How to accurately acquire line segments from the projection plot? - image

So this is basically something very simple, as in just get the horizontal projection plot and from that get the location of the lines on the image. But the problem is that the threshold that is applied is very variable. If I stay at a safe level, the correct number of lines are extracted whereas on the other hand unwanted results are extracted.
For example here is the image:
And its horizontal projection:
And here is the code I am using to extract the text lines:
%complementing as text must be non zero and background should be 0
img_comp = imcomplement(img);
%calculate the horizontal projections and plot it to verify the threshold
horizontal_projections = sum(img_comp, 2);
plot(horizontal_projections)
%A very crude method of automatically detecting the threshold
proj_mean = mean(horizontal_projections);
lines = horizontal_projections > floor(proj_mean);
% Find Rising and falling edges
d = diff(lines);
startingColumns = find(d>0);
endingColumns = find(d<0);
% Extract each line and save it in a cell
for lines_k = 1 : length(startingColumns)
lines_extracted{lines_k} = img(startingColumns(lines_k):endingColumns(lines_k), :);
end
I want to automate the threshold selection but am having trouble, if I use the threshold shown in my code that is the mean of the projections, it does extract 9 lines which are correct but the lines lose a lot of data as in:
This is the second line, the extenders and descenders of the letters have been cut off. Using the half of mean or third of it works but its different for every image and does not automate it at all.

What about converting to YCbCr color space? Using the conversion formula from Wikipedia.
img = im2double(imread('StackOverflow-Example.jpg'));
rp = img(:, :, 1) / 255 ;
bp = img(:, :, 2) / 255 ;
gp = img(:, :, 3) / 255 ;
kb = 0.114;
kr = 0.299;
y = kr * rp + (1 - kr - kb) * gp + kb * bp;
y = max(max(y))-y;
y = y ./ y;
surf(y,'EdgeColor','none','LineStyle','none')
view(0, -90)
It looks like a good job of maintaining the information.
Edit:
I think you want each line
%% Load image and find intensity %%
img = im2double(imread('test.jpg')); % load image and convert to doubles to allow for calculations
rp = img(:, :, 1) / 255 ; % normalized red portion
bp = img(:, :, 2) / 255 ; % normalized blue portion
gp = img(:, :, 3) / 255 ; % normalized green portion
kb = 0.114; % blue constant from Wikipedia
kr = 0.299; % red constant from Wikipedia
x = kr * rp + (1 - kr - kb) * gp + kb * bp; % normalized intensity in image
x = max(max(x))-x; % removed background
y = x ./ x; % everything left is high
z = y;
z(isnan(y)) = 0; % turn nan's to zero
divisions = find(sum(z,2) > 5); % find all lines that have less than 5 pixels
divisions = [divisions(1); divisions(diff(divisions) > 10); size(z, 1)]; % find the line breaks
rows = cell(length(divisions), 1);
for i = 1:numel(rows)-1
line = z(divisions(i):divisions(i+1), :); % grab line
j = divisions(i) + find(sum(line,2) > 5) - 1; % remove the white space
line = y(j, :);
rows{i} = line; %store the line
end
rows(numel(rows)) = [];
%% plot each line %%
for i = 1:numel(rows) ;
figure(i) ;
surf(rows{i},'EdgeColor','none','LineStyle','none');
view(0, -90) ;
end
%% plot entire page %%
figure(numel(rows) + 1)
surf(y,'EdgeColor','none','LineStyle','none') % plot of entire image
view(0, -90)
Edit: 2015/05/18 15:45 GMT
This has the values for the intensity left in:
img = im2double(imread('test.jpg'));
rp = img(:, :, 1) / 255 ;
bp = img(:, :, 2) / 255 ;
gp = img(:, :, 3) / 255 ;
kb = 0.114;
kr = 0.299;
x = kr * rp + (1 - kr - kb) * gp + kb * bp;
x = max(max(x))-x;
xp = x;
xp(xp == min(min(xp))) = nan;
y = x ./ x;
z = y;
z(isnan(y)) = 0;
divisions = find(sum(z,2) > 5);
divisions = [divisions(1); divisions(diff(divisions) > 10); size(z, 1)];
rows = cell(length(divisions) - 1, 1);
for i = 1:numel(rows)
line = z(divisions(i):divisions(i+1), :);
j = divisions(i) + find(sum(line,2) > 5) - 1;
line = xp(j, :);
rows{i} = line;
figure(i) ;
surf(rows{i},'EdgeColor','none','LineStyle','none');
axis('equal')
view(0, -90) ;
end
figure(numel(rows) + 1)
surf(xp,'EdgeColor','none','LineStyle','none')
axis('equal')
view(0, -90)
Edit 2015-05-22 13:21 GMT
%Turn warning message off
warning('off', 'Images:initSize:adjustingMag');
%Read in image in int8
originalImg = imread('test.jpg');
%Convert to double
img = im2double(originalImg);
%Take R, G, & B components
rp = img(:, :, 1) ;
gp = img(:, :, 2) ;
bp = img(:, :, 3) ;
%Get intensity
kb = 0.114;
kr = 0.299;
yp = kr * rp + (1 - kr - kb) * gp + kb * bp;
%Flip to opposite of intensity
ypp = max(max(yp))-yp;
%Normalize flipped intensity
z = ypp ./ ypp;
z(isnan(z)) = 0;
%Find lines, this may need to be tuned
MaxPixelsPerLine = 5;
MinRowsPerLine = 10;
divisions = find(sum(z,2) > MaxPixelsPerLine);
divisions = [divisions(1); divisions(diff(divisions) > MinRowsPerLine); size(z, 1)];
%Preallocate for number of lines
colorRows = cell(length(divisions) - 1, 1);
for i = 1:numel(rows)
%Extract the lines in RGB
line = z(divisions(i):divisions(i+1), :);
j = divisions(i) + find(sum(line,2) > 5) - 1;
colorRows{i} = originalImg(j, :, :);
%Print out the line
figure(i) ;
imshow(colorRows{i})
end
%Print out the oringinal image
figure(numel(rows) + 1)
imshow(originalImg)
%Turn the warning back on
warning('on', 'Images:initSize:adjustingMag');

