Commit f280465a authored by Jean-Yves TINEVEZ's avatar Jean-Yves TINEVEZ
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Merge branch 'rework-pub' into 'master'

Rework the whole code for the upcoming publication.

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# DeProj output and properties.
We give here the list of properties stored in the DeProj classes and their definition.
**Table of Contents**
* [DeProj output and properties.](#deproj-output-and-properties)
* [The core classes: deproj and epicell.](#the-core-classes-deproj-and-epicell)
* [The epicell class properties.](#the-epicell-class-properties)
* [boundary](#boundary)
* [center](#center)
* [junction_ids](#junction_ids)
* [n_neighbors](#n_neighbors)
* [area](#area)
* [perimeter](#perimeter)
* [euler_angles](#euler_angles)
* [curvatures](#curvatures)
* [ellipse_fit](#ellipse_fit)
* [eccentricity](#eccentricity)
* [proj_direction](#proj_direction)
* [uncorrected_area](#uncorrected_area)
* [uncorrected_perimeter](#uncorrected_perimeter)
* [id](#id)
* [The deproj class properties.](#the-deproj-class-properties)
* [epicells](#epicells)
* [junction_graph](#junction_graph)
* [units](#units)
## The core classes: `deproj` and `epicell`.
The DeProj toolbox revolves around two MATLAB classes:
- The `epicell`class is used to store the data for one cell in a tissue. It is made of several fields we describe below:
o =
epicell with properties:
boundary: [26×3 single]
center: [2.4705 11.1826 3.1008]
junction_ids: [5×1 double]
area: 8.0176
perimeter: 12.5227
euler_angles: [-2.0734 0.4195 -0.2500]
curvatures: [0.0110 -4.8103e-05 0.0240 -0.0020]
ellipse_fit: [2.2284 11.1114 3.1008 2.3848 1.1178 0.4528]
eccentricity: 0.8834
proj_direction: 1.2539
uncorrected_area: 7.3173
uncorrected_perimeter: 12.1116
id: 4
- The `deproj` class manages a collection of `epicell`s, and represent for instance the results of the analysis of a whole image.
dpr =
deproj with properties:
epicells: [426×1 epicell]
junction_graph: [1×1 graph]
units: 'µm'
## The `epicell` class properties.
### `boundary`
The `boundary` property stores a 3D polygon that delimits the cell. It is represented as a `N x 3` matrix, with points sorted along the polygon. The coordinates are in physical units. The Z-values are the position of the vertices on the tissue surface, given the by the smoothed height-map.
There are fewer than on vertex per pixel on the original segmentation image: we prune redundant points to lower the memory footprint of segmentation results.
o = dpr.epicells(1);
p = o.boundary;
plot3( p(:,1), p(:,2), p(:,3), 'k-o' )
xlabel('x (µm)'), ylabel('y (µm)'), zlabel('z (µm)')
axis equal
<img src="static/BoundaryPlot.png" alt="BoundaryPlot" width="400" />
### `center`
The cell center in physical coordinates. `1 x 3` array.
### `junction_ids`
The list of indices of junctions that this cell touches.
You can notice that a `deproj` instance has a `junction_graph` property. This is the graph of the junctions in the tissues. A junction is a location on the tissue surface where at least 3 cells connect. We give more details in the next section on `deproj` properties.
dpr =
deproj with properties:
epicells: [426×1 epicell]
junction_graph: [1×1 graph]
units: 'µm'
>> ids = o.junction_ids
ids =
>> j = dpr.junction_graph.Nodes( ids, : )
j =
4×2 table
Centroid ID
___________________________ __
0.366 23.424 0.36189 1
0.976 24.034 0.3217 5
1.647 21.228 0.90516 10
2.257 21.838 0.92981 16
>> pj = j.Centroid;
>> plot3( p(:,1), p(:,2), p(:,3), 'k-o' )
>> axis equal, hold on
>> plot3( pj(:,1), pj(:,2), pj(:,3), 'ro', 'MarkerFaceColor', 'r' )
>> xlabel('x (µm)'), ylabel('y (µm)'), zlabel('z (µm)')
<img src="static/BoundaryJunctionPlug.png" alt="BoundaryJunctionPlug" width="400" />
### `n_neighbors`
How many neighbours have a cell. Note that for cells on the border of the tissue, we try to deal with border effects. For a cell at the border, we count the number of neighbours including all cells, even the ones not drawn because they are cropped by the image borders.
### `area`
The area of the apical surface of the cell, delimeted by its boundary. This value reports the 3D area, of the de-projected cell on the tissue surface. Units are physical units; if you used a pixel size in µm, the area will be in µm².
