I am trying to follow this example from Matlab about coloring scatter points as a rainbow, while the x-position of the points is progressing towards the right side.
Here under "Vary Circle Color":
https://de.mathworks.com/help/matlab/ref/scatter.html
x = linspace(0,3*pi,200);
y = cos(x) + rand(1,200);
c = linspace(1,10,length(x));
scatter(x,y,[],c)
While c as a variable goes from 1 to 20 with 200 interpolations. I am trying to replicate this for my piece of code, but I keep getting random color and the x-axis isn't matching the rainbow distribution as this:
g = 6;
pt_x = [0, g, -g];
pt_y = [g, -g, -g];
sz = 10;
loop = 100;
% var(1, loop) = 0;
% c = linspace(-10,10,length(var));
% c = 1:loop;
c = -loop/2:1:loop/2 -1;
rand_x = randi([-g,g],1,1);
rand_y = randi([-g,g],1,1);
for i = 1:loop
r = randi([1,3],1,1);
x1 = (rand_x + pt_x(r)) / 2;
y1 = (rand_y + pt_y(r)) / 2;
seq_x(1, i) = x1;
seq_y(1, i) = y1;
rand_x = x1;
rand_y = y1;
end
scatter(seq_x, cos(seq_x),[],c, 'filled');
What am I missing here exactly? I would appreciate any help!
Expected to get a rainbow pattern
It resulted in a random pattern
I work to about missile routing. I calculated throuhout the flight x,y,z coordinates of missile . I have data set about missile x,y,z coordinates. My goal is to move the servo motor according to x, y, z coordinates.
My input is 3-dimensional(x,y,z). I want to simulate in two dimensions. And for this I use vectoral calculation. The servo motor can take values between 0-1. But the result larger than 1 . When the results are reduced at the same rate, result is smaller than 0. But I get still the error
Undefined function 'writePosition' for input arguments of type 'matlab.graphics.chart.primitive.Surface'.
I will be grateful if you could help me.
My data example:
missile_x = 0.015
missile_y = 0.054
missile_z = 0.254
missile_flight = 0.00018794
My flight rotation code:
missile_x = vpa(Xval{id}(k)/10,5)
missile_y = vpa(Yval{id}(k)/10,5)
missile_z = vpa(Zval{id}(k)/10,5)
missile_flight = vpa(0.00555556*(missile_x^2+missile_y^2+missile_z^2)^1/2,5)
writePosition(s, missile_flight);
current_pos = readPosition(s);
current_pos = current_pos*missile_flight;
fprintf('Current motor position is %d degrees\n', current_pos);
pause(2);
Missile X,Y,Z calculation code:
dt = 0.005; %time step
g = 9.81; %gravity
ro = 1.2; %air density
A = pi*(0.2)^2; % reference area
Vmag = 0; % missile velocity vectoral value [m/sn]
t = 0;
T(1) = t;
U(1) = 0; %the missile is initially at rest at t = 0; So the velocity is 0
V(1) = 0;
W(1) = 0;
X(1) = X0;
Y(1) = Y0;
Z(1) = Z0;
n = 1;
h = interp2(x_terrain, y_terrain, h_terrain,X(1), Y(1));
while (Z(n) >= h)
[Thx, Thy, Thz] = thrust(t, Thmag0, theta, phi, Tburn, U(n), V(n), W(n));
Vmag = (U(n)^2 + V(n)^2 + W(n)^2)^(1/2);
Thmag = (Thx^2 + Thy^2 + Thz^2)^(1/2);
m = mass(t, m0, mf, Tburn);
[rho,sound_speed] = atmosphere(Z(n));
Cd = drag_coeff(Vmag,sound_speed);
U(n+1) = U(n) + (Thx/m - (Cd*rho*A/(2*m))*(U(n)*(U(n)^2+V(n)^2+W(n)^2)^(1/2)))*dt;
V(n+1) = V(n) + (Thy/m - (Cd*rho*A/(2*m)*(V(n)*(U(n)^2+V(n)^2+W(n)^2)^(1/2))))*dt;
W(n+1) = W(n) + (Thz/m - (Cd*rho*A/(2*m))*(W(n)*(U(n)^2+V(n)^2+W(n)^2)^(1/2)) - g)*dt;
X(n+1) = X(n) + U(n+1)*dt;
Y(n+1) = Y(n) + V(n+1)*dt;
Z(n+1) = Z(n) + W(n+1)*dt;
h = interp2(x_terrain, y_terrain, h_terrain, ...
