function?[HHnorminv_Hnorm]?=?compute_homography（mM）
?
%compute_homography?
%?
%[HHnorminv_Hnorm]?=?compute_homography（mM）?
%?
%Computes?the?planar?homography?between?the?point?coordinates?on?the?plane?（M）?and?the?image?
%point?coordinates?（m）.?
%?
%INPUT:?m:?homogeneous?coordinates?in?the?image?plane?（3xN?matrix）?
%???????M:?homogeneous?coordinates?in?the?plane?in?3D?（3xN?matrix）?
%?
%OUTPUT:?H:?Homography?matrix?（3x3?homogeneous?matrix）?
%????????Hnorm:?Normalization?matrix?used?on?the?points?before?homography?computation?
%???????????????（useful?for?numerical?stability?is?points?in?pixel?coordinates）?
%????????inv_Hnorm:?The?inverse?of?Hnorm?
%?
%Definition:?m?~?H*M?where?“~“?means?equal?up?to?a?non?zero?scalar?factor.?
%?
%Method:?First?computes?an?initial?guess?for?the?homography?through?quasi-linear?method.?
%????????Then?if?the?total?number?of?points?is?larger?than?4?optimize?the?solution?by?minimizing?
%????????the?reprojection?error?（in?the?least?squares?sense）.?
%?
%?
%Important?functions?called?within?that?program:?
%?
%comp_distortion_oulu:?Undistorts?pixel?coordinates.?
%?
%compute_homography.m:?Computes?the?planar?homography?between?points?on?the?grid?in?3D?and?the?image?plane.?
%?
%project_points.m:?Computes?the?2D?image?projections?of?a?set?of?3D?points?and?also?returns?te?Jacobian?
%??????????????????matrix?（derivative?with?respect?to?the?intrinsic?and?extrinsic?parameters）.?
%??????????????????This?function?is?called?within?the?minimization?loop.?
Np?=?size（m2）;?
?
if?size（m1）<3?
???m?=?[m;ones（1Np）];?
end;?
?
if?size（M1）<3?
???M?=?[M;ones（1Np）];?
end;?
?
?
m?=?m?./?（ones（31）*m（3:））;?
M?=?M?./?（ones（31）*M（3:））;?
?
%?Prenormalization?of?point?coordinates?（very?important）:?
%?（Affine?normalization）?
?
ax?=?m（1:）;?
ay?=?m（2:）;?
?
mxx?=?mean（ax）;?
myy?=?mean（ay）;?
ax?=?ax?-?mxx;?
ay?=?ay?-?myy;?
?
scxx?=?mean（abs（ax））;?
scyy?=?mean（abs（ay））;?
?
?
Hnorm?=?[1/scxx?0?-mxx/scxx;0?1/scyy?-myy/scyy;0?0?1];?
inv_Hnorm?=?[scxx?0?mxx?;?0?scyy?myy;?0?0?1];?
?
mn?=?Hnorm*m;?
?
%?Compute?the?homography?between?m?and?mn:?
?
%?Build?the?matrix:?
?
L?=?zeros（2*Np9）;?
?
L（1:2:2*Np1:3）?=?M‘;?
L（2:2:2*Np4:6）?=?M‘;?
L（1:2:2*Np7:9）?=?-（（ones（31）*mn（1:））.*?M）‘;?
L（2:2:2*Np7:9）?=?-（（ones（31）*mn（2:））.*?M）‘;?
?
if?Np?>?4?
	L?=?L‘*L;?
end;?
?
[USV]?=?svd（L）;?
?
hh?=?V（:9）;?
hh?=?hh/hh（9）;?
?
Hrem?=?reshape（hh33）‘;?
%?Final?homography:??
H?=?inv_Hnorm*Hrem;?
?
if?0?
???m2?=?H*M;?
???m2?=?[m2（1:）./m2（3:）?;?m2（2:）./m2（3:）];?
???merr?=?m（1:2:）?-?m2;?
end;?
?
%keyboard;?
??
%%%?Homography?refinement?if?there?are?more?than?4?points:?
?
if?Np?>?4?
????
???%?Final?refinement:?
???hhv?=?reshape（H‘91）;?
???hhv?=?hhv（1:8）;?
????
???for?iter=1:10?
???????	mrep?=?H?*?M;??
		J?=?zeros（2*Np8）;??
		MMM?=?（M?./?（ones（31）*mrep（3:）））;?
?
		J（1:2:2*Np1:3）?=?-MMM‘;?
		J（2:2:2*Np4:6）?=?-MMM‘;?
		?
		mrep?=?mrep?./?

?屬性????????????大小?????日期????時(shí)間???名稱
-----------?---------??----------?-----??----
?????目錄???????????0??2018-10-18?22:52??單目測(cè)量\
?????文件?????2560685??2018-10-18?20:58??單目測(cè)量\1.jpg
?????文件?????2914215??2018-10-18?22:34??單目測(cè)量\2.jpg
?????文件????????3818??2018-10-18?22:50??單目測(cè)量\compute_homography.m
?????文件?????????793??2007-10-03?16:34??單目測(cè)量\homography.m
?????文件????????1114??2018-10-23?21:45??單目測(cè)量\zuoye1.m