Extracting information from a plot

Question

jgillis16 2016-1-6

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评论： jgillis16 2016-1-8

I have a map of objects on a basic plot. there are areas on the plot that don’t have many objects at all. I want to identify and extract these ‘void’ areas on my plot. I was thinking of setting a threshold of less than 5 objects per ‘degree’ on the plot will count as a ‘void’ area. How would I go about doing this?

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jgillis16 2016-1-7

But, just focusing on the midsection 'u band' you can see on the plot.

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Answer 1

Image Analyst 2016-1-7

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https://ww2.mathworks.cn/matlabcentral/answers/262923-extracting-information-from-a-plot#answer_205358

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You can create an image where you place a dot (set a pixel to a value of 1) wherever there is a data point. If the pixel is already set, then add 1 to the pixel value. Then you can scan it with a moving window with conv2() to count the dots in the window and find out where the count is less than some number. For example (untested)

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 20;
% Create random data.
numPoints = 100000;
x = rand(1,numPoints);
y = rand(1, numPoints);
scaleFactor = 1000; % Adjust depending on the range of x and y.
% Aim to have rows and columns be around a thousand or so.
rows = ceil(max(y) * scaleFactor);
columns = ceil(max(x) * scaleFactor);
% Allocate empty array - no counts at all.
dotImage = zeros(rows, columns);
% Place dots in proper locations on our dot image.
for k = 1 : length(x)
    row = ceil(scaleFactor * y(k));
    col = ceil(scaleFactor * x(k));
    dotImage(row, col) = dotImage(row, col) + 1;
end
subplot(2,2,1);
imshow(dotImage, []);
title('Dots Image', 'FontSize', fontSize, 'Interpreter', 'None');
% Now count the dots in a 11-by-11 moving window
filterWindow = ones(11);
countsImage = conv2(dotImage, filterWindow, 'same');
subplot(2,2,2);
imshow(countsImage, []);
title('Counts Image', 'FontSize', fontSize, 'Interpreter', 'None');
% Set up figure properties:
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0 0 1 1]);
% Get rid of tool bar and pulldown menus that are along top of figure.
set(gcf, 'Toolbar', 'none', 'Menu', 'none');
% Give a name to the title bar.
set(gcf, 'Name', 'Demo by ImageAnalyst', 'NumberTitle', 'Off') 
% Let's compute and display the histogram.
[pixelCount, grayLevels] = hist(countsImage(:), 30);
subplot(2, 2, 3); 
bar(grayLevels, pixelCount); % Plot it as a bar chart.
grid on;
title('Histogram of counts image', 'FontSize', fontSize, 'Interpreter', 'None');
xlabel('Gray Level', 'FontSize', fontSize);
ylabel('Pixel Count', 'FontSize', fontSize);
xlim([0 grayLevels(end)]); % Scale x axis manually.
% Find out where the counts in the window is less than 50.
lowCountsImage = countsImage < 7;
subplot(2,2,4);
imshow(lowCountsImage, []);
title('Low Counts Map', 'FontSize', fontSize, 'Interpreter', 'None');

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jgillis16 2016-1-7

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Well, I had previously written code to import my data into matlab to produce the graph you see above.

    load GWGCCatalog222.txt %loads text into workspace
    readCatalog( GWGCCatalog222 )
    fid = fopen( 'GWGCCatalog222.txt');
    trashLine = fgets(fid); %Skips the first line
    data = textscan(fid, '%f%s%f%f%s%f%f%f%f%f%f%f%f%f%f%f%f%f', 'Delimiter', '|', 'TreatAsEmpty','~');
    fclose(fid);
    GalList.ra = data{3};
    GalList.dec = data{4};
    GalList.ra1 = GalList.ra * pi/12;
    GalList.dec1 = GalList.dec * pi/180 +90;
    GalaxyList = GalList;

And, I (naively) incorporated this code into your demo code as the following.