X(end), Y(end));
t = t + dt;
T(n+1) = t;
n = n+1 ;
end
Tval = T;
Xval = X;
Yval = Y;
Zval = Z;
I have to draw a hipsometric map on a 3D plot. I have two vectors 1x401 (named xLabels and yLabels) which are the geo coordinates, and401x401(namedA`) matrix with the altitude data. To plot the data I use:
surf(xLabels, yLabels,A,'EdgeColor','None','Marker','.');
which leads to something like that:
But i would like to have something like that:
On the second image, only the surface is plotted, while my image looks like pillars.
I tried even make my vectors to 401x401 using meshgrid but it did not have any effect.
Do you have any idea what I should change?
#EDIT
I checked for X and Y data. I quess is too small interval (0.0083), but when i try plot good second of upper plots with same interval it draws correctly.
#EDIT2:
sizeX = 4800;
sizeY = 6000;
pixdegree = 0.0083; % 1 pixel is 0.0083 degree on map
intSize = 2;
lon = 37 + (35/60);
lat = 55+ (45/60);
fDEM = 'E020N90';
fHDR = 'E020N90.HDR';
[startXY, endXY] = calcFirstPixel(lon, lat); %calc borders for my area
f = fopen('E020N90.DEM');
offset = (startXY(1,2)*sizeX*intSize)+(startXY(1,1)*intSize);
fseek(f, offset,0); %seek from curr file pos
x = 0;
A = [];
BB = [];
jump = (intSize*sizeX)-(401*2);
while x<401
row = fread(f, 802);
fseek(f, jump, 0); %jump 2 next row
A = [A row];
x = x+1;
end
fclose(f);
A = A';
A = A(:,2:2:802);
m1 = min(A(:)); %wartość minimalna dla naszej podziałki
m2 = max(A(:)); %wartość maksymalna dla naszej podziałki
step = m2/8; % będzie 8 kolorów
highScale = m1:step:m2-step; %wartości graniczne dla każdego z nich
%handles.axes1 = A;
colormap(hObject, jet(8));
startXtick = 20 + pixdegree*startXY(1,1);
endXtick = 20 + pixdegree*endXY(1,1);
startYtick = 90 - pixdegree*endXY(1,2);
endYtick = 90 - pixdegree*startXY(1,2);
[XX,YY] = ndgrid(startXtick:pixdegree:endXtick,startYtick:pixdegree:endYtick);
xLabels = startXtick:pixdegree:endXtick;
yLabels = startYtick:pixdegree:endYtick;
surf(xLabels, yLabels,A,'EdgeColor','None','Marker','.');
set(gca,'YDir','normal');
grid on;
view([45 45])
And .DEM files
function [startXY, endXY] = calcFirstPixel(lon,lat)
global fHDR;
format = '%s %s';
f = fopen(fHDR);
cont = textscan(f, format);
LonStart = str2double(cont{1,2}{11,1});
LatStart = str2double(cont{1,2}{12,1});
diffPerPix = str2double(cont{1,2}{13,1});
fclose(f);
x = LonStart;
countX = 0
y = LatStart;
countY= 0;
while x<lon
x=x+diffPerPix
countX = countX +1;
end
while y>lat
y=y-diffPerPix
countY = countY+1;
end
startXY= [countX-200 countY-200];
endXY = [countX+200 countY+200];
end
I have a 3D volume and a 2D image and an approximate mapping (affine transformation with no skwewing, known scaling, rotation and translation approximately known and need fitting) between the two. Because there is an error in this mapping and I would like to further register the 2D image to the 3D volume. I have not written code for registration purposes before, but because I can't find any programs or code to solve this I would like to try and do this. I believe the standard for registration is to optimize mutual information. I think this would also be suitable here, because the intensities are not equal between the two images. So I think I should make a function for the transformation, a function for the mutual information and a function for optimization.
I did find some Matlab code on a mathworks thread from two years ago, based on an article. The OP reports that she managed to get the code to work, but I'm not getting how she did that exactly. Also in the IP package for matlab there is an implementation, but I dont have that package and there does not seem to be an equivalent for octave. SPM is a program that uses matlab and has registration implemented, but does not cope with 2d to 3d registration. On the file exchange there is a brute force method that registers two 2D images using mutual information.