Short: graythresh(img) migth solve your problem
Longer:
With some morphological Methodes, you can extract the lines pretty easy. Small drawback though: they are somewhat out of order.
load your image
original = imread('o6WEN.jpg');
make it into a greyscale
img=rgb2gray(original); .
define a rectangular structuring element with about textheight and 'very' long
se = strel('rectangle',[30 200]);
Filter it with a tophat filter. Long rectangular shapes with about textheight will be more prominent after this.
img = imtophat(img,se);
Adjust the contrast:
img = imadjust(img);
define another structuring element, this time a line a bit shorter than textheight:
se = strel('line',20,0);
Dilate the picture with it to get rid of presisting gapps between letters
img = imdilate(img,se);
make image into black and with:
img=im2bw(img,graythresh(img));
use regionprops to get all the BoundingBoxes form your lines
stats=regionprops(img,'BoundingBox');
figure, imshow(img)
In Stats are now the Bounding Boxes from all your lines, sadly out of order. Maybe this could be corrected with BWlables or some sort of correlation.
I just looked at the y-Koordinates of the BoundingBoxes and sorted accordingly.
BoundingBoxes=struct2cell(stats);
BoundingBoxes=cell2mat(BoundingBoxes'); % making it into an array
[~,ind]=sort(BoundingBoxes(:,2)); % sorting it to y
BoundingBoxes=BoundingBoxes(ind,:); % apply the sorted vector
lineNr=8;
imshow(original(BoundingBoxes(2,lineNr):BoundingBoxes(2,lineNr)+BoundingBoxes(4,lineNr),BoundingBoxes(1,lineNr):BoundingBoxes(1,lineNr)+BoundingBoxes(3,lineNr) ))
hope that works for you

