Let's say, I have a matrix (by imread) as following:
A = [0 0 1 0 0;
0 0 1 0 0;
0 1 1 1 0;
0 0 1 0 0;
0 0 0 0 0];
I would like to get the bounding box of non-zero elements as
BB = show_me_the_bounding_box(A);
BB = [1, 2, 4, 4]; % y0, x0, y1, x0
What function I should use to do that?
Use REGIONPROPS
stats = regionprops(A,'BoundingBox');
BB = stats.BoundingBox;
To get the result you want, please use:
[y,x] = ind2sub(size(A), find(A))
coord = [y, x]
[min(coord) max(coord)] % [1 2 4 4]
Note however that, with the correct conventions, the bounding box is:
[y,x] = ind2sub(size(A), find(A))
coord = [x, y]
mc = min(coord)-0.5
Mc = max(coord)+0.5
[mc Mc-mc] % [1.5 0.5 3 4]
which yields the same result as:
stats = regionprops(A, 'BoundingBox')
BB = stats.BoundingBox % [1.5 0.5 3 4]
The code can easily be adapted to 3D images, by using:
[y,x,z] = ind2sub(size(A), find(A));
coord = [x, y, z];
mc = min(coord)-0.5;
Mc = max(coord)+0.5;
[mc Mc-mc]
Related
I have two matrices each of which contains two vectors (each row is a vector):
u = [1 0 0; 2 0 0]
v = [1 1 0; 2 2 0]
I want to calculate two angles between the vectors of the corresponding rows in the matrices (angle between [1 0 0] , [1 1 0] and angle between [2 0 0] , [2 2 0]). In this example, both angles will be 45 degrees. So what I want is a new matrix like this:
angles = [45; 45]
When I try this:
u = [1 0 0; 2 0 0]
v = [1 1 0; 2 2 0]
dp = u(:,1) .* v(:,1) + u(:,2) .* v(:,2) + u(:,3) .* v(:,3);
angles = atan2d(norm(cross(u,v)),dp)
The anwser will be:
angles = [76.3670 ; 45.8683]
and when I try this (change norm to normr):
u = [1 0 0; 2 0 0]
v = [1 1 0; 2 2 0]
dp = u(:,1) .* v(:,1) + u(:,2) .* v(:,2) + u(:,3) .* v(:,3);
angles = atan2d(norm(crossr(u,v)),dp)
The anwser will be:
angles = [0 0 45.0000 ; 0 0 14.0362]
How can I make it calculate the angle between the vectors of each row?
Try:
u=[1 0 0;2 0 0];
v = [1 1 0;2 2 0];
atan2(cross(u,v,2),dot(u,v,2)) % radians
atan2d(cross(u,v,2),dot(u,v,2)) % degrees
The ,2 in the cross and dot functions specifies the dimension to operate, since you are storing each vector in a row.
There a discussion here, with many other ways to calculate, and you may find one more suitable to your particular case of application.
Show mask by meshc function
z = [0 0 0 0;0 1 1 0;0 0 0 0];
meshc(z)
Output is:
Desired output:
There is a lot of guessing on my side, and I guess you want something like this:
%// data
z = [0 0 0 0;0 1 1 0;0 0 0 0];
%// grid
[n,m] = size(z);
[x,y] = ndgrid(1:n,1:m);
%// finer grid
[xq, yq] = ndgrid(linspace(1,n,100),linspace(1,m,100));
%// interpolation
F = griddedInterpolant(x, y, z, 'cubic')
zq = F(xq, yq);
%// interpolated plot
figure(1)
meshc(xq,yq,zq)
For example my vector is
a = [0 1]
I want to add number 0 into vector but in FOR path 3 times. I want to get this vector
a = [0 1 0 0 0]
You don't need a loop to do this. This can be accomplished using concatenation and the zeros function.
nzeros = 3;
a = [0 1];
a = cat(2, a, zeros(1, nzeros));
% or a = [a zeros(1, nzeros)];
Alternatively:
nzeros = 3;
a = [0 1];
a(end+nzeros) = 0;
If you are talking about a for-loop. This will do what you asked for
a = [0 1];
for i=1:3
a = [a,0];
end
I am using Matlab and Euler Angles in order to reorient a 3axes coordinate system. Specifically,
Rz = [cos(ψ) sin(ψ) 0;-sin(ψ) cos(ψ) 0;0 0 1];
Ry = [cos(φ) 0 -sin(φ);0 1 0;sin(φ) 0 cos(φ)];
Rx = [1 0 0;0 cos(θ) -sin(θ);0 sin(θ) cos(θ)];
Rtotal = Rz*Ry*Rz
Then I loop through my old system coordinates (x,y,z) and make a vector coord_old. Then I get the reoriented system with (xn,yn,zn)
for i=1:size(num,1)
coord_old = [x(i,1);y(i,1);z(i,1)];
coord_new = Rtotal*coord_old;
xn(i,1) = coord_new(1,1);
yn(i,1) = coord_new(2,1);
zn(i,1) = coord_new(3,1);
end
My issue is that when θ,φ,ψ≃0 then x->-y and y->x and when θ,φ≃0 and ψ=90 then x and y will not rotate! That means that when x,y should rotate they don't and when they shouldn't rotate they stay as they were!
--EDIT--
For example, when ψ=20.0871, φ=0.0580 and θ=0.0088 I get these results
See that x->-y and y->x while z doesn't change at all!
Any thoughts?
