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camera.m
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camera.m
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%% camera class - a distorted camera model.
%
% This class is an implementation of a distorted camera model.
% Note: Uses <http://docs.opencv.org/modules/calib3d/doc/camera_calibration_and_3d_reconstruction.html the same distorted camera model as opencv>.
%
%
% camera properties:
% imgsz - size of image in pixels [#rows, #columns]
% f - focal length in pixel units (two element vector [fx,fy])
% c - camera center in pixel coordinates (two element vector: [cx,cy])
% k - radial distortion coefficients. (six element vector: [k1-k6])
% p - tangential distortion coefficients (two element vector: [p1,p2])
% xyz - world coordinates of camera.
% viewdir - [yaw,pitch,roll]. Yaw: rotation about z (0=looking east)
% Pitch: look up/down angle
% Roll: camera roll (horizon tilt).
%
% camera Dependent/derived properties:
% (i.e. properties calculated from the camera parameters)
% R - camera rotation matrix calculated from camera view
% direction (read only)
% fullmodel - a 20-element vector containing all camera properties.
% [camx,camy,camz,imgszy,imgszx,viewdiryaw,viewdirpitch,viewdirroll,fx,fy,cx,cy,k1-6,p1-2]
%
% camera Methods:
% camera - constructor
% optimizecam - optimize the camera to mimimize misfit between
% projected world coordinates and pixel coordinates.
% project - project world coordinates to image coordinates (3d->2d)
% invproject - project image coordinates to world coordinates (2d->3d)
%
%
% ImGRAFT - An image georectification and feature tracking toolbox for MATLAB
% Copyright (C) 2014 Aslak Grinsted (<www.glaciology.net glaciology.net>)
% Permission is hereby granted, free of charge, to any person obtaining a copy
% of this software and associated documentation files (the "Software"), to deal
% in the Software without restriction, including without limitation the rights
% to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
% copies of the Software, and to permit persons to whom the Software is
% furnished to do so, subject to the following conditions:
%
% The above copyright notice and this permission notice shall be included in
% all copies or substantial portions of the Software.
%
% THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
% IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
% FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
% AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
% LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
% OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
% THE SOFTWARE.
classdef camera
properties
xyz = [0 0 0]; %world coordinates of camera;
imgsz = [100 100]; %size of image in pixels [#rows, #columns] Note: swapped xy
viewdir = [0 0 0]; %view direction: yaw/pitch/roll. Yaw: rotation about z (0=looking east) | Pitch: look up/down angle | Roll: camera roll (horizon tilt)
f = [5000 5000]; %focal length (two element vector).
c = [50 50]; %camera center in pixel coordinates
k = [0 0 0 0 0 0]; %k1-k6: radial distortion coefficients.
p = [0 0]; %p1-p2: tangential distortion coefficients
end
properties (Dependent)
% Camera rotation matrix calculated from viewdir. (read-only)
R
% All camera properties serialized into a 20 element vector.
% fullmodel=[camx,camy,camz,imgszy,imgszx,viewdiryaw,viewdirpitch,viewdirroll,fx,fy,cx,cy,k1-6,p1-2]
% Remark: Setting does not validate inputs!
fullmodel
end
methods
function cam = camera(varargin)
%This is the camera constructor
%
%There are three ways of constructing a new camera object:
%
% 1. specifying all camera properties in the constructor:
% cam = camera(xyz,imgsz[,viewdir,f,c,k,p])
%
% 2. Use the default camera and then modifying the camera properties
% cam = camera()
% cam.viewdir = [pi 0 0]; %look west.
%
% 3. provide a "<a href="matlab:help camera.fullmodel">fullmodel</a>" specifying all the camera
% properties in a single 20-element vector.
% (beware: no error checking).
% cam = camera([1 1 0 1024 768 pi 0 0 1000 1000 512 384 0 0 0 0 0 0 0 0])
%
if nargin==0, return, end
if nargin==1
cam.fullmodel=varargin{1};
return
end
if nargin<7,varargin{7}=[];end;
cam.xyz = varargin{1};
cam.imgsz = varargin{2};
cam.viewdir=varargin{3};
cam.f=varargin{4};
cam.c=varargin{5};
cam.k=varargin{6};
cam.p=varargin{7};
if length(cam.imgsz)<2, error('malformed image size.'); end
cam.imgsz(3:end)=[];
cam.f(end+1:2)=cam.f(end);
if isempty(cam.c), cam.c=(cam.imgsz([2 1])+1)/2; end
cam.k(end+1:6)=0;
cam.p(end+1:2)=0;
end
function value = get.R(cam)
%Camera rotation matrix calculated from viewdir
C = cos( cam.viewdir ); S = sin( cam.viewdir );
value = [S(3).*S(2).*C(1)-C(3).*S(1) , S(3).*S(2).*S(1) + C(3).*C(1) , S(3).*C(2); C(3).*S(2).*C(1) + S(3).*S(1), C(3).*S(2).*S(1) - S(3).*C(1) , C(3).*C(2); C(2).*C(1) , C(2).*S(1) , -S(2)];
value(1:2,:)=-value(1:2,:);
end
function value = get.fullmodel(cam)
value=[cam.xyz,cam.imgsz,cam.viewdir,cam.f,cam.c,cam.k,cam.p];
end
function cam = set.fullmodel(cam,value)
cam.xyz=value(1:3); cam.imgsz=value(4:5); cam.viewdir=value(6:8); cam.f=value(9:10);
cam.c=value(11:12); cam.k=value(13:18); cam.p=value(19:20);
end
function [uv,depth,inframe]=project(cam,xyz)
% project the xyz world coordinates into image coordinates (uv)
%
% [uv,depth,inframe]=cam.project(xyz)
%
% Inputs:
% xyz: world coordinates
%
% Outputs:
% uv: pixel coordinates in image
% depth: view depth
% inframe: boolean vector containing whether each projected
% 3d point is inside the frame.