Related

Matlab - Scale Colorbar of Image

How can I scale the colorbar axis of a false color image?
I read this post,and copied the code but it seems not to work correctly:
MATLAB Colorbar - Same colors, scaled values
Please see the two images below. In the first (without the scaling) the coloraxis goes
[1 2 3 4 5 6]*10^4
In the second image, it goes
[0.005 0.01 0.015 0.02 0.025]
The correct scaling (with C = 100000) would be
[0.1 0.2 0.3 0.4 0.5 0.6]
Without scaling
Wrong scaling
I want that the coloraxis is scaled by 1/C and I can freely choose C, so that when the pixel value = 10^4 and C=10^6 the scale should show 10^-2.
The reason why I multiply my image first by C is to get more decimals places, because all values below 1 will be displayed as zero without the C scaling.
When I run the code I get yticks as a workspace variable with the following values:
[500 1000 1500 2000 2500]
My code:
RGB = imread('IMG_0043.tif');% Read Image
info = imfinfo('IMG_0043.CR2'); % get Metadata
C = 1000000; % Constant to adjust image
x = info.DigitalCamera; % get EXIF
t = getfield(x, 'ExposureTime');% save ExposureTime
f = getfield(x, 'FNumber'); % save FNumber
S = getfield(x, 'ISOSpeedRatings');% save ISOSpeedRatings
date = getfield(x,'DateTimeOriginal');
I = rgb2gray(RGB); % convert Image to greyscale
K = 480; % Kamerakonstante(muss experimentel eavaluiert werden)
% N_s = K*(t*S)/power(f,2))*L
L = power(f,2)/(K*t*S)*C; %
J = immultiply(I,L); % multiply each value with constant , so the Image is Calibrated to cd/m^2
hFig = figure('Name','False Color Luminance Map', 'ToolBar','none','MenuBar','none');
% Create/initialize default colormap of jet.
cmap = jet(16); % or 256, 64, 32 or whatever.
% Now make lowest values show up as black.
cmap(1,:) = 0;
% Now make highest values show up as white.
cmap(end,:) = 1;
imshow(J,'Colormap',cmap) % show Image in false color
colorbar % add colorbar
h = colorbar; % define colorbar as variable
y_Scl = (1/C);
yticks = get(gca,'YTick');
set(h,'YTickLabel',sprintfc('%g', [yticks.*y_Scl]))
ylabel(h, 'cd/m^2')% add unit label
title(date); % Show date in image
caxis auto % set axis to auto
datacursormode on % enable datacursor
img = getframe(gcf);
nowstr = datestr(now, 'yyyy-mm-dd_HH_MM_SS');
folder = 'C:\Users\Taiko\Desktop\FalseColor\';
ImageFiles = dir( fullfile(folder, '*.jpg') );
if isempty(ImageFiles)
next_idx = 1;
else
lastfile = ImageFiles(end).name;
[~, basename, ~] = fileparts(lastfile);
file_number_str = regexp('(?<=.*_)\d+$', basename, 'match' );
last_idx = str2double(file_number_str);
next_idx = last_idx + 1;
end
newfilename = fullfile( folder, sprintf('%s_%04d.jpg', nowstr, next_idx) );
imwrite(img.cdata, newfilename);
Problems:
1) You are getting YTick of the figure (gca) but not the color bar. That would give you the "pixel" coordinates of the graph, instead of the actual values. Use yticks = get(h,'YTick');.
2) caxis auto Should come before overwriting YTicks (and after enabling the color bar); otherwise the scale and ticks will mismatch.
3) Do you mean C = 100000?
Result:

Check for pixel values in a neighborhood

I'm trying to write a MATLAB script that does the following:
Given: pixel coordinates(x,y) for a .jpg image
Goal: Check, within a 5 pixel radius of given coordinates, if there is a pixel of a certain value.
For example, let's say I'm given the coordinates (100,100), then I want to check the neighborhood of (100,100) within my image for any pixels that are black (0,0,0). So perhaps, pixel (103, 100) and (104,100) might have the value (0,0,0).
Current code:
x_coord = uint32(coord(:,1));
y_coord = uint32(coord(:,2));
count = 0;
for i = 1:length(x_coord)
%(img(x,y) returns pixel value at that (x,y)
%Note 0 = black. Indicating that, at that position, the image is just
% black
if img(x_coord(i),y_coord(i)) == 0
count = count + 1;
end
end
It currently only checks at an exact location. Not in a local neighborhood. How to could I extend this?
EDIT: Also note, as long as there as at least one pixel in the neighborhood with the value, I increment count. I'm not trying to enumerate how many pixels in the neighborhood have that value, just trying to find evidence of at least one pixel that has that value.
EDIT:
Even though I am unable to identify an error with the code, I am not able to get the exact results I want. Here is the code I am using.
val = 0; %pixel value to check
N = 50; % neighbourhood radius
%2D grid of coordinates surrounding center coordinate
[R, C] = ndgrid(1 : size(img, 1), 1 : size(img, 2));
for kk = 1 : size(coord, 1)
r = coord(kk, 1); c = coord(kk, 2); % Get pixel locations
% mask of valid locations within the neighbourhood (avoid boundary problems)
mask = (R - r).^2 + (C - c).^2 <= N*N;
pix = img(mask); % Get the valid pixels
valid = any(pix(:) ~= val);
% Add either 0 or 1 depending if we have found any matching pixels
if(valid == 1)
img = insertMarker(img, [r c], 'x', 'color', 'red', 'size', 10);
imwrite(img, images(i).name,'tiff');
end
count = count + valid;
end
An easier way to do this would be to use indexing to grab a neighbourhood, then to check to see if any of the pixels in the neighbourhood have the value that you're looking for, use any on a flattened version of this neighbourhood. The trick with grabbing the right neighbourhood is to first generate a 2D grid of coordinates that span the entire dimensions of your image, then simply use the equation of a circle with the centre of it being each coordinate you are looking at and determine those locations that satisfy the following equation:
(x - a)^2 + (y - b)^2 <= N^2
N is the radius of the observation window, (a, b) is a coordinate of interest while (x, y) is a coordinate in the image. Use meshgrid to generate the coordinates.
You would use the above equation to create a logical mask, index into your image to pull the locations that are valid within the mask and check how many pixels match the one you want. Another added benefit with the above approach is that you are not subject to any out of bounds errors. Because you are pre-generating the list of all valid coordinates in your image, generating the mask will confine you within the boundaries of the image so you never have to check for out of boundaries conditions.... even when you specify coordinates to search that are out of bounds.
Specifically, assuming your image is stored in img, you would do:
count = 0; % Remembers total count of pixels matching a value
val = 0; % Value to match
N = 50; % Radius of neighbourhood
% Generate 2D grid of coordinates
[x, y] = meshgrid(1 : size(img, 2), 1 : size(img, 1));
% For each coordinate to check...
for kk = 1 : size(coord, 1)
a = coord(kk, 1); b = coord(kk, 2); % Get the pixel locations
mask = (x - a).^2 + (y - b).^2 <= N*N; % Get a mask of valid locations
% within the neighbourhood
pix = img(mask); % Get the valid pixels
count = count + any(pix(:) == val); % Add either 0 or 1 depending if
% we have found any matching pixels
end
The proposed solution:
fc = repmat(-5:5,11,1);
I = (fc.^2+fc'.^2)<=25;
fc_x = fc(I);
fc_y = fc'; fc_y = fc_y(I);
for i = 1:length(x_coord)
x_toCheck = fc_x + x_coord(i);
y_toCheck = fc_y + y_coord(i);
I = x_toCheck>0 & x_toCheck<=yourImageWidth;
I = I.*(y_toCheck>0 & y_toCheck<=yourImageHeight);
x_toCheck = x_toCheck(logical(I));
y_toCheck = y_toCheck(logical(I));
count = sum(img(x_toCheck(:),y_toCheck(:)) == 0);
end
If your img function can only check one pixel at a time, just add a for loop:
for i = 1:length(x_coord)
x_toCheck = fc_x + x_coord(i);
y_toCheck = fc_y + y_coord(i);
I = x_toCheck>0 & x_toCheck<=yourImageWidth;
I = I.*(y_toCheck>0 & y_toCheck<=yourImageHeight);
x_toCheck = x_toCheck(logical(I));
y_toCheck = y_toCheck(logical(I));
for j = 1:length(x_toCheck)
count = count + (img(x_toCheck(j),y_toCheck(j)) == 0);
end
end
Step-by-step:
You first need to get all the coordinates within 5 pixels range of the given coordinate.
We start by building a square of 11 pixels in length/width.
fc = repmat(-5:5,11,1);
fc_x = fc;
fc_y = fc';
plot(fc_x,fc_y,'.');
We now need to build a filter to get rid of those points outside the 5-pixel radius.
I = (fc.^2+fc'.^2)<=25;
Apply the filter, so we can get a circle of 5-pixel radius.
fc_x = fc_x(I);
fc_y = fc_y(I);
Next translate the centre of the circle to the given coordinate:
x_toCheck = fc_x + x_coord(i);
y_toCheck = fc_y + y_coord(i);
You need to check whether part of the circle is outside the range of your image:
I = x_toCheck>0 & x_toCheck<=yourImageWidth;
I = I.*(y_toCheck>0 & y_toCheck<=yourImageHeight);
x_toCheck = x_toCheck(logical(I));
y_toCheck = y_toCheck(logical(I));
Finally count the pixels:
count = sum(img(x_toCheck,y_toCheck) == 0);