What she does is pass a multi planar reconstruction function and an similarity/error function into a minimization algorithm. But the details I don't quite understand. Maybe it would be better to start fresh:
load mri; volume = squeeze(D);
phi = 3; theta = 2; psi = 5; %some small angles
tx = 1; ty = 1; tz = 1; % some small translation
dx = 0.25, dy = 0.25, dz = 2; %different scales
t = [tx; ty; tz];
r = [phi, theta, psi]; r = r*(pi/180);
dims = size(volume);
p0 = [round(dims(1)/2);round(dims(2)/2);round(dims(3)/2)]; %image center
S = eye(4); S(1,1) = dx; S(2,2) = dy; S(3,3) = dz;
Rx=[1 0 0 0;
0 cos(r(1)) sin(r(1)) 0;
0 -sin(r(1)) cos(r(1)) 0;
0 0 0 1];
Ry=[cos(r(2)) 0 -sin(r(2)) 0;
0 1 0 0;
sin(r(2)) 0 cos(r(2)) 0;
0 0 0 1];
Rz=[cos(r(3)) sin(r(3)) 0 0;
-sin(r(3)) cos(r(3)) 0 0;
0 0 1 0;
0 0 0 1];
R = S*Rz*Ry*Rx;
%make affine matrix to rotate about center of image
T1 = ( eye(3)-R(1:3,1:3) ) * p0(1:3);
T = T1 + t; %add translation
A = R;
A(1:3,4) = T;
Rold2new = A;
Rnew2old = inv(Rold2new);
%the transformation
[xx yy zz] = meshgrid(1:dims(1),1:dims(2),1:1);
coordinates_axes_new = [xx(:)';yy(:)';zz(:)'; ones(size(zz(:)))'];
coordinates_axes_old = Rnew2old*coordinates_axes_new;
Xcoordinates = reshape(coordinates_axes_old(1,:), dims(1), dims(2), dims(3));
Ycoordinates = reshape(coordinates_axes_old(2,:), dims(1), dims(2), dims(3));
Zcoordinates = reshape(coordinates_axes_old(3,:), dims(1), dims(2), dims(3));
%interpolation/reslicing
method = 'cubic';
slice= interp3(volume, Xcoordinates, Ycoordinates, Zcoordinates, method);
%so now I have my slice for which I would like to find the correct position
% first guess for A
A0 = eye(4); A0(1:3,4) = T1; A0(1,1) = dx; A0(2,2) = dy; A0(3,3) = dz;
% this is pretty close to A
% now how would I fit the slice to the volume by changing A0 and examining some similarity measure?
% probably maximize mutual information?
% http://www.mathworks.com/matlabcentral/fileexchange/14888-mutual-information-computation/content//mi/mutualinfo.m
Ok I was hoping for someone else's approach, that would probably have been better than mine as I have never done any optimization or registration before. So I waited for Knedlsepps bounty to almost finish. But I do have some code thats working now. It will find a local optimum so the initial guess must be good. I wrote some functions myself, took some functions from the file exchange as is and I extensively edited some other functions from the file exchange. Now that I put all the code together to work as an example here, the rotations are off, will try and correct that. Im not sure where the difference in code is between the example and my original code, must have made a typo in replacing some variables and data loading scheme.
What I do is I take the starting affine transformation matrix, decompose it to an orthogonal matrix and an upper triangular matrix. I then assume the orthogonal matrix is my rotation matrix so I calculate the euler angles from that. I directly take the translation from the affine matrix and as stated in the problem I assume I know the scaling matrix and there is no shearing. So then I have all degrees of freedom for the affine transformation, which my optimisation function changes and constructs a new affine matrix from, applies it to the volume and calculates the mutual information. The matlab optimisation function patternsearch then minimises 1-MI/MI_max.
What I noticed when using it on my real data which are multimodal brain images is that it works much better on brain extracted images, so with the skull and tissue outside of the skull removed.
