diff --git a/DeProjMethods.md b/DeProjMethods.md
index 7669bdfcda83cf4701157068e27ccefeb7b7bd84..71335183718f692de41bc47ace107bc8bd8ecc8e 100644
--- a/DeProjMethods.md
+++ b/DeProjMethods.md
@@ -2,8 +2,240 @@
We document here the methods of the two DeProj classes `deproj` and `epicell`. We separate methods in the ones that are useful for users of DeProj and the secondary ones that are used by other methods.
+But the really important methods are those who create a `deproj` analysis results from the images. You can directly jump to the `deproj.from_heightmap` method.
+
[TOC]
+## The `deproj` class methods.
+
+A `deproj` instance has several interesting methods, that let you export and display the analysis results. In particular the plotting routines: you will most likely be adapting them to your needs with a bit of MATLAB.
+
+### Main `deproj` methods.
+
+#### Static method `from_heightmap`
+
+This is the most important method of DeProj. It generates analysis results in the shape of a `deproj` object from a segmentation mask and a height-map image.
+
+```matlab
+obj = deproj.from_heightmap( ...
+ I, ...
+ H, ...
+ pixel_size, ...
+ voxel_depth, ...
+ units, ...
+ invert_z, ...
+ inpaint_zeros, ...
+ prune_zeros )
+```
+
+Returns a `deproj` object built from segmentation and height-map.
+
+You need two images as input.
+
+The **segmentation mask image** is the results of the segmentation step, and must be a black and white image where each object is white and separated from its neighbor by a black ridge. Importantly the ridge must be connected using 8-connectivity. For instance, this is good (the ridges can be connected by the pixel diagonals):
+
+
+
+
+
+The following is **not good** (the ridges only move east west north and south):
+
+The height-map.The height-map is an image of the exact same size that the segmentation image, and for which the pixel value reports the Z position of the tissue surface. For instance:
+
+
+
+On this example the pixel value is an integer that gives the Z-plane from which the projection pixel was taken.
+
+We now explain the meaning of other parameters in an example using the images that are present in the `samples` folder of this repository. They are a small excerpt of a 3D image of a drosophila pupal notum labelled for E-cadherin, and projected with the LocalZProjector (courtesy of Léo Valon, [Romain Levayer lab](https://research.pasteur.fr/en/team/cell-death-and-epithelial-homeostasis/), Institut Pasteur).
+
+```matlab
+% You must first load the two images.
+% Path to the images.
+>> root_folder = 'samples';
+
+>> mask_filename = 'Segmentation-2.tif';
+>> I = imread( fullfile( root_folder, mask_filename ) );
+
+>> heightmap_filename = 'HeightMap-2.tif';
+>> H = imread( fullfile( root_folder, heightmap_filename ) );
+
+% We can directly report all the measurements in physical units.
+% To do so we need to specify what is the unit of length,
+% and what is the pixel size in X & Y:
+>> pixel_size = 0.183; % µm
+>> units = 'µm';
+>> voxel_depth = 1.; % µm
+
+% Finally we have some options to deal with tissue orientation and missing tissue.
+% When we have `value =Â 0` in a region of the height-map, this signals that the
+% projection is not defined at this location, for instance if the tissue is not
+% imaged in these regions. We can then extrapolate the height-map there,
+% and/or remove cells that touch such a region.
+
+% If this flag is set to true, the height-map will be extrapolated in regions
+% where its value is 0.
+>> inpaint_zeros = true;
+
+% Remove objects that have a Z position equal to 0. Normally this
+% value reports objects that are out of the region-of-interest.
+>> prune_zeros = true;
+
+% Often inverted microscopes are used to image these tissues. When the
+% sample is arranged on its back, this leads the bottom of the tissue
+% surface to have large Z value (this is the case for the sample data).
+% The following flag is a convenience that flips it for better display.
+% Invert z for plotting.
+>> invert_z = true;
+
+
+% The method call itself.
+>> dpr = deproj.from_heightmap( ...
+ I, ...
+ H, ...
+ pixel_size, ...
+ voxel_depth, ...
+ units, ...
+ invert_z, ...
+ inpaint_zeros, ...
+ prune_zeros );
+
+____
+Opening mask image: Segmentation-2.tif
+Opening height-map image: HeightMap-2.tif
+Converting mask to objects.
+Converted a 282 x 508 mask in 2.7 seconds. Found 426 objects and 1840 junctions.
