Best fit an Ellipse from Imperfect Data and determine outer boundary as u show on this picture and this code ,I want the code achievement the plot in the figure

function ellipse_t = fit_ellipse( x,y,d,g )

% initialize

orientation_tolerance = 1e-3;

% empty warning stack

warning( '' );

% prepare vectors, must be column vectors

X=xlsread('Xiong',1,'G3:G584')

Y=xlsread('Xiong',1,'H3:H584')

x=X(:);

y=Y(:);

% remove bias of the ellipse - to make matrix inversion more accurate. (will be added later on).

mean_x = mean(x);

mean_y = mean(y);

x = x-mean_x;

y = y-mean_y;

% the estimation for the conic equation of the ellipse

X = [x.^2, x.*y, y.^2, x, y ];

a = sum(X)/(X'*X);

% check for warnings

if ~isempty( lastwarn )

disp( 'stopped because of a warning regarding matrix inversion' );

ellipse_t = [];

return

end

% extract parameters from the conic equation

[a,b,c,d,e] = deal( a(1),a(2),a(3),a(4),a(5) );

% remove the orientation from the ellipse

if ( min(abs(b/a),abs(b/c)) > orientation_tolerance )

orientation_rad = 1/2 * atan( b/(c-a) );

cos_phi = cos( orientation_rad );

sin_phi = sin( orientation_rad );

[a,b,c,d,e] = deal(...

a*cos_phi^2 - b*cos_phi*sin_phi + c*sin_phi^2,...

0,...

a*sin_phi^2 + b*cos_phi*sin_phi + c*cos_phi^2,...

d*cos_phi - e*sin_phi,...

d*sin_phi + e*cos_phi );

[mean_x,mean_y] = deal( ...

cos_phi*mean_x - sin_phi*mean_y,...

sin_phi*mean_x + cos_phi*mean_y );

else

orientation_rad = 0;

cos_phi = cos( orientation_rad );

sin_phi = sin( orientation_rad );

end

% check if conic equation represents an ellipse

test = a*c;

switch (1)

case (test>0), status = '';

case (test==0), status = 'Parabola found'; warning( 'fit_ellipse: Did not locate an ellipse' );

case (test<0), status = 'Hyperbola found'; warning( 'fit_ellipse: Did not locate an ellipse' );

end

% if we found an ellipse return it's data

if (test>0)

% make sure coefficients are positive as required

if (a<0), [a,c,d,e] = deal( -a,-c,-d,-e ); end

% final ellipse parameters

X0 = mean_x - d/2/a;

Y0 = mean_y - e/2/c;

F = 1 + (d^2)/(4*a) + (e^2)/(4*c);

[a,b] = deal( sqrt( F/a ),sqrt( F/c ) );

long_axis = 2*max(a,b);

short_axis = 2*min(a,b);

% rotate the axes backwards to find the center point of the original TILTED ellipse

R = [ cos_phi sin_phi; -sin_phi cos_phi ];

P_in = R * [X0;Y0];

X0_in = P_in(1);

Y0_in = P_in(2);

% pack ellipse into a structure

ellipse_t = struct( ...

'a',a,...

'b',b,...

'phi',orientation_rad,...

'X0',X0,...

'Y0',Y0,...

'X0_in',X0_in,...

'Y0_in',Y0_in,...

'long_axis',long_axis,...

'short_axis',short_axis,...

'status','' );

else

% report an empty structure

ellipse_t = struct( ...

'a',[],...

'b',[],...

'phi',[],...

'X0',[],...

'Y0',[],...

'X0_in',[],...

'Y0_in',[],...

'long_axis',[],...

'short_axis',[],...

'status',status );

end

% check if we need to plot an ellipse with it's axes.

%if (nargin>2) & ~isempty( axis_handle ) & (test>0)

% rotation matrix to rotate the axes with respect to an angle phi

R = [ cos_phi sin_phi; -sin_phi cos_phi ];

% the axes

ver_line = [ [X0 X0]; Y0+b*[-1 1] ];

horz_line = [ X0+a*[-1 1]; [Y0 Y0] ];

new_ver_line = R*ver_line;

new_horz_line = R*horz_line;

% the ellipse

theta_r = linspace(0,2*pi);

ellipse_x_r = X0 + a*cos( theta_r );

ellipse_y_r = Y0 + b*sin( theta_r );

xaligned_ellipse = [ellipse_x_r;ellipse_y_r];

rotated_ellipse = R * [ellipse_x_r;ellipse_y_r];

% draw

hold on

plot( rotated_ellipse(1,:),rotated_ellipse(2,:),'r' )

d=xlsread('Xiong',1,'G3:G584')

g=xlsread('Xiong',1,'H3:H584')

plot(d,g,'g')

xlabel('x')

ylabel('y');

title('target 4')

drawnow

ellipse_t.xaligned_ellipse = xaligned_ellipse;

ellipse_t.rotated_ellipse = rotated_ellipse;

ellipse_t.ellipse_x_r = ellipse_x_r;

ellipse_t.ellipse_y_r = ellipse_y_r;

ellipse_t.R = R;

end