%data
load mri; volume = double(squeeze(D));
%transformation parameters
phi = 3; theta = 1; psi = 5; %some small angles
tx = 1; ty = 1; tz = 3; % some small translation
dx = 0.25; dy = 0.25; dz = 2; %different scales
t = [tx; ty; tz];
r = [phi, theta, psi]; r = r*(pi/180);
%image center and size
dims = size(volume);
p0 = [round(dims(1)/2);round(dims(2)/2);round(dims(3)/2)];
%slice coordinate ranges
range_x = 1:dims(1)/dx;
range_y = 1:dims(2)/dy;
range_z = 1;
%rotation
R = dofaffine([0;0;0], r, [1,1,1]);
T1 = ( eye(3)-R(1:3,1:3) ) * p0(1:3); %rotate about p0
%scaling
S = eye(4); S(1,1) = dx; S(2,2) = dy; S(3,3) = dz;
%translation
T = [[eye(3), T1 + t]; [0 0 0 1]];
%affine
A = T*R*S;
% first guess for A
r00 = [1,1,1]*pi/180;
R00 = dofaffine([0;0;0], r00, [1 1 1]);
t00 = T1 + t + ( eye(3) - R00(1:3,1:3) ) * p0;
A0 = dofaffine( t00, r00, [dx, dy, dz] );
[ t0, r0, s0 ] = dofaffine( A0 );
x0 = [ t0.', r0, s0 ];
%the transformation
slice = affine3d(volume, A, range_x, range_y, range_z, 'cubic');
guess = affine3d(volume, A0, range_x, range_y, range_z, 'cubic');
%initialisation
Dt = [1; 1; 1];
Dr = [2 2 2].*pi/180;
Ds = [0 0 0];
Dx = [Dt', Dr, Ds];
%limits
LB = x0-Dx;
UB = x0+Dx;
%other inputs
ref_levels = length(unique(slice));
Qref = imquantize(slice, ref_levels);
MI_max = MI_GG(Qref, Qref);
%patternsearch options
options = psoptimset('InitialMeshSize',0.03,'MaxIter',20,'TolCon',1e-5,'TolMesh',5e-5,'TolX',1e-6,'PlotFcns',{#psplotbestf,#psplotbestx});
%optimise
[x2, MI_norm_neg, exitflag_len] = patternsearch(#(x) AffRegOptFunc(x, slice, volume, MI_max, x0), x0,[],[],[],[],LB(:),UB(:),options);
%check
p0 = [round(size(volume)/2).'];
R0 = dofaffine([0;0;0], x2(4:6)-x0(4:6), [1 1 1]);
t1 = ( eye(3) - R0(1:3,1:3) ) * p0;
A2 = dofaffine( x2(1:3).'+t1, x2(4:6), x2(7:9) ) ;
fitted = affine3d(volume, A2, range_x, range_y, range_z, 'cubic');
overlay1 = imfuse(slice, guess);
overlay2 = imfuse(slice, fitted);
figure(101);
ax(1) = subplot(1,2,1); imshow(overlay1, []); title('pre-reg')
ax(2) = subplot(1,2,2); imshow(overlay2, []); title('post-reg');
linkaxes(ax);
function normed_score = AffRegOptFunc( x, ref_im, reg_im, MI_max, x0 )
t = x(1:3).';
r = x(4:6);
s = x(7:9);
rangx = 1:size(ref_im,1);
rangy = 1:size(ref_im,2);
rangz = 1:size(ref_im,3);
ref_levels = length(unique(ref_im));
reg_levels = length(unique(reg_im));
t0 = x0(1:3).';
r0 = x0(4:6);
s0 = x0(7:9);
p0 = [round(size(reg_im)/2).'];
R = dofaffine([0;0;0], r-r0, [1 1 1]);
t1 = ( eye(3) - R(1:3,1:3) ) * p0;
t = t + t1;
Ap = dofaffine( t, r, s );
reg_im_t = affine3d(reg_im, A, rangx, rangy, rangz, 'cubic');
Qref = imquantize(ref_im, ref_levels);
Qreg = imquantize(reg_im_t, reg_levels);
MI = MI_GG(Qref, Qreg);
normed_score = 1-MI/MI_max;
end
function [ varargout ] = dofaffine( varargin )
% [ t, r, s ] = dofaffine( A )
% [ A ] = dofaffine( t, r, s )
if nargin == 1
%affine to degrees of freedom (no shear)
A = varargin{1};
[T, R, S] = decompaffine(A);
r = GetEulerAngles(R(1:3,1:3));
s = [S(1,1), S(2,2), S(3,3)];
t = T(1:3,4);
varargout{1} = t;
varargout{2} = r;
varargout{3} = s;
elseif nargin == 3
%degrees of freedom to affine (no shear)
t = varargin{1};
r = varargin{2};
s = varargin{3};
R = GetEulerAngles(r); R(4,4) = 1;
S(1,1) = s(1); S(2,2) = s(2); S(3,3) = s(3); S(4,4) = 1;
T = eye(4); T(1,4) = t(1); T(2,4) = t(2); T(3,4) = t(3);
A = T*R*S;
varargout{1} = A;
else
error('incorrect number of input arguments');
end
end
function [ T, R, S ] = decompaffine( A )
%I assume A = T * R * S
T = eye(4);
R = eye(4);
S = eye(4);
%decompose in orthogonal matrix q and upper triangular matrix r
%I assume q is a rotation matrix and r is a scale and shear matrix
%matlab 2014 can force real solution
[q r] = qr(A(1:3,1:3));
R(1:3,1:3) = q;
S(1:3,1:3) = r;
% A*S^-1*R^-1 = T*R*S*S^-1*R^-1 = T*R*I*R^-1 = T*R*R^-1 = T*I = T
T = A*inv(S)*inv(R);
t = T(1:3,4);
T = [eye(4) + [[0 0 0;0 0 0;0 0 0;0 0 0],[t;0]]];
end
function [varargout]= GetEulerAngles(R)
assert(length(R)==3)
dims = size(R);
if min(dims)==1
rx = R(1); ry = R(2); rz = R(3);
R = [[ cos(ry)*cos(rz), -cos(ry)*sin(rz), sin(ry)];...
