function?val?=?bilinear_interpolate（im?rc）

%BILINEAR_INTERPOLATE?performs?bilinear?interpolation.
%
%???val?=?bilinear_interpolate（im?rc）?returns?the?bilinearly?interpolated
%???pixel?values?at?the?given?list?of?positions?rc.
%
%???Input?arguments:
%???-?im?should?be?a?m-by-n-by-3?（colour）?image?or?a?m-by-n?（grey?scale）?image.
%???-?rc?should?be?a?2-by-k?matrix?where?k?is?the?number?of?positions
%?????whose?values?are?to?be?computed?via?bilinear?interpolation.??The?first
%?????row?of?the?matrix?should?contain?the?row-coordinates?and?the?second?row?the
%?????column-coordinates?of?these?positions.??It?is?important?that?all?the
%?????（rowcolumn）-positions?stored?in?the?matrix?rc?are?within?the?boundary
%?????of?the?image?im.
%
%???Output?argument:
%???-?val?is?the?output?k-by-3?（if?image?im?has?3?colour?bands）?or?k-by-1
%?????（if?image?im?is?a?grey?scale?image）?matrix?containing?the?interpolated?pixel
%?????values.
%
%Created?July?2002.
%Last?modified?September?2003.
%
%Copyright?Du?Huynh
%The?University?of?Western?Australia
%School?of?Computer?Science?and?Software?Engineering

nrows?=?size（im1）;??ncols?=?size（im2）;
%?number?of?bands?（3?for?coloured?images;?1?for?gray?scale?images）
nobands?=?size（im3）;

%?check?that?all?the?entries?in?matrix?rc?are?within?the?boundary?of?image?im.
if?sum（rc（1:）??nrows?|?rc（2:）??ncols）
???error（‘bilinear_interpolate:?elements?of?the?rc?matrix?must?be?within?the?image?boundary‘）;
end


%?The?four?corner?points?used?in?the?bilinear?interpolation:
%??c4??????c3
%??+--------+
%??|????????|
%??|?o??????|?????（a?point?o?which?is?stored?in?a?column?vector?of?rc
%??|????????|?????and?the?two?corner?points?used?for?its?bilinear?interpoation）
%??+--------+
%??c1??????c2
%?The?row-column?coordinate?system?is?used.??All?the?corner?points?c1?c2?c3
%?and?c4?are?two?vectors?whose?1st?components?contains?the?row?coordinates
%?and?2nd?components?contains?the?column?coordinates.

%?note?that?we?should?have?given?a?small?margin?for?variable?rc
%?so?that?the?four?corner?pixels?surrounding?rc?are?within?the
%?image?boundary?of?im.??This?condition?should?be?enforced?in?the
%?caller?of?this?function.
c4?=?（floor（rc））;
c2?=?（ceil（rc））;
c3?=?（[c4（1:）;?c2（2:）]）;
c1?=?（[c2（1:）;?c4（2:）]）;

%?d（diffRC_idx）?=?（rc（diffRC_idx）?-?c1）?./?（c4?-?c1?+?eps）;
%
%?the?interpolation?procedure?above?fails?for?those?points?in
%?rc?whose?x-?or?y-?component?is?a?whole?number?（in?which?case
%?the?respective?components?of?these?points?in?the?c1?and?c4?matrices
%?would?be?the?same.??the?formula?for?d?below?would?cause?a?division
%?by?zero?problem.
sameC_idx?=?find（c2（2:）?==?c4（2:））;
sameR_idx?=?find（c2（1:）?==?c4（1:））;
diffRC_idx?=?find（c2（1:）?~=?c4（1:）?&?c2（2:）?~=?c4（2:））;
%?now?the?formula?for?d?can?be?safely?applied...
d（:diffRC_idx）?=?（rc（:diffRC_idx）?-?c4（:diffRC_idx））?./?...
???（c2（:diffRC_idx）?-?c4（:diffRC_idx）?+?eps）;
d（2s

?屬性????????????大小?????日期????時間???名稱
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?????文件???????3888??2003-12-05?10:27??極線矯正_很有效\bilinear_interpolate.m

?????文件???????1584??2003-09-22?19:55??極線矯正_很有效\calib1.dat

?????文件??????31395??2002-07-16?17:26??極線矯正_很有效\calib1.jpg

?????文件???????1584??2003-09-22?19:55??極線矯正_很有效\calib2.dat

?????文件??????29239??2002-07-16?17:26??極線矯正_很有效\calib2.jpg

?????文件???????4247??2003-12-11?16:28??極線矯正_很有效\example.m

?????文件???????9290??2005-06-28?15:27??極線矯正_很有效\fundmatrix_nonlin.m

?????文件???????2242??2003-12-08?18:50??極線矯正_很有效\index.html

?????文件????????423??2003-12-11?16:23??極線矯正_很有效\in_range.m

?????文件?????921654??2000-11-03?18:05??極線矯正_很有效\j1.bmp

?????文件????????220??2003-09-20?00:30??極線矯正_很有效\j1.dat

?????文件?????921654??2000-11-03?18:05??極線矯正_很有效\j2.bmp

?????文件????????220??2003-09-20?00:30??極線矯正_很有效\j2.dat

?????文件???????1333??2003-12-11?16:23??極線矯正_很有效\kb_input.m

?????文件???????5738??2005-07-14?14:31??極線矯正_很有效\lmeds.m

?????文件???????6956??2005-07-13?10:46??極線矯正_很有效\lmeds_options.m

?????文件????????502??1999-04-28?16:24??極線矯正_很有效\pflat.m

?????文件???????1635??2003-12-11?16:28??極線矯正_很有效\rectification_angle.m

?????文件???????1993??2003-12-11?16:28??極線矯正_很有效\rectification_H.m

?????文件???????2492??2004-01-18?20:38??極線矯正_很有效\rectification_transf.m

?????文件???????3040??2012-12-26?14:34??極線矯正_很有效\rectify_im.asv

?????文件???????3040??2012-12-26?14:35??極線矯正_很有效\rectify_im.m

?????文件???????4339??2003-12-11?16:28??極線矯正_很有效\rectify_images.m

?????文件????????377??2003-12-02?17:29??極線矯正_很有效\skew.m

????..A.SH.?????16384??2013-01-16?20:34??極線矯正_很有效\Thumbs.db

?????目錄??????????0??2013-04-25?20:25??極線矯正_很有效

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