I have a picture which shows the magnitude of some value in terms of color, like this one:
The higher the magnitude, the more it looks red. However there are only a few points at the edge has very high values and most of the points have much lower values. If a colorbar with equal intervals is used the picture just looks blue throughout and the values in most areas cannot be distinguished.
Is it possible to set a colorbar that has, say, exponentially increasing intervals (or others) so that the center part can also show different colors?
Here is one way, it's not quite right but it's close. The idea is to make your own log spaced colour map. I do it by using linear interpolation between log spaced break points. It could probably be improved to use logarithmic interpolation (and maybe have better end cases):
First I simulate some data (open to suggestions for simulating data that better illustrates this example):
M = exp(rand(50)*10)
Then plot it (ignore the figure(2), that's just to make this match the image later)
n = 64
figure(2)
imagesc(M)
colormap(jet(n))
colorbar
now create a log spaced colour map
linMap = jet(n);
breaks = round(0:n/5:n)';
breaks(1) = 1;
cBreaks = linMap(breaks,:);
idx = 2.^(6:-1:1)';
idx(end) = 0; %// this part is hacky
logMap = interp1(((idx)/64)*max(M(:)),flipud(cBreaks),linspace(0,max(M(:)),64)); %// based on http://stackoverflow.com/questions/17230837/how-to-create-a-custom-colormap-programatically
figure(1)
imagesc(M)
colormap(logMap)
colorbar
results in
as you can see, the data remain unchanged and the data inspector still gives you back the same values but the colour bar is pretty much on a log scale now. I'd be interested to see what this looks like on your data.
Related
I am trying to detect the edge from black horizontal line to the gray-smeared foreground.
The desired edge/result is slightly marked red.
What have I tried so far :
My approach was to use the standard Chan-Vese Segmentation combined with several preprocseeing methods like gaussian blurring, maximum filter or morpholigocal operator like erosion. However, when I am initializing the level set function at the lower part of the image, the contour gets stuck right before the dersired edge.
Due to the noise I can't get rid off without destroying important information of the image, simple methods like the sobel or prewitt filtering might fail.
Another apporoach of me was to search for the maximum/minimum intensity columnwise of the image and mark the darkest pixel per column.
As you can assume, this will fail too because the edge I am looking for is not the only part that has dark pixels, that's why this method is very error-prone.
Edit
Snakes does not help either.
The active contour, marked as blue, simply goes over the edge and at the left and right the contour gets stuck. The Code I tried wasthe function Snake2D(I,P,Options) taken from here.
Here is the original image if you would like to help me.
I think your approach using the rows and finding the maximum is probably easiest.
The one problem you have is distinguishing the two main maxima. For this, you can apply a rough smoothing, to find the middle between the two maxima (blue line in image below). You can then only take the lower bit, which is the one you are interested in and find the maximum of this bit.
In a final step, just add up the two indices.
Result:
Could go like this:
ib = imread('LHkm2.png'); %Read image
sz = size(ib); %get dimensions
for i = 1:sz(2)
[~, ind_mid(i)] = max(smooth(-double(ib(:, i)), 130));%First round
line_to_smooth = ib(ind_mid(i):end, i);%Get line with one maximum
[~, ind(i)] = min(smooth(double(line_to_smooth), 10));%Second round
ind(i) = ind(i) + ind_mid(i);%Add indices to get final position
end
imshow(ib,[]);
hold on;
plot(ind_mid, 'LineWidth', 3);
plot(ind, 'LineWidth', 3);
Note: You can of course smooth the final line just like any other graphs to get rid of bumps like this:
ind = smooth(ind, 10)
where 10 is your smoothing window (the higher the broader, see here.
My x-axis is latitudes, y-axis is longitudes, and z-axis is the hist3 of the two. It is given by: z=hist3(location(:,1:2),[180,360]), where location(:,1) is the latitude column, and location(:,2) is the longitude column.
What I now want is, instead of plotting on a self-created XY plane, I want to plot the same on a worldmap. And instead of representing the frequency of each latitude-longitude pair with the height of the bars of hist3, I want to represent the frequency of each location by a heat map on top of the world map, corresponding to each latitude-longitude pair's frequency on the dataset. I have been searching a lot for this, but have not found much help. How to do this? I could only plot the skeleton of the worldmap like this:
worldmap world
load geoid
geoshow(geoid, geoidrefvec, 'DisplayType', 'texturemap');
load coast
geoshow(lat, long)
I don't know what the colour is being produced based on.