[ cos(rx)*sin(rz) + cos(rz)*sin(rx)*sin(ry), cos(rx)*cos(rz) - sin(rx)*sin(ry)*sin(rz), -cos(ry)*sin(rx)];...
[ sin(rx)*sin(rz) - cos(rx)*cos(rz)*sin(ry), cos(rz)*sin(rx) + cos(rx)*sin(ry)*sin(rz), cos(rx)*cos(ry)]];
varargout{1} = R;
else
ry=asin(R(1,3));
rz=acos(R(1,1)/cos(ry));
rx=acos(R(3,3)/cos(ry));
if nargout > 1 && nargout < 4
varargout{1} = rx;
varargout{2} = ry;
varargout{3} = rz;
elseif nargout == 1
varargout{1} = [rx ry rz];
else
error('wrong number of output arguments');
end
end
end
can someone help me how to show gabor filter in matlab, i can show it but its not what i want. this is my code :
[Gf,gabout] = gaborfilter1(B,sx,sy,f,theta(j));
G{m,n,i,j} = Gf;
and this is gabor filter class:
function [Gf,gabout] = gaborfilter(I,Sx,Sy,f,theta);
if isa(I,'double')~=1
I = double(I);
end
for x = -fix(Sx):fix(Sx)
for y = -fix(Sy):fix(Sy)
xPrime = x * cos(theta) + y * sin(theta);
yPrime = y * cos(theta) - x * sin(theta);
Gf(fix(Sx)+x+1,fix(Sy)+y+1) = exp(-.5*((xPrime/Sx)^2+(yPrime/Sy)^2))*cos(2*pi*f*xPrime);
end
end
Imgabout = conv2(I,double(imag(Gf)),'same');
Regabout = conv2(I,double(real(Gf)),'same');
gabout = sqrt(Imgabout.*Imgabout + Regabout.*Regabout);
Then, I imshow with this code:
imshow(G{m,n,i,j},[]);
and the results :
But i want this result, can someone help me how to slove this?
Use the following function. I hope this is useful.
----------------------------------------------------------------
gfs = GaborFilter(51,0.45,0.05,6,4);
n=0;
for s=1:6
for d=1:4
n=n+1;
subplot(6,4,n)
imshow(real(squeeze(gfs(s,d,:,:))),[])
end
end
Sample Image
----------------------------------------------------------------
function gfs = GaborFilter(winLen,uh,ul,S,D)
% gfs(SCALE, DIRECTION, :, :)
winLen = winLen + mod(winLen, 2) -1;
x0 = (winLen + 1)/2;
y0 = x0;
if S==1
a = 1;
su = uh/sqrt(log(4));
sv = su;
else
a = (uh/ul)^(1/(S-1));
su = (a-1)*uh/((a+1)*sqrt(log(4)));
if D==1
tang = 1;
else
tang = tan(pi/(2*D));
end
sv = tang * (uh - log(4)*su^2/uh)/sqrt(log(4) - (log(4)*su/uh)^2);
end
sx = 1/(2*pi*su);
sy = 1/(2*pi*sv);
coef = 1/(2*pi*sx*sy);
gfs = zeros(S, D, winLen, winLen);
for d = 1:D
theta = (d-1)*pi/D;
for s = 1:S
scale = a^(-(s-1));
gab = zeros(winLen);
for x = 1:winLen
for y = 1:winLen
X = scale * ((x-x0)*cos(theta) + (y-y0)*sin(theta));
Y = scale * (-(x-x0)*sin(theta) + (y-y0)*cos(theta));
gab(x, y) = -0.5 * ( (X/sx).^2 + (Y/sy).^2 ) + (2*pi*1j*uh)*X ;
end
end
gfs(s, d, :, :) = scale * coef * exp(gab);
end
end
Replace the "cos" component by complex part->complex(0, (2*pi*f*xprime)) ans also multiply equation by scaling factor of (1/sqrt(2*Sy*Sx)).