### `perimeter`
The perimeter of the cell boundary, in physical coordinates. Again, using the real 3D coordinates and physical units of length.
### `euler_angles`
The orientation of the cell apical surface plane. This property is not entirely trivial.
The 3D boundary of the cell define an oblique plane to which they are the closest. This local plane has a certain orientation, that we give as the Euler angles, in radians, as a `1 x 3` array. The Euler angles are reported using the [ZX'Z'' convention]( Repeating what we said in the example:
- The first one, `alpha` is the orientation of the cell plane. As an analogy, imaging you are facing a hill, the slope going up. The direction (south, west…) in which the slope is the largest is given by the angle `alpha`. Values within `[-π ; π[`.
- The second one, `beta` measures the slope of this plane with XY plane (middle panel). A value of 0º indicates that the cell plane is parallel to XY. Values within `[0 ; π[`.
- The third one , `gamma` measures the cell main orientation in the cell plane (bottom panel). Because the cell plane was rotated a first time by `alpha`, this angle does not give a result immediately usable.
### `curvatures`
Local curvature metrics at the cell center.
The height-maps gives the shape of the tissue surface, so we can derive the local curvature from it. The `curvatures` property is a `1 x 4` array that gives respectively:
- The [mean curvature](
- The [Gaussian curvature](
- The first [principle curvature](
- The second principle curvature.
They are in physical units. If you used a pixel size in µm, the mean curvature, the first and second principle cuvature will be in 1/µm, and the Gaussian curvature will be in 1/µm².
### `ellipse_fit`
Results of the fit of a 2D ellipse on the 3D boundary of the cell.
The cell apical plane we discribe above, and which orientation is given by the `euler_angles` property, is the plane to which the 3D points of the boundary are the closest. If we project the 3D points on this plane, we can fit an ellipse to the projected 2D plane and yield a description of the cell extend and orientation. Caution: the ellipse fit is not made on the XY plane, but on an oblique plane locally tangent to the tissue. Check the Figure 3 on the example, and rotate it, to see that the ellipses have a 3D orientation.
The `ellipse_fit` contains the result of the fit, in this tangent plane, as a `1 x 6` array, containing respectively:
- The x coordinate of the ellipse center, in physical units.
- The y coordinate of the ellipse center, in physical units.
- The z coordinate of the ellipse center, in physical units. These 3 coordinates should have values very close that of the `center` property.
- The [semi-major axis of the ellipse]( `a`, in physical units.
- The semi-minor axis of the ellipse `b`, in physical units. We always have `a > b` and both values are positive.
- The angle of the semi-major axis with the X'' axis in the rotated tangent plane, in radians. Because this plane was rotated twice with respect to the tissue (euler angles alpha and gamma, this value is not directly usable. See the `proj_direction` property.
### `eccentricity`
The ellipse [eccentricity](, derived from the `ellipse_fit` field.
It measures how elongated it the cell and varies from 0 to 1. Cells with an eccentricity of 0 resemble a circle. Cells with an eccentricity close to 1 are very elongated.
### `proj_direction`
The angle of the long axis of the cell ellipse, with respect to the X axis of the tissue. In radians. See the Figure 3 of the main example.
### `uncorrected_area`
The area of the cell, *if it was projected and measured on the XY plane*.This property is included only to assess the impact of the projection distorsion artifact. In physical units.
### `uncorrected_perimeter`
The same, for the cell perimeter.
### `id`
The cell unique ID within a `deproj` instance. Strictly positive integers.
## The `deproj` class properties.
A `deproj` instance has only 3 properties.
### `epicells`
A `N x 1` array of `epicell` instances. Each `epicell` represents a cell in the tissue. See above for its properties. The `id` property of an `epicell` corresponds to its index in this array.
### `junction_graph`
A undirected graph of junction connections.
A junction is a location on the tissue surface where at least 3 cells connect.
<img src="static/JunctionExample.png" alt="JunctionExample" width="300" />
The graph stored in the `junction_graph` property is made of the junctions as nodes, and of their connection of edges. If two junctions are linked by an edge in this graph, it means that there is exactly one ridge between two cells that connects them.
The nodes store their ID and the 3D position of their centroid, in physical units. Because a junction can be made of several pixels, the `Centroid` matrix gives the X, Y, Z position of the pixels that compose a junction.