Additionally, if possible, I would also like to know how to plot the hist3 on a 3D map of the world (or globe), where each bar of the hist3 would correspond to the frequency of each location (i.e., each latitude-longitude pair). Thank you.
The hist3 documentation, which you can find here hist3, says:
Color the bars based on the frequency of the observations, i.e. according to the height of the bars. set(get(gca,'child'),'FaceColor','interp','CDataMode','auto');
If that's not what you need, you might wanna try it with colormap. More info about it here colormap. I haven't tried using colormap on histograms directly, so If colormap doesn't help, then you can try creating a new matrix manually which will have values in colors instead of the Z values the histogram originally had.
To do that, you need to first calculate the maximum Z value with:
maxZ=max(Z);
Then, you need to calculate how much of the colors should overlap. For example, if you use RGB system and you assign Blue for the lowest values of the histogram, then Green for the middle and Red for the High, and the green starts after the Blue with no overlap, than it will look artificial. So, if you decide that you will have, for example overlapping of 10 values, than, having in mind that every R, G and B component of the RGB color images have 255 values (8 bits) and 10 of each overlap with the former, that means that you will have 255 values (from the Blue) + 245 values (From the Green, which is 255 - 10 since 10 of the Green overlap with those of the Blue) + 245 (From the Red, with the same comment as for the Green), which is total amount of 745 values that you can assign to the new colored Histogram.
If 745 > maxZ there is no logic for you to map the new Z with more than maxZ values. Then you can calculate the number of overlaping values in this manner:
if 745 > maxZ
overlap=floor(255- (maxZ-255)/2)
end
At this point you have 10 overlapping values (or more if you still think that it doesn't looks good) if the maximum value of the Z is bigger than the total amount of values you are trying to assign to the new Z, or overlap overlapping values, if the maximum of Z is smaller.
When you have this two numbers (i.e. 745 and maxZ), you can write the following code so you can create the newZ.
First you need to specify that newZ is of the same size as Z. You can achieve that by creating a zero matrix with the same size as Z, but having in mind that in order to be in color, it has to have an additional dimension, which will specify the three color components (if you are working with RGB).
This can be achieved in the following manner:
newZ=zeros(size(Z),3)
The number 3 is here, as I said, so you would be able to give color to the new histogram.
Now you need to calculate the step (this is needed only if maxZ > The number of colors you wish to assign). The step can be calculated as:
stepZ=maxZ/Total_Number_of_Colors
If maxZ is, for example 2000 and Total_Number_of_Colors is (With 10 overlaping colours) 745, then stepZ=2.6845637583892617449664429530201. You will also need a counter so you would know what color you would assign to the new matrix. You can initialize it here:
count=0;
Now, finally the assignment is as follows:
For i=1:stepZ:maxZ
count=count+1;
If count>245
NewZ(Z==stepz,3)=count;
elseif count>245 && count<256
NewZ(Z==stepz,3)=count;
NewZ(Z==stepz,2)=count-245;
elseif count>255
NewZ(Z==stepz,2)=count-245;
elseif count>500 && count<511
NewZ(Z==stepz,2)=count-245;
NewZ(Z==stepz,1)=count-500;
else
NewZ(Z==stepz,1)=count-500;
end
end
At this point you have colored your histogram. Note that you can manually color it in different colors than red, green and blue (even if you are working in RGB), but it would be a bit harder, so if you don't like the colors you can experiment with the last bit of code (the one with the for loops), or check the internet of some other automatic way to color your newZ matrix.
Now, how do you think to superimpose this matrix (histogram) over your map? Do you want only the black lines to be shown over the colored histogram? If that's the case, than it can be achieved by resampling the NewZ matrix (the colored histogram) with the same precision as the map. For example, if the map is of size MxN, then the histogram needs to be adjusted to that size. If, on the other hand, their sizes are the same, then you can directly continue to the next part.
Your job is to find all pixels that have black in the map. Since the map is not binary (blacks and whites), it will be a bit more harder, but still achievable. You need to find a satisfactory threshold for the three components. All the lines under this threshold should be the black lines that are shown on the map. You can test these values with imshow(worldmap) and checking the values of the black lines you wish to preserve (borders and land edges, for example) by pointing the cross tool on the top of the figure, in the tools bar on every pixel which is of interest.