Matlab image - how to count number of white pixels

The matlab code below splits up an image into a number of smaller images. It then counts the number of black pixels in the image and displays it as a percentage of the total number of pixels in the picture. example of image
My question is - instead of counting the black pixels and displaying the percentage, how can I count the white pixels? (essentially the opposite!)
Thanks
% Divide an image up into blocks (non-overlapping tiles).
clc; % Clear the command window.
close all; % Close all figures (except those of imtool.)
workspace; % Make sure the workspace panel is showing.
fontSize = 20;
% Read the image from disk.
rgbImage = imread('edge-diff.jpg');
% Display image full screen.
imshow(rgbImage);
% Enlarge figure to full screen.
set(gcf, 'units','normalized','outerposition',[0 0 1 1]);
drawnow;
% Get the dimensions of the image. numberOfColorBands should be = 3.
[rows columns numberOfColorBands] = size(rgbImage)
%==========================================================================
% The first way to divide an image up into blocks is by using mat2cell().
blockSizeR = 400; % Rows in block.
blockSizeC = 400; % Columns in block.
% Figure out the size of each block in rows.
% Most will be blockSizeR but there may be a remainder amount of less than that.
wholeBlockRows = floor(rows / blockSizeR);
blockVectorR = [blockSizeR * ones(1, wholeBlockRows), rem(rows, blockSizeR)];
% Figure out the size of each block in columns.
wholeBlockCols = floor(columns / blockSizeC);
blockVectorC = [blockSizeC * ones(1, wholeBlockCols), rem(columns, blockSizeC)];
% Create the cell array, ca.
% Each cell (except for the remainder cells at the end of the image)
% in the array contains a blockSizeR by blockSizeC by 3 color array.
% This line is where the image is actually divided up into blocks.
if numberOfColorBands > 1
% It's a color image.
ca = mat2cell(rgbImage, blockVectorR, blockVectorC, numberOfColorBands);
else
ca = mat2cell(rgbImage, blockVectorR, blockVectorC);
end
percentBlack = cellfun(#(x)sum(sum(all(x == 0, 3))) / (numel(x) / size(x,3)), ca);
% Now display all the blocks.
plotIndex = 1;
numPlotsR = size(ca, 1);
numPlotsC = size(ca, 2);
for r = 1 : numPlotsR
for c = 1 : numPlotsC
fprintf('plotindex = %d, c=%d, r=%d\n', plotIndex, c, r);
% Specify the location for display of the image.
subplot(numPlotsR, numPlotsC, plotIndex);
ax2 = subplot(numPlotsR, numPlotsC, plotIndex);
% Extract the numerical array out of the cell
% just for tutorial purposes.
rgbBlock = ca{r,c};
imshow(rgbBlock); % Could call imshow(ca{r,c}) if you wanted to.
[rowsB columnsB numberOfColorBandsB] = size(rgbBlock);
set(ax2, 'box', 'on', 'Visible', 'on', 'xtick', [], 'ytick', []);
% Make the caption the block number.
averageBlack = percentBlack(r,c);
disp(numPlotsR);
disp(averageBlack);
caption = sprintf('Frame #%d of %d\n Percentage information content %0.2f', ...
plotIndex, numPlotsR*numPlotsC, averageBlack*100);
title(caption);
drawnow;
% Increment the subplot to the next location.
plotIndex = plotIndex + 1;
end
end
This line:
percentBlack = cellfun(#(x)sum(sum(all(x == 0, 3))) / (numel(x) / size(x,3)), ca);
specifically the part that says all(x == 0, 3) means "all color channels have value 0". You want to change it to "all color channels have value 1 (or 255 depends on your image)"
So basically, change that 0 to 1 or 255, deependinf if your image is unit8 or double

