Question

MATLAB QUESTION

Implement Least squares fitting for linear line detection in MATLAB. Using Any input image, After detection you need to plot output line on the input image used (you can use MATLAB functions for this purpose)

Hint: find an appropriate input image and apply edge detection first. Then use MATLAB edge detector function and Implement Sobel edge detector.

Write a report about it (written codes need to be included as a text as well).

Answer 1

Solution:

A series of numbers are taken in 1D matrix x and corresponding functions in matrix y. They are plotted .Then the least square fitting method are used to find a approximate plot for the series based on the values of x,y matrices .The fitted curve is plotted which approximately follows the x,y matrix values.

%%------------------ MATLAB CODE ----------------------%%

%least square regression
x=[2 5 6 8 9 13 15];
y=[7 8 10 11 12 14 15];
plot(x,y,'k*')
xlabel('x');ylabel('y')
title('data points')
grid on
hold on
%% p=polyfit(X_R,Y_R,1)

Y_R=y';
X_R=x';
H=[];
%N=5 is used for best fit
N=5;
for idx=0:N
H=[H,X_R.^idx];
end
Astar=inv(H' *H)*H'*Y_R;
Ytilde=H*Astar;
R=sum((Y_R-Ytilde).^2);
plot(X_R,Ytilde,'r-','LineWidth',2)
%%------------------------ END -------------------------------%%

plot:

N.B: Please copy the code and save it in a mfile and simulate using MATLAB tool to have the best result.