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 20;
load GWGCCatalog222.txt %loads text into workspace
readCatalog( GWGCCatalog222 )
fid = fopen( 'GWGCCatalog222.txt');
trashLine = fgets(fid); %Skips the first line
data = textscan(fid, '%f%s%f%f%s%f%f%f%f%f%f%f%f%f%f%f%f%f', 'Delimiter', '|', 'TreatAsEmpty','~');
fclose(fid);
GalList.ra = data{3};
GalList.dec = data{4};
GalList.ra1 = GalList.ra * pi/12;
GalList.dec1 = GalList.dec * pi/180 +90;
GalaxyList = GalList;
% % Create random data.
% numPoints = 100000;
% x = rand(1,numPoints);
% y = rand(1, numPoints);
scaleFactor = 1000; % Adjust depending on the range of x and y.
% Aim to have rows and columns be around a thousand or so.
rows = ceil(max(GalList.dec1) * scaleFactor);
columns = ceil(max(GalList.ra1) * scaleFactor);
% Allocate empty array - no counts at all.
dotImage = zeros(rows, columns);
% Place dots in proper locations on our dot image.
for k = 1 : length(GalList.ra1)
    row = ceil(scaleFactor * GalList.dec1(k));
    col = ceil(scaleFactor * GalList.ra1(k));
    dotImage(row, col) = dotImage(row, col) + 1;
end
subplot(2,2,1);
imshow(dotImage, []);
title('Dots Image', 'FontSize', fontSize, 'Interpreter', 'None');
% Now count the dots in a 11-by-11 moving window
filterWindow = ones(11);
countsImage = conv2(dotImage, filterWindow, 'same');
subplot(2,2,2);
imshow(countsImage, []);
title('Counts Image', 'FontSize', fontSize, 'Interpreter', 'None');
% Set up figure properties:
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0 0 1 1]);
% Get rid of tool bar and pulldown menus that are along top of figure.
%set(gcf, 'Toolbar', 'none', 'Menu', 'none');
% Give a name to the title bar.
%set(gcf, 'Name', 'Demo', 'NumberTitle', 'Off') 
% Let's compute and display the histogram.
[pixelCount, grayLevels] = hist(countsImage(:), 30);
subplot(2, 2, 3); 
bar(grayLevels, pixelCount); % Plot it as a bar chart.
grid on;
title('Histogram of counts image', 'FontSize', fontSize, 'Interpreter', 'None');
xlabel('Gray Level', 'FontSize', fontSize);
ylabel('Pixel Count', 'FontSize', fontSize);
xlim([0 grayLevels(end)]); % Scale x axis manually.
% Find out where the counts in the window is less than 50.
lowCountsImage = countsImage < 7;
subplot(2,2,4);
imshow(lowCountsImage, []);
title('Low Counts Map', 'FontSize', fontSize, 'Interpreter', 'None');

And, then proceeded to have the following error returned.

Error using zeros
Requested 91560x6283 (4.3GB) array exceeds maximum array size preference. Creation of arrays greater than this limit may take a long
time and cause MATLAB to become unresponsive. See array size limit or preference panel for more information.
Error in GPcounttest (line 36)
dotImage = zeros(rows, columns);

Any suggestions on where I am going wrong?

jgillis16 2016-1-8

编辑：jgillis16 2016-1-8

在 MATLAB Online 中打开

I adjusted the scale factor, but it seems that I left out a constant to multiply GalList.dec1 originally by, but the min is -89.3346 and max is 89.3464. I understand the scale factor issue, but now we face the problem that the min value is less than zero...

Could we possibly just adjust the following piece of code:

GalList.dec1 = GalList.dec;

to the following?

GalList.dec1 = GalList.dec + 90;

Now, with the scale factor set to 5, the search was 'too' refined. But, I had another question on explicitly what the moving window does? For example, what does it mean when I increase the window from an 11x11 to a 30x30?

jgillis16 2016-1-8

And, (sorry again for all the questions!) how would I convert back to the x,y coordinates from the pixel values? I would like to have essentially a text output of all the sparse regions associated with the low counts image in an 'x,y value' format.

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Answer 2

Walter Roberson 2016-1-7

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/262923-extracting-information-from-a-plot#answer_205360

See the technique in http://www.mathworks.com/matlabcentral/fileexchange/31726-data-density-plot

Or you could do a 2D histogram.

I do not understand what you mean by 5 objects per degree in reference to a 2D plot: that would only make sense to me if you had a fixed origin point and you were more or less doing a radon transform.

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jgillis16 2016-1-7

Now, my end goal (Walter this might help clarify the original question as well) is to impose a number (a correction in a sense) to the identified areas on the graph that fall below the galaxy threshold.

So what I mean is that, for example, I should know that in the sections of 100-150 on the x axis and -40 to -60, I should multiply the data set by that number.

Hope it's clear, and thanks again guys.

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