You don't need to test all black lines that you wish to preserve. You just need to have some basic info about what values the threshold should have. Then you continue with the rest of the code and if you don't like the result so much, you just adjust the threshold in some trial and error manner. When you have figured that this threshold is, for example, (40, 30, 60) for all of the RGB values of the map that you wish to preserve (have in mind that only values that are between (0,0,0) and (40,30,60) will be kept this way, all others will be erased), then you can add the black lines with the following few commands:
for i = 1:size(worldmap,1)
for j = 1:size(worldmap,2)
if worldmap(i,j,1)<40 && worldmap(i,j,2)<30 && worldmap(i,j,3)<60
newZ(i,j,:)=worldmap(i,j,:)
end
end
I want to note that I haven't tested this code, since I don't have Matlab near me atm, so It can have few errors, but those should be easily debugable.
Hopes this is what you need,
Cheers!
I am trying to make a simple plot (for this example doing a plot of y=x^2 will suffice) where I want to set the colors of the points based on their magnitude given some colormap.
Following along my simple example say I had:
x = 1:10;
y = x.^2;
Use gscatter(x,y,jet(10)); legend hide; colorbar which produces a plot with the points colored but the colorbar does not agree with the colored values. (Can't post picture as this is my first post). Using a caxis([1,100]) command gives the right range but the colors are still off.
So I have two questions:
(1) How can I fix the colors to fit to a colorbar given a range? In my real data, I am looking at values that range from -50 to 50 in some instances and have many more data points.
(2) I want to create a different plot with the same points (but on different axes) and I want the colors of each point on this new plot to have the same colors as their counterparts in the previous plot. How can I, programmatically, extract the color from each point so I can plot it on two different sets of axes?
I would just move the points into a matrix and do an imagesc() command but they aren't spaced as integers or equally so simple scaling wouldn't work either.
Thanks for any help!
Regarding you first question, you need to interpolate the y values into a linear index to the colormap. Something like:
x = 1:10;
y = x.^4;
csize = 128;
cmap = jet(csize);
ind = interp1(linspace(min(y),max(y),csize),1:csize,y,'nearest');
scatter(x,y,14,cmap(ind,:),'filled')
colorbar
caxis([min(y) max(y)])
Using interp1 in this case is an overkill; you could calculate it directly. However, I think in this way it is clearer.
I think it also answers your 2nd question, since you have the index of the color of each data point, so you can use it again in the same way.
What we want is to draw several solid circles at random locations, with random gray scale colors, on a dark gray background. How can we do this? Also, if the circles overlap, we need them to change color in the overlapping part.
Since this is an assignment for school, we are not looking for ready-made answers, but for a guide which tools to use in MATLAB!
Here's a checklist of things I would investigate if you want to do this properly:
Figure out how to draw circles in MATLAB. Because you don't have the Image Processing Toolbox (see comments), you will probably have to make a function yourself. I'll give you some starter code:
function [xout, yout] = circle(x,y,r,rows,cols)
[X,Y] = meshgrid(x-r:x+r, y-r:y+r);
ind = find(X.^2 + Y.^2 <= r^2 & X >= 1 & X <= cols & Y >= 1 & Y <= rows);
xout = X(ind);
yout = Y(ind);
end
What the above function does is that it takes in an (x,y) co-ordinate as well as the radius of
the circle. You also will need to specify how many rows and how many columns you want in your image. The reason why is because this function will prevent giving you co-ordinates that are out of bounds in the image that you can't draw. The final output of this will give you co-ordinates of all values inside and along the boundary of the circle. These co-ordinates will already be in integer so there's no need for any rounding and such things. In addition, these will perfectly fit when you're assigning these co-ordinates to locations in your image. One caveat to note is that the co-ordinates assume an inverted Cartesian. This means that the top left corner is the origin (0,0). x values increase from left to right, and y values increase from top to bottom. You'll need to keep this convention in mind when drawing circles in your image.
Take a look at the rand class of functions. rand will generate random values for you and so you can use these to generate a random set of co-ordinates - each of these co-ordinates can thus serve as your centre. In addition, you can use this class of functions to help you figure out how big you want your circles and also what shade of gray you want your circles to be.
Take a look at set operations (logical AND, logical OR) etc. You can use a logical AND to find any circles that are intersecting with each other. When you find these areas, you can fill each of these areas with a different shade of gray. Again, the rand functions will also be of use here.
