{"id":59332,"date":"2026-01-13T18:09:02","date_gmt":"2026-01-13T10:09:02","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/59332.html"},"modified":"2026-01-13T18:09:02","modified_gmt":"2026-01-13T10:09:02","slug":"%e7%82%b9%e4%ba%91%e9%85%8d%e5%87%86%e4%b9%8b-coloricp%e4%b8%ad%e5%85%ac%e5%bc%8f%e8%af%a6%e7%bb%86%e6%8e%a8%e5%af%bc","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/59332.html","title":{"rendered":"\u70b9\u4e91\u914d\u51c6\u4e4b-ColorICP\u4e2d\u516c\u5f0f\u8be6\u7ec6\u63a8\u5bfc"},"content":{"rendered":"

\u76f8\u5173\u5185\u5bb9： 1\u3001\u70b9\u4e91\u914d\u51c6\u4e4b-Colored Point Cloud Registration（ColorICP）<\/p>\n

\u4e00\u3001\u8ba1\u7b97\u68af\u5ea6<\/h2>\n

\u8ba1\u7b97\u68af\u5ea6 <\/p>\n

d<\/p>\n

p<\/p>\n

d_p<\/p>\n

<\/span><\/span>d<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u6700\u5c0f\u4e8c\u4e58\u76ee\u6807\u51fd\u6570\u4e3a：<\/p>\n

<\/p>\n

L<\/p>\n

(<\/p>\n

d<\/p>\n

p<\/p>\n

)<\/p>\n

=<\/p>\n

\u2211<\/p>\n

p<\/p>\n

\u2032<\/p>\n

\u2208<\/p>\n

N<\/p>\n

p<\/p>\n

(<\/p>\n

C<\/p>\n

p<\/p>\n

(<\/p>\n

f<\/p>\n

(<\/p>\n

p<\/p>\n

\u2032<\/p>\n

)<\/p>\n

\u2212<\/p>\n

p<\/p>\n

)<\/p>\n

\u2212<\/p>\n

C<\/p>\n

(<\/p>\n

p<\/p>\n

\u2032<\/p>\n

)<\/p>\n

)<\/p>\n

2<\/p>\n

\u2248<\/p>\n

\u2211<\/p>\n

p<\/p>\n

\u2032<\/p>\n

\u2208<\/p>\n

N<\/p>\n

p<\/p>\n

(<\/p>\n

C<\/p>\n

(<\/p>\n

p<\/p>\n

)<\/p>\n

+<\/p>\n

d<\/p>\n

p<\/p>\n

\u22a4<\/p>\n

(<\/p>\n

f<\/p>\n

(<\/p>\n

p<\/p>\n

\u2032<\/p>\n

)<\/p>\n

\u2212<\/p>\n

p<\/p>\n

)<\/p>\n

\u2212<\/p>\n

C<\/p>\n

(<\/p>\n

p<\/p>\n

\u2032<\/p>\n

)<\/p>\n

)<\/p>\n

2<\/p>\n

,<\/p>\n

(10)<\/p>\n

L(d_p) = \\\\sum_{p' \\\\in N_p} \\\\big(C_p(f(p') – p) – C(p')\\\\big)^2 \\\\approx \\\\sum_{p' \\\\in N_p} \\\\big(C(p) + d_p^\\\\top(f(p') – p) – C(p')\\\\big)^2, \\\\tag{10} <\/p>\n

<\/span><\/span>L<\/span>(<\/span>d<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>p<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2208<\/span>N<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>C<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>f<\/span>(<\/span>p<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>p<\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>C<\/span>(<\/span>p<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>)<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2248<\/span><\/span><\/span><\/span><\/span>p<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2208<\/span>N<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>C<\/span>(<\/span>p<\/span>)<\/span><\/span>+<\/span><\/span><\/span><\/span>d<\/span><\/span>p<\/span><\/span><\/span><\/span>\u22a4<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>f<\/span>(<\/span>p<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>p<\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>C<\/span>(<\/span>p<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>)<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span><\/span>(<\/span>10<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u540c\u65f6\u7ea6\u675f <\/p>\n

d<\/p>\n

p<\/p>\n

\u22a4<\/p>\n

n<\/p>\n

p<\/p>\n

=<\/p>\n

0<\/p>\n

d_p^\\\\top n_p = 0<\/p>\n

<\/span><\/span>d<\/span><\/span>p<\/span><\/span><\/span><\/span>\u22a4<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>n<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