%
if size(xyz,2)>3
xyz=xyz';
end
xyz=bsxfun(@minus,xyz,cam.xyz);
xyz=xyz*cam.R';
xy=bsxfun(@rdivide,xyz(:,1:2),xyz(:,3));
if any(cam.k~=0)||any(cam.p~=0) %TODO:optimize further
r2=sum(xy.^2,2);
r2(r2>4)=4;
if any(cam.k(3:6)~=0)
a=(1+cam.k(1)*r2+cam.k(2)*r2.^2+cam.k(3)*r2.^3)./(1+cam.k(4)*r2+cam.k(5)*r2.^2+cam.k(6)*r2.^3);
else
a=(1+cam.k(1)*r2+cam.k(2)*r2.^2+cam.k(3)*r2.^3);
end
xty=xy(:,1).*xy(:,2);
xy=[a.*xy(:,1)+2*cam.p(1)*xty+cam.p(2)*(r2+2*xy(:,1).^2), a.*xy(:,2)+2*cam.p(1)*xty+cam.p(2)*(r2+2*xy(:,2).^2)];
end
uv=[cam.f(1)*xy(:,1)+cam.c(1) cam.f(2)*xy(:,2)+cam.c(2)];
uv(xyz(:,3)<=0,:)=nan;
if nargout>1
depth=xyz(:,3);
end
if nargout>2
inframe=(depth>0)&(uv(:,1)>=1)&(uv(:,2)>=1)&(uv(:,1)<=cam.imgsz(2))&(uv(:,2)<=cam.imgsz(1)); %todo: additional constraint for negative k1 and r2>1. (See orthorectification example)
end
end
function xyz=invproject(cam,uv,X,Y,Z,xy0)
% Inverse projection from 2d to 3d coordinates. (pixel->world)
%
% There are 3 ways to call this method:
%
% 1. Return a set of world coordinates which when projected
% results in the pixel coordinates (uv).
%
% xyz=cam.invproject(uv)
%
%
% 2. Inverse projection constrained to DEM surface.
% (Project DEM to camera-view and use interpolation to find xyz.)
%
% xyz=cam.invproject(uv,X,Y,Z)
%
%
% 3. Minimize misfit between projected DEM point and UV. (least squares)
%
% xyz=cam.invproject(uv,X,Y,Z,xy0)
%
%
%
% Inputs:
% uv: 2 column matrix with pixel coordinates.
% [X,Y,Z]: DEM. (X,Y expected to be consistent with output from meshgrid.)
% [xy0]: initial guess of some xy points on the DEM which are
% consistent with pixel coordinates in uv.
%
% Outputs:
% xyz: 3-column matrix with world coordinates consistent with
% pixel coordinates in uv.
%
%
nanix=any(isnan(uv),2);
anynans=any(nanix);
if anynans
uv(nanix,:)=[];
end
if nargin==2
%first an exact calculation based on non-distorted model...
depth=1000;
xyz=[(uv(:,1)-cam.c(1))/cam.f(1) (uv(:,2)-cam.c(2))/cam.f(2)]*depth;
xyz(:,3)=depth;
xyz=xyz*cam.R;
xyz=bsxfun(@plus,xyz,cam.xyz);
%then tune that so that it is consistent with distorted model
if any(cam.k~=0)||any(cam.p~=0)
E=[1 0 0;0 1 0]*cam.R; % perturb in these directions.
for ii=1:size(uv,1)
nxyz=@(m)xyz(ii,:)+m'*E;
%misfit=@(m)sum((cam.project(nxyz(m))-uv(ii,:)).^2);
%m=fminsearch(misfit,[0 0]); %THIS REQUIRES A TOOLBOX!!!
misfitlm=@(m)(cam.project(nxyz(m))-uv(ii,:))'.^2;
m=LMFnlsq(misfitlm,[0;0]);
xyz(ii,:)=nxyz(m);
end
end
else
visible=voxelviewshed(X,Y,Z,cam.xyz);
Z=Z./visible;
xyz=nan(size(uv,1),3);
if nargin<6
[uv0,~,inframe]=cam.project([X(visible(:)),Y(visible(:)),Z(visible(:))]);
uv0(:,3)=X(visible(:));
uv0(:,4)=Y(visible(:));
uv0(:,5)=Z(visible(:));
uv0=uv0(inframe,:);
if exist('scatteredInterpolant','file')>1
Xscat=scatteredInterpolant(uv0(:,3),uv0(:,4),uv0(:,3));
Xscat.Points=uv0(:,1:2);
Yscat=Xscat; Yscat.Values=uv0(:,4);
Zscat=Xscat; Zscat.Values=uv0(:,5);
else
%fallback for older versions of matlab.