>> g = dpr.junction_graph
g =
graph with properties:
Edges: [1329×1 table]
Nodes: [920×2 table]
>> head(g.Nodes)
ans =
8×2 table
Centroid ID
___________________________ __
0.366 23.424 0.36189 1
0.732 19.581 0.98203 2
0.732 24.705 0.19083 3
1.098 4.575 3.898 4
0.976 24.034 0.3217 5
1.281 10.614 2.8064 6
1.464 3.294 4.3027 7
1.586 14.335 2.0956 8
The edges simply store theirs source and target node ids:
>> head(g.Edges)
ans =
8×1 table
1 5
1 10
3 5
3 11
4 7
4 14
5 16
6 12
Edges are undirected and there are no duplicates.
We can use this junction graph to plot a topological representation of the segmentation results:
% Path to the images.
>> root_folder = 'samples';
% Load the segmentation image.
>> mask_filename = 'Segmentation-2.tif';
>> I = imread( fullfile( root_folder, mask_filename ) );
% Because we want to display the image with the same coordinates
% that of the junctions, we need to specify the pixel size and use
% the 'XData' and 'YData' arguments of imshow.
>> pixel_size = 0.183; % µm
% Display the segmentation.
>> imshow( ~I , [ 0 1 ], ...
'Border', 'tight', ...
'Xdata', pixel_size * [ 1 size(I,2) ], ...
'YData', pixel_size * [ 1 size(I,1) ] )
>> hold on
% Get the junction graph (run the RunExample.m file first)
g = dpr.junction_graph;
% Display the junction graph. We use the graph builtin plot method. We just use a 2D plot.
>> plot( g, ...
'XData', g.Nodes.Centroid(:,1), ...
'YData', g.Nodes.Centroid(:,2), ...
'LineWidth', 2, ...
'EdgeColor', 'b', ...
'EdgeAlpha', 1, ...
'Marker', 'o', ...
'MarkerSize', 4, ...
'NodeColor', 'r' )
% Another simpler solution is to directly use a special deproj plotting method.
% This one plots the junction graph in 3D, with white edges. Uncomment it to try.
% dpr.plot_values_junction( 'w', gca )
### `units`
This property simply stores the name of the physical unit of length that was specified at creation. It is useful to generate properly annotated figures.
close all
mask_path = 'GT.tif';
% ImageJ mask.
I = imread( mask_path );
[ objects, junction_graph ] = mask_to_objects( I );
fprintf('Analyzed a %d x %d mask in %.1f seconds.\n', size(I,1), size(I,2), toc )
%% Plot everything.
imshow( ~I , [ 0 2 ], 'Border', 'tight' )
hold on
plot( junction_graph, ...
'XData', junction_graph.Nodes.Centroid(:,1), ...
'YData', junction_graph.Nodes.Centroid(:,2), ...
'LineWidth', 2, ...
'EdgeColor', 'b', ...
'EdgeAlpha', 1, ...
'Marker', 'o', ...
'MarkerSize', 4, ...
'NodeColor', 'r' )
function displayCombinedMap(tableOutputDeproj,tableOutputBell,contour3D,outputFolder)
% If not specified, the default display is now in real space (not projected)
% For shape descriptor see publication Zdilla et al. 2016
% Usual call is
% displayCombinedMap(tableOutputDeproj,tableOutputBell,dataCells.cellContour3D)
% close all
scriptVersion = 'displayCombinedMap_v0p5';
nSec = 5; % give 5 sec to the software to save the image before going to the next
if nargin==3
outputFolder = uigetdir(pwd,'Select the output folder');
dataBool.doApical = true;
dataBool.doNeighbours = true;
dataBool.doAreaRatioRP = true;
dataBool.doAreaRatioPB = true;
dataBool.doPerimeter = true;
dataBool.doAnisotropy = true;
dataBool.doCircularity = true;
dataBool.doRoundness = true;
dataBool.doOrientation = true;
% dataBool.doApical = false;
% dataBool.doNeighbours = false;
% dataBool.doAreaRatioRP = false;
% dataBool.doAreaRatioPB = false;
% dataBool.doPerimeter = false;
% dataBool.doAnisotropy = false;
% dataBool.doCircularity = false;
% dataBool.doRoundness = false;
% dataBool.doOrientation = true;
% %% Ask the user for which data to plot => For later...
% prompt = {'Enter the matrix size for x^2:';'Enter the colormap name:'};
% name = 'Please select the variable to display';
% Formats = {};
% Formats(1,1).type = 'list';
% Formats(1,1).style = 'listbox';
% Formats(1,1).items = {'Apical area','Nbr of neighbours','Area ratio (Real/Proj)',...