+Typical object scale: 10.1 pixels or 1.84 µm.
+Collecting Z coordinates.
+Done in 0.4 seconds.
+Removed 0 junctions at Z=0.
+Removed 0 objects touching these junctions.
+Computing tissue local curvature.
+Computing morphological descriptors of all objects.
+Done in 3.3 seconds.
+____
+
+>> dpr
+
+dpr =
+
+ deproj with properties:
+
+ epicells: [426×1 epicell]
+ junction_graph: [1×1 graph]
+ units: 'µm'
+
+```
+
+In the following we suppose that `dpr` is an instance of `deproj` created by this example.
+
+#### `to_table`
+
+`T = to_table( obj )`
+
+Export masurements to a MATLAB table.
+
+```matlab
+>> T = dpr.to_table;
+>> head(T)
+
+ans =
+
+ 8×23 table
+
+ id xc yc zc area perimeter euler_alpha ...
+ __ ______ ______ _______ ______ _________ ___________ ...
+
+ 1 1.3039 22.669 0.61254 2.507 7.2365 0.71603 ...
+ 2 2.4739 23.827 0.66689 8.0899 11.849 0.90395 ...
+ 3 3.5615 3.6656 5.0947 12.317 15.599 -2.0397 ...
+ 4 2.4705 11.183 3.1008 8.0176 12.523 -2.0734 ...
+ 5 2.6884 26.749 0.24663 5.141 9.1999 -2.1016 ...
+ 6 3.6096 14.773 2.7521 13.812 16.114 -2.1033 ...
+ 7 5.0077 8.8491 4.6461 40.057 26.8 -2.0163 ...
+ 8 3.9601 29.361 0.22428 7.6378 11.323 -2.0704 ...
+```
+
+The table also stores the physical units of each columns:
+
+```matlab
+>> T.Properties.VariableUnits
+
+ans =
+
+ 1×23 cell array
+
+ Columns 1 through 7
+
+ {0×0 char} {'µm'} {'µm'} {'µm'} {'µm²'} {'µm'} {'radians'} ...
+```
+
+A short description of the columns is present:
+
+```matlab
+>> T.Properties.VariableDescriptions{7}
+
+ans =
+
+ 'First Euler angle for the cell plane (rotation around Z)'
+```
+
+And a table description:
+
+```matlab
+>> T.Properties.Description
+
+ans =
+
+ 'Data generated from DeProj software, exported on 21-Jul-2020 23:07:02.'
+```
+
+#### `to_file`
+
+`to_file( obj, file_name, include_header )`
+
+Exports results to a spreadsheet file.
+
+If `file_name` has `.csv` as extension, the data is saved as a CSV file. If it has `.xlsx` as an extension, it is saved as an Excel spreadsheet. The boolean flag `include_header` specifies whether the file will have a header with column names and units.
+
+```matlab
+dpr.to_file( 'table.csv' )
+dpr.to_file( 'table.xlsx' )
+```
+
+
+
+#### `plot_sizes`
+
+`[ hf, ax1, ax2 ] = plot_sizes( obj, scale_bar_length )`
+
+Generate a figure with the cells area and perimeter. All the plots generated by the `plot_*` methods are 3D plots. The cells are drawn with their 3D coordinates and you can zoom, rotate, pan to make the curvature of the tissue appear.
+
+The `scale_bar_length` parameter specifies what should be the length (in physical units) of the scale bar added to the bottom left of the plot. By default it is 10. The output arguments `[ hf, ax1, ax2 ]` are respectfully the handles to the figure created, to the top axes and to the bottom axes.
+
+```matlab
+>> dpr.plot_sizes
+```
+
+
+
+#### `plot_fit_plane`
+
+`[ hf, ax1, ax2, ax3 ] = plot_fit_plane( obj, scale_bar_length )`
+
+Generate a figure with the local plane orientation for each cell. This orientation is given as 3 Euler angles in the [ZX'Z'' convention](https://en.wikipedia.org/wiki/Euler_angles#Chained_rotations_equivalence).
+
+- The first one, `alpha` is the orientation of the cell plane (top panel below). 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`. On these figures we wrap the angle between 0º and 180º to and because of MATLAB convention, this angle is measured counterclockwise from the Y axis (so 90º corresponds to a slope going up in the east-west direction).
+- 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.
+- 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.