\u5b9e\u73b0\u4ee3\u7801\u7247\u6bb5\u5982\u4e0b：<\/p>\n

for<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> frame::<\/span>size<\/span>(<\/span>*<\/span>frame)<\/span>;<\/span> i++<\/span>)<\/span> {<\/span>
\n \/\/ Estimate color gradient<\/span>
\n const<\/span> auto<\/span>&<\/span> point =<\/span> frame::<\/span>point<\/span>(<\/span>*<\/span>frame,<\/span> i)<\/span>;<\/span>
\n const<\/span> auto<\/span>&<\/span> normal =<\/span> frame::<\/span>normal<\/span>(<\/span>*<\/span>frame,<\/span> i)<\/span>;<\/span>
\n const<\/span> double<\/span> intensity =<\/span> frame::<\/span>intensity<\/span>(<\/span>*<\/span>frame,<\/span> i)<\/span>;<\/span><\/p>\n

Eigen::<\/span>Matrix<<\/span>double<\/span>,<\/span> –<\/span>1<\/span>,<\/span> 4<\/span>><\/span> A =<\/span> Eigen::<\/span>Matrix<\/span><<\/span>double<\/span>,<\/span> –<\/span>1<\/span>,<\/span> 4<\/span>><\/span>::<\/span>Zero<\/span>(<\/span>k_photo_neighbors,<\/span> 4<\/span>)<\/span>;<\/span>
\n Eigen::<\/span>VectorXd b =<\/span> Eigen::<\/span>VectorXd<\/span>::<\/span>Zero<\/span>(<\/span>k_photo_neighbors)<\/span>;<\/span><\/p>\n

\/\/ dp^T np = 0<\/span>
\n A.<\/span>row<\/span>(<\/span>0<\/span>)<\/span> =<\/span> normal;<\/span>
\n b[<\/span>0<\/span>]<\/span> =<\/span> 0.0<\/span>;<\/span><\/p>\n

\/\/ Intensity gradient in the tangent space<\/span>
\n for<\/span> (<\/span>int<\/span> j =<\/span> 1<\/span>;<\/span> j <<\/span> k_photo_neighbors;<\/span> j++<\/span>)<\/span> {<\/span>
\n const<\/span> int<\/span> index =<\/span> neighbors[<\/span>k *<\/span> i +<\/span> j]<\/span>;<\/span>
\n const<\/span> auto<\/span>&<\/span> point_ =<\/span> frame::<\/span>point<\/span>(<\/span>*<\/span>frame,<\/span> index)<\/span>;<\/span>
\n const<\/span> double<\/span> intensity_ =<\/span> frame::<\/span>intensity<\/span>(<\/span>*<\/span>frame,<\/span> index)<\/span>;<\/span>
\n const<\/span> Eigen::<\/span>Vector4d projected =<\/span> point_ –<\/span> (<\/span>point_ –<\/span> point)<\/span>.<\/span>dot<\/span>(<\/span>normal)<\/span> *<\/span> normal;<\/span>
\n A.<\/span>row<\/span>(<\/span>j)<\/span> =<\/span> projected –<\/span> point;<\/span>
\n b<\/span>(<\/span>j)<\/span> =<\/span> (<\/span>intensity_ –<\/span> intensity)<\/span>;<\/span>
\n }<\/span><\/p>\n

Eigen::<\/span>Matrix3d H =<\/span> (<\/span>A.<\/span>transpose<\/span>(<\/span>)<\/span> *<\/span> A)<\/span>.<\/span>block<\/span><<\/span>3<\/span>,<\/span> 3<\/span>><\/span><\/span><\/span>(<\/span>0<\/span>,<\/span> 0<\/span>)<\/span>;<\/span>
\n Eigen::<\/span>Vector3d e =<\/span> (<\/span>A.<\/span>transpose<\/span>(<\/span>)<\/span> *<\/span> b)<\/span>.<\/span>head<\/span><<\/span>3<\/span>><\/span><\/span><\/span>(<\/span>)<\/span>;<\/span>
\n gradients-><\/span>intensity_gradients[<\/span>i]<\/span> <<<\/span> H.<\/span>inverse<\/span>(<\/span>)<\/span> *<\/span> e,<\/span> 0.0<\/span>;<\/span>
\n }<\/span><\/p>\n

\u4e00\u3001\u7b26\u53f7\u4e0e\u80cc\u666f\u5148\u8bf4\u660e<\/h3>\n

\u4e0a\u9762\u516c\u5f0f10\u662f ColorICP\u4e2d\u5f3a\u5ea6\u68af\u5ea6\u4f30\u8ba1\u6216\u5149\u5ea6\u4e00\u81f4\u6027\u5efa\u6a21\u7684\u6807\u51c6\u5f62\u5f0f\u3002ColorICP<\/p>\n

1 \u70b9\u4e0e\u90bb\u57df<\/h4>\n