Cubic to equirectangular projection algorithm

I have a cube map texture which defines a surrounding, however I need to pass it to a program which only works with latitude/longitude maps. I am really at lost here on how to do the translation. Any help here?
In other words, I need to come from here:
To this (I think that image has an aditional -90° rotation over the x axis):
update: I got the official names of the projections. By the way, I found the opposite projection here
A general procedure for projecting raster images like this is:
for each pixel of the destination image:
calculate the corresponding unit vector in 3-dimensional space
calculate the x,y coordinate for that vector in the source image
sample the source image at that coordinate and assign the value to the destination pixel
The last step is simply interpolation. We will focus on the other two steps.
The unit vector for a given latitude and longitude is (+z towards the north pole, +x towards the prime meridian):
x = cos(lat)*cos(lon)
y = cos(lat)*sin(lon)
z = sin(lat)
Assume the cube is +/- 1 unit around the origin (i.e. 2x2x2 overall size).
Once we have the unit vector, we can find the face of the cube it's on by looking at the element with the largest absolute value. For example, if our unit vector was <0.2099, -0.7289, 0.6516>, then the y element has the largest absolute value. It's negative, so the point will be found on the -y face of the cube. Normalize the other two coordinates by dividing by the y magnitude to get the location within that face. So, the point will be at x=0.2879, z=0.8939 on the -y face.
I'd like to share my MATLAB implementation of this conversion. I also borrowed from the OpenGL 4.1 specification, Chapter 3.8.10 (found here), as well as Paul Bourke's website (found here). Make sure you look under the subheading: Converting to and from 6 cubic environment maps and a spherical map.
I also used Sambatyon's post above as inspiration. It started off as a port from Python over to MATLAB, but I made the code so that it is completely vectorized (i.e. no for loops). I also take the cubic image and split it up into 6 separate images, as the application I'm building has the cubic image in this format. Also there is no error checking with the code, and that this assumes that all of the cubic images are of the same size (n x n). This also assumes that the images are in RGB format. If you'd like to do this for a monochromatic image, simply comment out those lines of code that require access to more than one channel. Here we go!
function [out] = cubic2equi(top, bottom, left, right, front, back)
% Height and width of equirectangular image
height = size(top, 1);
width = 2*height;
% Flags to denote what side of the cube we are facing
% Z-axis is coming out towards you
% X-axis is going out to the right
% Y-axis is going upwards
% Assuming that the front of the cube is towards the
% negative X-axis
FACE_Z_POS = 1; % Left
FACE_Z_NEG = 2; % Right
FACE_Y_POS = 3; % Top
FACE_Y_NEG = 4; % Bottom
FACE_X_NEG = 5; % Front
FACE_X_POS = 6; % Back
% Place in a cell array
stackedImages{FACE_Z_POS} = left;
stackedImages{FACE_Z_NEG} = right;
stackedImages{FACE_Y_POS} = top;
stackedImages{FACE_Y_NEG} = bottom;
stackedImages{FACE_X_NEG} = front;
stackedImages{FACE_X_POS} = back;
% Place in 3 3D matrices - Each matrix corresponds to a colour channel
imagesRed = uint8(zeros(height, height, 6));
imagesGreen = uint8(zeros(height, height, 6));
imagesBlue = uint8(zeros(height, height, 6));
% Place each channel into their corresponding matrices
for i = 1 : 6
im = stackedImages{i};
imagesRed(:,:,i) = im(:,:,1);
imagesGreen(:,:,i) = im(:,:,2);
imagesBlue(:,:,i) = im(:,:,3);
end
% For each co-ordinate in the normalized image...
[X, Y] = meshgrid(1:width, 1:height);
% Obtain the spherical co-ordinates
Y = 2*Y/height - 1;
X = 2*X/width - 1;
sphereTheta = X*pi;
spherePhi = (pi/2)*Y;
texX = cos(spherePhi).*cos(sphereTheta);
texY = sin(spherePhi);
texZ = cos(spherePhi).*sin(sphereTheta);
% Figure out which face we are facing for each co-ordinate
% First figure out the greatest absolute magnitude for each point
comp = cat(3, texX, texY, texZ);
[~,ind] = max(abs(comp), [], 3);
maxVal = zeros(size(ind));
% Copy those values - signs and all
maxVal(ind == 1) = texX(ind == 1);
maxVal(ind == 2) = texY(ind == 2);
maxVal(ind == 3) = texZ(ind == 3);
% Set each location in our equirectangular image, figure out which
% side we are facing
getFace = -1*ones(size(maxVal));
% Back
ind = abs(maxVal - texX) < 0.00001 & texX < 0;
getFace(ind) = FACE_X_POS;
% Front
ind = abs(maxVal - texX) < 0.00001 & texX >= 0;
getFace(ind) = FACE_X_NEG;
% Top
ind = abs(maxVal - texY) < 0.00001 & texY < 0;
getFace(ind) = FACE_Y_POS;
% Bottom
ind = abs(maxVal - texY) < 0.00001 & texY >= 0;
getFace(ind) = FACE_Y_NEG;
% Left
ind = abs(maxVal - texZ) < 0.00001 & texZ < 0;
getFace(ind) = FACE_Z_POS;
% Right
ind = abs(maxVal - texZ) < 0.00001 & texZ >= 0;
getFace(ind) = FACE_Z_NEG;
% Determine the co-ordinates along which image to sample
% based on which side we are facing
rawX = -1*ones(size(maxVal));
rawY = rawX;
rawZ = rawX;
% Back
ind = getFace == FACE_X_POS;
rawX(ind) = -texZ(ind);
rawY(ind) = texY(ind);
rawZ(ind) = texX(ind);
% Front
ind = getFace == FACE_X_NEG;
rawX(ind) = texZ(ind);
rawY(ind) = texY(ind);
rawZ(ind) = texX(ind);
% Top
ind = getFace == FACE_Y_POS;
rawX(ind) = texZ(ind);
rawY(ind) = texX(ind);
rawZ(ind) = texY(ind);
% Bottom
ind = getFace == FACE_Y_NEG;
rawX(ind) = texZ(ind);
rawY(ind) = -texX(ind);
rawZ(ind) = texY(ind);
% Left