As such, here is a (possible) algorithm to help you do this:
Take a matrix of whatever size you want, and initialize all of the elements to dark gray. Perhaps an intensity of 32 may work.
Generate a random set of (x,y) co-ordinates, a random set of radii and a random set of intensity values for each circle.
For each pair of circles, check to see if there are any co-ordinates that intersect with each other. If there are such co-ordinates, generate a random shade of gray and fill in these co-ordinates with this new shade of gray. A possible way to do this would be to take each set of co-ordinates of the two circles and draw them on separate temporary images. You would then use the logical AND operator to find where the circles intersect.
Now that you have your circles, you can plot them all. Take a look at how plot works with plotting matrices. That way you don't have to loop through all of the circles as it'll be inefficient.
Good luck!
Let's get you home, shall we? Now this stays away from the Image Processing Toolbox functions, so hopefully these must work for you too.
Code
%%// Paramters
numc = 5;
graph_size = [300 300];
max_r = 100;
r_arr = randperm(max_r/2,numc)+max_r/2
cpts = [randperm(graph_size(1)-max_r,numc)' randperm(graph_size(2)-max_r,numc)']
color1 = randperm(155,numc)+100
prev = zeros(graph_size(1),graph_size(2));
for k = 1:numc
r = r_arr(k);
curr = zeros(graph_size(1),graph_size(2));
curr(cpts(k,1):cpts(k,1)+r-1,cpts(k,2):cpts(k,2)+r-1)= color1(k)*imcircle(r);
common_blob = prev & curr;
curr = prev + curr;
curr(common_blob) = min(color1(1),color1(2))-50;
prev = curr;
end
figure,imagesc(curr), colormap gray
%// Please note that the code uses a MATLAB file-exchange tool called
%// imcircle, which is available at -
%// http://www.mathworks.com/matlabcentral/fileexchange/128-imcircle
Screenshot of a sample run
As you said that your problem is an assignment for school I will therefore not tell you exactly how to do it but what you should look at.
you should be familiar how 2d arrays (matrices) work and how to plot them using image/imagesc/imshow ;
you should look at the strel function ;
you should look at the rand/randn function;
such concepts should be enough for the assignment.
I am trying to plot x and y velocities using quiver function in MATLAB.
I have x,y,u and v arrays(with their usual meanings) with dimension 100x100
So, the result is my quiver plot is dense and I cannot see the arrows unless I zoom in.
Somewhat like this: quiver not drawing arrows just lots of blue, matlab
Take a look at my plot:
Is there any way to make quiver plot less dense(and with bigger arrows)? I am planning to clip x-axis range to 0-4. But anything apart from that?
I cannot make my mesh less dense for accuracy concerns. I am, however willing to ignore some fine data points if that's required to make the plot look better.
You can plot a reduced number of arrows by plotting, for example, (assuming your data are in arrays)
quiver(x(1:2:end,1:2:end),y(1:2:end,1:2:end),u(1:2:end,1:2:end),v(1:2:end,1:2:end))
where the 2 in this example means we plot only a quarter as many arrows. You can of course change it, as long as you change all of the 2's so that the arrays are all appropriately sized.
If you want to change the length of the arrows there are two options. Firstly, you can use the scale option scale=2 to scale the arrows by the amount specified, or you can normalise the velocities if you want to have all the arrows the same length. You do lose information doing that, because you can't compare the magnitude of the velocity by looking at the arrows, but it may be useful in some situations. You can do this by dividing u and v both by sqrt(u.^2+v.^2) (at the points you wish to plot arrows at.
Hope that helps and sets everything out nicely.
You need to make your interval value a bit larger in order to make your matrix more sparse.
This is very dense:
1:0.0001:100
This is very sparse:
1:1:100
EDIT:
If you have the Image Processing Toolkit you can use the imresize function to reduce the matrix resolution:
newMat = imresize(oldMat, newSize);
And if you don't have the Toolbox then you can resize in a similar manner to this example using interp2 Interpolation:
orgY = 1:size(oldMat,1);
orgX = 1:size(oldMat,2);
[orgX,orgY] = meshgrid(orgX ,orgY);
newY = linspace(1,size(mat,1),newHeight);
newX = linspace(1,size(mat,2),newWidth);
[newX,newY] = meshgrid(newX,newY);
newMat = interp2(orgX,orgY,mat,newX,newY);
And thanks to #David, if you want to just strip out some individual points you can simply do:
xPlot=x(1:2:end)