% 'Area ratio (Proj/Bell)','Perimeter (Real)','Circularity (Real)','Roundness (Real)'};
% Formats(1,1).limits = [0 numel(Formats(1).items)]; % multi-select
% [Answer, Cancelled] = inputsdlg(prompt, name, Formats);
%% Data to plot
% Apical area
if dataBool.doApical
dataVal = tableOutputDeproj.AreaReal;
titleFig = 'Cell apical surface area (Real)';
figName = 'mapApicalArea';
% Nbr of neighbours
if dataBool.doNeighbours
dataVal = tableOutputDeproj.NbrNeighbours;
titleFig = 'Nbr of neighbours';
figName = 'mapNbrNeighbours';
% Area ratio (real vs proj)
if dataBool.doAreaRatioRP
dataVal = tableOutputDeproj.AreaReal./tableOutputDeproj.AreaProj;
titleFig = 'Cell apical surface area ratio (Real/Proj)';
figName = 'mapAreaRatio_RP';
% Area ratio (Proj vs Bell)
if dataBool.doAreaRatioPB
dataVal = tableOutputDeproj.AreaProj./tableOutputBell.AreaBell;
titleFig = 'Cell apical surface area ratio (Proj/Bell)';
figName = 'mapAreaRatio_PB';
% Perimeter
if dataBool.doPerimeter
dataVal = tableOutputDeproj.PerimeterReal;
titleFig = 'Cell perimeter (Real)';
figName = 'mapPerimeter';
% Anisotropy (Real) (as calculated by Bellaiche lab: 1-1/elongation)
if dataBool.doAnisotropy
dataVal = tableOutputDeproj.AnisotropyReal;
titleFig = 'Cell anisotropy (Real)';
figName = 'mapAnisotropy';
% Circularity is a shape descriptor that can mathematically indicate the degree of similarity to a perfect circle
if dataBool.doCircularity % Error in the method
dataVal = (4*pi*(tableOutputDeproj.AreaEllipseReal) ./ (tableOutputDeproj.PerimeterEllipseReal.^2));
titleFig = 'Cell circularity (Real)';
figName = 'mapCircularity';
% Roundness is similar to circularity but is insensitive to irregular borders along the perimeter
if dataBool.doRoundness
dataVal = 4*tableOutputDeproj.AreaEllipseReal./(pi*(tableOutputDeproj.semiMajAxReal*2).^2);
titleFig = 'Cell roundness (Real)';
figName = 'mapRoundness';
% Orientation of the cell is representing the orientation of the fitted
% ellipse on the cell contour on the mesh. Vector length is weighted by the
if dataBool.doOrientation
% Arrow length is function of the anisotropy
dataVec = tableOutputDeproj.OrientationEllipseReal.*...
% Set the origin of the arrow
dataOri = tableOutputDeproj.centerEllipseReal;
titleFig = 'Cell orientation (Real)';
figName = 'mapOrientation';
function dispPolygonMap(dataVal,titleFig,figName,contour3D,nSec)
%% Preparing the colormap
dataRange = max(dataVal)-min(dataVal);
greyLvlNbr = 200;
color2plot = round(((dataVal-min(dataVal))/dataRange)*(greyLvlNbr-1)+1);
fprintf('displaying: %s\n',titleFig);
dataColor = parula(greyLvlNbr);
%% Plot the figure
hold on
for bioCell = 1:numel(dataVal)
if isnan(dataVal(bioCell))
fprintf('Warning: A value was not set properly: skipping cell %d\n',bioCell);
dataColor(color2plot(bioCell),:), ...
'LineStyle', 'none');
%% Set axes and colorbar
h = colorbar;
caxis([min(dataVal) max(dataVal)])
axis equal
xlabel('X position ({\mu}m)'); ylabel('Y position ({\mu}m)');
zlabel('Z position ({\mu}m)');
function dispQuiverMap(dataOri,dataVec,titleFig,figName,nSec)
fprintf('displaying: %s\n',titleFig);
% plot the figure
axis equal
%% Set axes and colorbar
axis equal
xlabel('X position ({\mu}m)'); ylabel('Y position ({\mu}m)');
zlabel('Z position ({\mu}m)');
function displaySubplotCellContour(cellListError, cellListContour, dim)
% Display the cell contour of a cell list into a subplot
% Display the cells with a fit error
if numel(cellListError) > 20
fprinf('Too many cells were not fitted properly. Only fitting the first 20 cells\n');
nSub = 20;
nSub = numel(cellListError);
[subPlotSize,~] = numSubplots(nSub);
hold on
for bioCell = 1:nSub
legend(sprintf('cell %d',cellListError(bioCell)))
supAxes=[.08 .08 .84 .84];
[~,~]=suplabel(sprintf('Not fitted cells (in %d dimension)\n',dim) ,'t', supAxes);