How to perform robust line fitting in a binary image

9 次查看(过去 30 天)
I am going to find the the best line for a binary image display below. When I use curve fitting functions, i.e., polyval or robustfit, both fail to give desire results. The ideal line would be close a vertical line passing these pixels at most.
:

采纳的回答

Rik
Rik 2020-3-25
They key is in how you define what a good fit is. The code below uses the root-mean-square of the orthogonal distance between all points and the line as the cost function. The code below needs my point_to_line_distance function, which you can find here on the FEX.
im=imread('image.png');
im=mean(im,3)>240;
[y,x]=find(flipud(im));
p_best=fit_line(x,y);
p_poly=polyfit(x,y,1);%polyfit for reference
x_bounds=[1 size(im,2)];
figure(1),clf(1)
subplot(1,2,1)
imshow(im)
subplot(1,2,2)
plot(x,y,'.','DisplayName','data'),hold on
plot(x_bounds,polyval(p_best ,x_bounds),'k--',...
'DisplayName',sprintf('R^2=%.2f (fit_line)',get_r_square(p_best ,x,y)))
plot(x_bounds,polyval(p_poly ,x_bounds),'r--',...
'DisplayName',sprintf('R^2=%.2f (polyfit)',get_r_square(p_poly ,x,y)))
hold off
axis equal
axis([1 size(im,2) 1 size(im,1)])
legend('Location','northeastoutside')
function p=fit_line(x,y)
%Fit a line to the data. Use the RMS of the orthogonal distance as a cost
%function instead of MSE_y, as polyfit probably does.
%
%This works with fminsearch, which is sensitive to initial values that are
%far from the optimum, sometimes returning local optima.
x=x(:);y=y(:);
pt=[x y];
%root mean square of the distance between the line defined by the two
%points in v and the points defined by x and y.
RMS=@(x) sqrt(mean(x.^2));
cost_fun=@(v) RMS(point_to_line_distance(pt, v([1 3]), v([2 4])));
%convert [x1 y1 phi2] to [x1 y1 x2 y2]
vr_2_v=@(vr) [vr(1:2) vr(1:2)+[cos(vr(3)) sin(vr(3))]];
%wrap the cost function and the converter
fun=@(vr) cost_fun(vr_2_v(vr));
%initialize to around the center of the data
init=[mean(x) mean(y) 0*pi];
%execute fit
opts = optimset('MaxFunEvals',50000, 'MaxIter',10000);
fit_val = fminsearch(fun, init, opts);
tmp=vr_2_v(fit_val);
p=polyfit(tmp(1:2),tmp(3:4),1);
end
function r2=get_r_square(p,x,y_real)
y_fit=polyval(p,x);
err=y_real-y_fit;
SSres=sum(err.^2);
SStot=sum((y_real-mean(y_real)).^2);
r2=1-(SSres./SStot);
end

更多回答(0 个)

类别

Help CenterFile Exchange 中查找有关 Get Started with Curve Fitting Toolbox 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by