I have a 3D matrix of a MRI image and used matlab edge function and it gave me a 3D matrix as follow which some of the points are 1 (means edges).
I want to show this surface in matlab but I don't know that how I should do this. I know that I should use surf.
As #bdecaf said, you can use find to determine the height of the points, or in other words, in which of the 100 layers does the point lie. You can do that as follows:
z1=zeros(30,100);
temp=find(b);
[row,col,layer]=ind2sub(size(b),temp);
for i=1:size(x,1)
z1(row(i),col(i))=layer(i);
end
You can get an image as follows:
Related
How do I apply a vector field obtained via quiver, to an image which causes the pixels to displace in the direction of the vectors (image is warped)?
Also, if the vector field I have is 3 dimensional, how would I do this? Think of it as laying down a flat 2 dimensional image over a 3 dimensional terrain. How would I go about viewing this in matlab?
Thank you for your time
EDIT: I have to warp the image not just in the Z axis, but along the X and Y axes as well.
Laying down a flat 2 dimensional image over a 3 dimensional terrain:
It's not very clear the way the axes are oriented but this is an image of a clown mapped on the peaks function. Exact steps are described in the documentation of surface in the example 'Display image along surface plot.'
load clown
C = flipud(X);
figure
surface(XD,YD,ZD,C,...
'FaceColor','texturemap',...
'EdgeColor','none',...
'CDataMapping','direct')
colormap(map)
view(-35,45)
Essentially, you create your surface with CData as the image you want to be displayed and set an appropriate colormap for the axes.
Use the imwarp function in the Image Processing Toolbox.
Basically, I have a many irregular circle on the ground in the form of x,y,z coordinates (of 200*3 matrix). but I want to fix a best circle in to the data of x,y,z coordinates (of 200*3 matrix).
Any help will be greatly appreciated.
I would try using the RANSAC algorithm which finds the parameters of your model (in your case a circle) given noisy data. The algorithm is quite easy to understand and robust against outliers.
The wikipedia article has a Matlab example for fitting a line but it shouldn't be too hard to adapt it to fit a circle.
These slides give a good introduction to the RANSAC algorithm (starting from page 42). They even show examples for fitting a circle.
Though this answer is late, I hope this helps others
To fit a circle to 3d points
Find the centroid of the 3d points (nx3 matrix)
Subtract the centroid from the 3D points.
Using RANSAC, fit a plane to the 3D points. You can refer here for the function to fit plane using RANSAC
Apply SVD to the 3d points (nx3 matrix) and get the v matrix
Generate the axes along the RANSAC plane using the axes from SVD. For example, if the plane norm is along the z-direction, then cross product between the 1st column of v matrix and the plane norm will generate the vector along the y-direction, then the cross product between the generated y-vector and plane norm will generate a vector along the x-direction. Using the generated vectors, form a Rotation matrix [x_vector y_vector z_vector]
Multiply the Rotation matrix with the centroid subtracted 3d points so that the points will be parallel to the XY plane.
Project the points to XY plane by simply removing the Z-axes from the 3d points
fit a circle using Least squares circle fit
Rotate the center of the circle using the inverse of the rotation matrix obtained from step 5
Translate back the center to the original location using the centroid
The circle in 3D will have the center, the radius will be the same as the 2D circle we obtained from step 8, the circle plane will be the RANSAC plane we obtained from step 3
I am trying to plot a 3d view of a very large CT dataset. My data is in a 3d matrix of 2000x2000x1000 dimension. The object is surrounded by air, which is set to NaN in my matrix.
I would like to be able to see the greyscale value of the surface of the object (no isosurface) but I cannot quite work out how to do that in Matlab. Can anyone help me please?
Given that I a dealing with a huge matrix and I am only interested in the surface of the object, does anyone know a good trick how to reduce the size of my dataset?
The function surf(X,Y,Z) allows you to plot 3d data, where (X,Y) gives the coordinates in the x-y-plane while Z gives the z-coordinate and the surface color.
By default the function does not plot anything for the NaN entries, so you should be good to go with the surf function.
To set the surf-function to use a grayscale plotting use:
surf(matrix3d);
colormap(gray);
This plots the matrix in a surface plot and sets the colormap to grayscale.
