction of the function E decrease, i.e. in the direction of its gradient:
- At each step we approximate the function E linearly as its current value plus Jacobian matrix multiplied by delta x which is concatenated delta R and delta t vectors.
- We find delta R and delta t by solving the equation E_approx(delta_x) = 0
- We apply delta R and delta t to current Rt transform and proceed to next iteration
To linearize E, let's approximate it in infinitesimal neighborhood.
modules/rgbd/doc/kinfu_icp.markdown
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| <img src="https://render.githubusercontent.com/render/math?math=E = \sum \left \| [f(x, p) %2B p- q]^{T} \cdot n \right \|_{2}"> | ||
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| Let's find out differential of ***E***: |
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*E is mininal when its differential is zero:
4 participants
Pull Request Readiness Checklist
Add info about ICP algorithm in RGBD
See details at https://github.com/opencv/opencv/wiki/How_to_contribute#making-a-good-pull-request
Patch to opencv_extra has the same branch name.