Xscat=TriScatteredInterp(uv0(:,3),uv0(:,4),uv0(:,3)); %#ok<REMFF1>
Xscat.X=uv0(:,1:2);
Yscat=Xscat; Yscat.V=uv0(:,4);
Zscat=Xscat; Zscat.V=uv0(:,5);
end
xy0=[Xscat(uv(:,1),uv(:,2)) Yscat(uv(:,1),uv(:,2)) Zscat(uv(:,1),uv(:,2))];
xyz=xy0;
if anynans
xyz(find(~nanix),:)=xyz; %find necessary because it ensures that xyz can grow.
xyz(find(nanix),:)=nan;
end
return
end
if Y(2,2)<Y(1,1)
X=flipud(X);Y=flipud(Y);Z=flipud(Z);
end
if X(2,2)<X(1,1)
X=fliplr(X);Y=fliplr(Y);Z=fliplr(Z);
end
if exist('griddedInterpolant','file')>1
zfun=griddedInterpolant(X',Y',Z'); %TODO: improve robustness.
else
%fallback for older versions of matlab. slower
zfun=@(x,y)interp2(X,Y,Z,x,y);
end
for ii=1:length(uv)
%misfit=@(xy)sum((cam.project([xy zfun(xy(1),xy(2))])-uv(ii,1:2)).^2);
misfitlm=@(xy)(cam.project([xy(:)' zfun(xy(1),xy(2))])-uv(ii,1:2))'.^2;
try
%[xyz(ii,1:2),err]=fminunc(misfit,xy0(ii,1:2),optimset('LargeScale','off','Display','off','TolFun',0.001)); %TODO: remove dependency. can i use LMFnlsq?
xyz(ii,1:2)=LMFnlsq(misfitlm,xy0(ii,1:2));
xyz(ii,3)=zfun(xyz(ii,1),xyz(ii,2));
if sum(misfitlm(xyz(ii,1:2)))>2^2
xyz(ii,:)=nan; %do not accept greater than 2 pixel error.
end
catch
end
end
end
if anynans
xyz(find(~nanix),:)=xyz; %find necessary because it ensures that xyz can grow.
xyz(find(nanix),:)=nan;
end
end
function [result,rmse,AIC]=optimizecam(cam,xyz,uv,freeparams)
% Tune the camera so that projecting xyz results in uv (least squares)
%
% [newcamera,rmse,AIC]=cam.optimizecam(xyz,uv,freeparams)
%
%
% If uv has three columns then the third column is interpreted as a
% weight in the misfit function.
%
%
% INPUTS:
% xyz: world coordinates.
% uv: target pixel coordinates.
% [optional 3rd column may specify weights]
% freeparams: a 20-element vector describing which camera
% parameters should be optimized. Follows same order as
% cam.fullmodel.
%
% OUTPUTS:
% newcamera: the optimized camera.
% rmse: root-mean-square-error
% aic: Akaike information criterion which can be used to
% help in determining an appropriate degree of complexity
% for the camera model (i.e. avoiding overfitting). [only
% strictly applicable for unweighted fitting]
%
% EXAMPLE:
% %optimize the three view direction parameters.
% %viewdir are the 6-8 columns in the <a href="matlab:help camera.fullmodel">camera.fullmodel</a>.
% [newcamera,rmse,AIC] = cam.optimizecam(xyz,uv,'00000111000000000000')
%
%
nanrows=any(isnan(xyz),2)|any(isnan(uv),2);
xyz(nanrows,:)=[];
uv(nanrows,:)=[];
fullmodel0=cam.fullmodel; %this describes the initial camera that is being perturbed.
freeparams=~(freeparams(:)==0|freeparams(:)=='0')'; %convert to bools
paramix=find(freeparams);
Nfree=length(paramix);
mbest=zeros(1,Nfree);
newcam=@(m)camera( fullmodel0 + sparse(ones(1,Nfree),paramix,m,1,length(fullmodel0)) );
if size(uv,2)==3
misfit=@(m)reshape((project(newcam(m),xyz)-uv(:,1:2)).*uv(:,[3 3]),[],1);%weighted least squares
else
misfit=@(m)reshape(project(newcam(m),xyz)-uv,[],1);
end
if isnan(misfit(mbest))
error('All GCPs must be infront of the initial camera location for optimizecam to work.'); %TODO: write better explanation. and remove requirement.
end
[mbest,RSS]=LMFnlsq(misfit,mbest); %WORKS SUPER FAST
Nuv=size(uv,1);
rmse=sqrt(RSS/Nuv);
AIC=numel(uv)*log(RSS/numel(uv)) + 2*Nfree;
result=newcam(mbest);
end
end % methods
end % classdef