ind = getFace == FACE_Z_POS;
rawX(ind) = texX(ind);
rawY(ind) = texY(ind);
rawZ(ind) = texZ(ind);
% Right
ind = getFace == FACE_Z_NEG;
rawX(ind) = -texX(ind);
rawY(ind) = texY(ind);
rawZ(ind) = texZ(ind);
% Concatenate all for later
rawCoords = cat(3, rawX, rawY, rawZ);
% Finally determine co-ordinates (normalized)
cubeCoordsX = ((rawCoords(:,:,1) ./ abs(rawCoords(:,:,3))) + 1) / 2;
cubeCoordsY = ((rawCoords(:,:,2) ./ abs(rawCoords(:,:,3))) + 1) / 2;
cubeCoords = cat(3, cubeCoordsX, cubeCoordsY);
% Now obtain where we need to sample the image
normalizedX = round(cubeCoords(:,:,1) * height);
normalizedY = round(cubeCoords(:,:,2) * height);
% Just in case.... cap between [1, height] to ensure
% no out of bounds behaviour
normalizedX(normalizedX < 1) = 1;
normalizedX(normalizedX > height) = height;
normalizedY(normalizedY < 1) = 1;
normalizedY(normalizedY > height) = height;
% Place into a stacked matrix
normalizedCoords = cat(3, normalizedX, normalizedY);
% Output image allocation
out = uint8(zeros([size(maxVal) 3]));
% Obtain column-major indices on where to sample from the
% input images
% getFace will contain which image we need to sample from
% based on the co-ordinates within the equirectangular image
ind = sub2ind([height height 6], normalizedCoords(:,:,2), ...
normalizedCoords(:,:,1), getFace);
% Do this for each channel
out(:,:,1) = imagesRed(ind);
out(:,:,2) = imagesGreen(ind);
out(:,:,3) = imagesBlue(ind);
I've also made the code publicly available through github and you can go here for it. Included is the main conversion script, a test script to show its use and a sample set of 6 cubic images pulled from Paul Bourke's website. I hope this is useful!
Project changed name to libcube2cyl. Same goodness, better working examples both in C and C++.
Now also available in C.
I happened to solve the exact same problem as you described.
I wrote this tiny C++ lib called "Cube2Cyl", you can find the detailed explanation of algorithm here: Cube2Cyl
Please find the source code from github: Cube2Cyl
It is released under MIT licence, use it for free!
So, I found a solution mixing this article on spherical coordinates from wikipedia and the Section 3.8.10 from the OpenGL 4.1 specification (plus some hacks to make it work). So, assuming that the cubic image has a height h_o and width w_o, the equirectangular will have a height h = w_o / 3 and a width w = 2 * h. Now for each pixel (x, y) 0 <= x <= w, 0 <= y <= h in the equirectangular projection, we want to find the corresponding pixel in the cubic projection, I solve it using the following code in python (I hope I didn't make mistakes while translating it from C)
import math
# from wikipedia
def spherical_coordinates(x, y):
return (math.pi*((y/h) - 0.5), 2*math.pi*x/(2*h), 1.0)
# from wikipedia
def texture_coordinates(theta, phi, rho):
return (rho * math.sin(theta) * math.cos(phi),
rho * math.sin(theta) * math.sin(phi),
rho * math.cos(theta))
FACE_X_POS = 0
FACE_X_NEG = 1
FACE_Y_POS = 2
FACE_Y_NEG = 3
FACE_Z_POS = 4
FACE_Z_NEG = 5
# from opengl specification
def get_face(x, y, z):
largest_magnitude = max(x, y, z)
if largest_magnitude - abs(x) < 0.00001:
return FACE_X_POS if x < 0 else FACE_X_NEG
elif largest_magnitude - abs(y) < 0.00001:
return FACE_Y_POS if y < 0 else FACE_Y_NEG
elif largest_magnitude - abs(z) < 0.00001:
return FACE_Z_POS if z < 0 else FACE_Z_NEG
# from opengl specification
def raw_face_coordinates(face, x, y, z):
if face == FACE_X_POS:
return (-z, -y, x)
elif face == FACE_X_NEG:
return (-z, y, -x)
elif face == FACE_Y_POS:
return (-x, -z, -y)
elif face == FACE_Y_NEG:
return (-x, z, -y)
elif face == FACE_Z_POS:
return (-x, y, -z)
elif face == FACE_Z_NEG:
return (-x, -y, z)
# computes the topmost leftmost coordinate of the face in the cube map
def face_origin_coordinates(face):
if face == FACE_X_POS:
return (2*h, h)
elif face == FACE_X_NEG:
return (0, 2*h)
elif face == FACE_Y_POS:
return (h, h)
elif face == FACE_Y_NEG:
return (h, 3*h)
elif face == FACE_Z_POS:
return (h, 0)
elif face == FACE_Z_NEG:
return (h, 2*h)
# from opengl specification
def raw_coordinates(xc, yc, ma):
return ((xc/abs(ma) + 1) / 2, (yc/abs(ma) + 1) / 2)
def normalized_coordinates(face, x, y):
face_coords = face_origin_coordinates(face)
normalized_x = int(math.floor(x * h + 0.5))
normalized_y = int(math.floor(y * h + 0.5))
# eliminates black pixels
if normalized_x == h:
--normalized_x
if normalized_y == h:
--normalized_y
return (face_coords[0] + normalized_x, face_coords[1] + normalized_y)
def find_corresponding_pixel(x, y):
spherical = spherical_coordinates(x, y)
texture_coords = texture_coordinates(spherical[0], spherical[1], spherical[2])
face = get_face(texture_coords[0], texture_coords[1], texture_coords[2])
raw_face_coords = raw_face_coordinates(face, texture_coords[0], texture_coords[1], texture_coords[2])
cube_coords = raw_coordinates(raw_face_coords[0], raw_face_coords[1], raw_face_coords[2])
# this fixes some faces being rotated 90°
if face in [FACE_X_NEG, FACE_X_POS]:
cube_coords = (cube_coords[1], cube_coords[0])
return normalized_coordinates(face, cube_coords[0], cube_coords[1])
at the end we just call find_corresponding_pixel for each pixel in the equirectangular projection
I think from your algorithm in Python you might have inverted x and y in the calculation of theta and phi.
def spherical_coordinates(x, y):
return (math.pi*((y/h) - 0.5), 2*math.pi*x/(2*h), 1.0)
from Paul Bourke's website here
theta = x pi
phi = y pi / 2
and in your code you are using y in the theta calculation and x in the phi calculation.
Correct me if I am wrong.