Ok, I see two main problems here:
Rtotal = Rz*Ry*Rz is probably not what you want since Rz is multiplied twice. I think you mean Rtotal = Rz*Ry*Rx.
Your rotation matrix seems to be incorrect. Check this Wikipedia artice to get the correct signs.
Here a corrected rotation matrix:
Rz = [cos(psi) -sin(psi) 0; sin(psi) cos(psi) 0; 0 0 1];
Ry = [cos(phi) 0 sin(phi); 0 1 0; -sin(phi) 0 cos(phi)];
Rx = [1 0 0; 0 cos(theta) -sin(theta); 0 sin(theta) cos(theta)];
Rtotal = Rz*Ry*Rx;
With this matrix I get the correct results:
x=1; y=2; z=3;
psi=0; phi=0; theta=0;
[xn,yn,zn] >> 1 2 3
x=1; y=2; z=3;
psi=90/180*pi; phi=0; theta=0;
[xn,yn,zn] >> -2 1 3
And here a full graphical example of a cube in 3d-space:
% Create cube (not in origin)
DVert = [0 0 0; 0 1 0; 1 1 0; 1 0 0 ; ...
0 0 1; 0 1 1; 1 1 1; 1 0 1];
DSide = [1 2 3 4; 2 6 7 3; 4 3 7 8; ...
1 5 8 4; 1 2 6 5; 5 6 7 8];
DCol = [0 0 1; 0 0.33 1; 0 0.66 1; ...
0 1 0.33; 0 1 0.66; 0 1 1];
% Rotation angles
psi = 20 /180*pi; % Z
phi = 45 /180*pi; % Y
theta = 0 /180*pi; % X
% Rotation matrix
Rz = [cos(psi) -sin(psi) 0; sin(psi) cos(psi) 0; 0 0 1];
Ry = [cos(phi) 0 sin(phi); 0 1 0; -sin(phi) 0 cos(phi)];
Rx = [1 0 0; 0 cos(theta) -sin(theta); 0 sin(theta) cos(theta)];
Rtotal = Rz*Ry*Rz;
% Apply rotation
DVertNew = Rtotal * DVert';
% Plot cubes
figure;
patch('Faces',DSide,'Vertices',DVert,'FaceColor','flat','FaceVertexCData',DCol);
patch('Faces',DSide,'Vertices',DVertNew','FaceColor','flat','FaceVertexCData',DCol);
% Customize view
grid on;
axis equal;
view(30,30);
When I use your code and insert 0 for all angles, I get Rtotal:
Rtotal =
1 0 0
0 1 0
0 0 1
This is the identity matrix and will not change your values.
You have an error in your matrix multiplication. I think you should multiply: Rtotal*coord_old. I think you are missing the _old. depending on what is in you coordvariable, this may be the bug.
When I run:
for i=1:size(1,1)
coord_old = [1;2;3];
coord_new = Rtotal*coord_old;
xn(i,1) = coord_new(1,1);
yn(i,1) = coord_new(2,1);
zn(i,1) = coord_new(3,1);
end
I get the correct result:
coord_new =
1
2
3
Thank you both #Steffen and #Matt. Unfortunately, my reputation is not high enough to vote Up your answers!
The problem was not with Rtotal as #Matt correctly stated. It should be as it was Rz*Ry*Rx. However, both your ideas helped me test my code with simple examples (5 sets of coordinates and right hand rule), and realize where my (amateur) mistake was.
I had forgotten I had erased parts of codes where I was expressing my angles to degrees... I should be using sind & cosd instead of sin and cos.
How to plot a square surface in Matlab?
More exactly I want to plot a square square with value 0.5 surface which is located at X:-1 to X=1 and Y:2.5 to 3.5.
I tried the following
[X,Y] = meshgrid(-3.5:.5:3.5);
Z = zeros(15);
Z(end-2:end,5:9) = 0.5;
surf(X,Y,Z);
This doesn't result in a perpendicular edge. How to archive that?
This is what the patch function is for.
Matlab documentation
so for your case:
X = [ -1 -1 1 1];
Y = [3.5 2.5 2.5 3.5];
Z = [0.5 0.5 0.5 0.5];
patch(X,Y,Z,'red')
view(45,45)
You need to provide multiple Z-values together with the same X, Y values. A small example:
>> [X, Y]= meshgrid([1,2,2,3,4], 1:2)
X =
1 2 2 3 4
1 2 2 3 4
Y =
1 1 1 1 1
2 2 2 2 2
>> Z = [0,0,1,1,0;0,0,1,1,0]
Z =
0 0 1 1 0
0 0 1 1 0
>> surf(X, Y, Z)
Yields this:
This should be the same in 2D, you just need to wrap you head around which X and Y values to duplicate and adjust the Z-Matrix accordingly.
I ended up with
figure;
hold on;
X = [ -2 -2 2 2];
Y = [2 4 4 2];
Z = [0 0 0 0];
patch(X,Y,Z,'blue');
X = [ -1 -1 1 1];
Y = [3.5 2.5 2.5 3.5];
Z = [0.5 0.5 0.5 0.5];
h = patch(X,Y,Z,'red');
X = [ -1 -1 1 1];
Y = [2.5 2.5 2.5 2.5];
Z = [0 0.5 0.5 0];
patch(X,Y,Z,'red');
X = [1, 1, 1, 1];
Y = [2.5 2.5 3.5 3.5];
Z = [0 0.5 0.5 0];
patch(X,Y,Z,'red');
view(45,30)
legend(h, 'F(u,v)')
xlabel('u')
ylabel('v')
zlabel('F(u,v)')