In addition, as I understand your data, you might be able to eliminate entire plane-segments in your matrix. If for instance the plane A(1,1:2000,1:1000) is NaN in all entries you could eliminate all those entries (thus the entire Y,Z-plane in entry X=1). This will however require some heavy for loops, which might be over the top. This depends on how many data matrices you have compared to how many different plot you want for each matrix.
I will try to give you some ideas. I assume lack of a direct 3D "surface detector".
Since you have a 3D matrix where XY-planes are CT scan slices and each slice is an image, I would try to find edges of each slice say with edge. This would require some preprocessing like first thresholding each slice image. Then I can either use scatter3 to display the edge data as a 3D point cloud or delaunay3 to display the edge data as a surface.
I hope this will help you achieve what you are asking for.
I managed to get it working:
function [X,Y,Z,C] = extract_surface(file_name,slice_number,voxel_size)
LT = imread(file_name);%..READ THE 2D MAP
BW = im2bw(LT,1);%..THRESHOLD TO BINARY
B = bwboundaries(BW,8,'noholes');%..FIND THE OUTLINE OF THE IMAGE
X = B{1}(:,1);%..EXTRACT X AND Y COORDINATES
Y = B{1}(:,2);
indices = sub2ind(size(LT),X,Y);%..FIND THE CORRESPONDING LINEAR INDICES
C = LT(indices);%..NOW READ THE VALUES AT THE OUTLINE POSITION
Z = ones(size(X))*slice_number;
I can then plot this with
figure
scatter3(X,Y,Z,2,C)
Now the only thing I could improve is to have all these points in the scatter plot connected with a surface. #upperBound you suggested delaunay3 for this purpose - I cannot quite figure out how to do this. Do you have a tip?
I have a 3D Matrix M(256x256x136) and each index(i,j,k) in M has a gray level value in it. I am interested in displaying M in some sort of a 3D plot in MATLAB, but am unable to do so. I cannot use plot3 because plot3 is for plotting points, not the values.
Thanks
If I understand your question correctly, you want to plot the 3D point cloud with i,j, and k as 3D coordinates and the gray level as the point value.
I would suggest using scatter3.
Sounds like you are looking for a volume renderer. For Matlab, you could try this one: Volume Render from Matlab Central
An isosurface plot might be useful as well.
I have a formula that depends on theta and phi (spherical coordinates 0<=theta<=2*pi and 0<=phi<=pi). By inserting each engle, I obtained a quantity. Now I have a set of data for different angles and I need to plot the surface. My data is a 180*360 matrix, so I am not sure if I can use SURF or MESH or PLOT3. The figure should be a surface that include all data and the axes should be in terms of the quantity, not the quantity versus the angles. How can I plot such a surface?
I see no reason why you cannot use mesh or surf to plot such data. Another option I tend to use is that of density plots. You basically display the dependent variable (quantity) as an image and include the independent variables (angles) along the axis, much like you would with the aforementioned 3D plotting functions. This can be done with imagesc.
Typically you would want your axes to be the dependent variables. Could you elaborate more on this point?
If I understand you correctly you have calculated a function f(theta,phi) and now you want to plot the surface containing all the points with the polar coordinated (r,theta,phi) where r=f(theta,phi).
If this is what you want to do, the 2D version of such a plot is included in MATLAB under the name polar. Unfortunately, as you pointed out, polar3 on MatlabCentral is not the generalization you are looking for.
I have been able to plot a sphere with the following code, using constant r=1. You can give it a try with your function:
phi1=0:1/(3*pi):pi; %# this would be your 180 points
theta1=-pi:1/(3*pi):pi; % your 360 points
r=ones(numel(theta1),numel(phi1));
[phi,theta]=meshgrid(phi1,theta1);
x=r.*sin(theta).*cos(phi);
y=r.*sin(theta).*sin(phi);
z=r.*cos(theta);
tri=delaunay(x(:),y(:),z(:));
trisurf(tri,x,y,z);
From my tests it seems that delaunay also includes a lot of triangles which go through the volume of my sphere, so it seems this is not optimal. So maybe you can have a look at fill3 and construct the triangles it draws itself: as a first approximation, you could have the points [x(n,m) x(n+1,m) x(n,m+1)] combined into one triangle, and [x(n+1,m) x(n+1,m+1) x(n+1,m+1)] into another...?