MATLAB coding problem

Hey guys, I got this error message when I tried to trigger the function below. Can anybody help me out? Thanks!
>> changeYuv('tilt.yuv',352,288,1:40,40);
??? Index exceeds matrix dimensions.
Error in ==> changeYuv at 32
j=histogram(imgYuv(:,:,1,k+1));
>> [x,y,z,a]=size(imgYuv)
x =
288
y =
352
z =
3
a =
40
The source code:
function [imgYuv, S]= changeYuv(fileName, width, height, idxFrame, nFrames)
% load RGB movie [0, 255] from YUV 4:2:0 file
fileId = fopen(fileName, 'r');
subSampleMat = [1, 1; 1, 1];
nrFrame = length(idxFrame);
for f = 1 : 1 : nrFrame
% search fileId position
sizeFrame = 1.5 * width * height;
fseek(fileId, (idxFrame(f) - 1) * sizeFrame, 'bof');
% read Y component
buf = fread(fileId, width * height, 'uchar');
imgYuv(:, :, 1,f) = reshape(buf, width, height).';
% read U component
buf = fread(fileId, width / 2 * height / 2, 'uchar');
imgYuv(:, :, 2,f) = kron(reshape(buf, width / 2, height / 2).', subSampleMat); % reshape and upsample
% read V component
buf = fread(fileId, width / 2 * height / 2, 'uchar');
imgYuv(:, :, 3,f) = kron(reshape(buf, width / 2, height / 2).', subSampleMat); % reshape and upsample
%histogram difference of Y component
for k=1:(nFrames-1)
h=histogram(imgYuv(:,:,1,k));
j=histogram(imgYuv(:,:,1,k+1));
X=abs(h-j)/256;
S(k)=sum(X);
end
end
fclose(fileId);
On every iteration of the outer loop, you appear to be growing imgYuv by one in the 4th dimension, starting from empty. But your inner loop always loops from 1 to nFrames-1. Therefore, it would seem to me like you're trying to access beyond the extent of imgYuv.
On an unrelated note, growing an array like this is typically very slow. You're much better off initialising imgYuv before you start, i.e. imgYuv = zeros([height,width,3,nFrames]).

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