+
+```matlab
+>> dpr.plot_fit_plane
+```
+
+
+
+### Secondary `deproj` methods.
+
## The `epicell` class methods.
In the following we suppose that `o` is an instance of `epicell`, for instance obtained by executing the a [self-contained example](RunExample.m) in this repository and for instance:
@@ -181,7 +413,7 @@ The second output argument `Q` contains the parametric ellipse parameter. It is
*A x² + B x y + C y² + D x + E y + F = 0*
-### Static method `fit_ellipse_3d`
+#### Static method `fit_ellipse_3d`
`[ f3d, R ] = fit_ellipse_3d( p, E, method )`
@@ -201,131 +433,3 @@ The first output arguments `f3d` contains the ellipse parameter in cartesian for
The second argument `R` is the rotation matrix computed from the Euler angles.
-
-## The `deproj` class methods.
-
-A `deproj` instance has several interesting methods, that let you export and display the analysis results. In particular the plotting routines: you will most likely be adapting them to your needs with a bit of MATLAB.
-
-In the following we suppose that `dpr` is an instance of `deproj`, for instance obtained by executing the a [self-contained example](RunExample.m) in this repository:
-
-```matlab
->> dpr
-
-dpr =
-
- deproj with properties:
-
- epicells: [426×1 epicell]
- junction_graph: [1×1 graph]
- units: 'µm'
-```
-
-### Main `deproj` methods.
-
-#### `to_table`
-
-`T = to_table( obj )`
-
-Export masurements to a MATLAB table.
-
-```matlab
->> T = dpr.to_table;
->> head(T)
-
-ans =
-
- 8×23 table
-
- id xc yc zc area perimeter euler_alpha ...
- __ ______ ______ _______ ______ _________ ___________ ...
-
- 1 1.3039 22.669 0.61254 2.507 7.2365 0.71603 ...
- 2 2.4739 23.827 0.66689 8.0899 11.849 0.90395 ...
- 3 3.5615 3.6656 5.0947 12.317 15.599 -2.0397 ...
- 4 2.4705 11.183 3.1008 8.0176 12.523 -2.0734 ...
- 5 2.6884 26.749 0.24663 5.141 9.1999 -2.1016 ...
- 6 3.6096 14.773 2.7521 13.812 16.114 -2.1033 ...
- 7 5.0077 8.8491 4.6461 40.057 26.8 -2.0163 ...
- 8 3.9601 29.361 0.22428 7.6378 11.323 -2.0704 ...
-```
-
-The table also stores the physical units of each columns:
-
-```matlab
->> T.Properties.VariableUnits
-
-ans =
-
- 1×23 cell array
-
- Columns 1 through 7
-
- {0×0 char} {'µm'} {'µm'} {'µm'} {'µm²'} {'µm'} {'radians'} ...
-```
-
-A short description of the columns is present:
-
-```matlab
->> T.Properties.VariableDescriptions{7}
-
-ans =
-
- 'First Euler angle for the cell plane (rotation around Z)'
-```
-
-And a table description:
-
-```matlab
->> T.Properties.Description
-
-ans =
-
- 'Data generated from DeProj software, exported on 21-Jul-2020 23:07:02.'
-```
-
-#### `to_file`
-
-`to_file( obj, file_name, include_header )`
-
-Exports results to a spreadsheet file.
-
-If `file_name` has `.csv` as extension, the data is saved as a CSV file. If it has `.xlsx` as an extension, it is saved as an Excel spreadsheet. The boolean flag `include_header` specifies whether the file will have a header with column names and units.
-
-```matlab
-dpr.to_file( 'table.csv' )
-dpr.to_file( 'table.xlsx' )
-```
-
-
-
-#### `plot_sizes`
-
-`[ hf, ax1, ax2 ] = plot_sizes( obj, scale_bar_length )`
-
-Generate a figure with the cells area and perimeter. All the plots generated by the `plot_*` methods are 3D plots. The cells are drawn with their 3D coordinates and you can zoom, rotate, pan to make the curvature of the tissue appear.
-
-The `scale_bar_length` parameter specifies what should be the length (in physical units) of the scale bar added to the bottom left of the plot. By default it is 10. The output arguments `[ hf, ax1, ax2 ]` are respectfully the handles to the figure created, to the top axes and to the bottom axes.
-
-```matlab
->> dpr.plot_sizes
-```
-
-
-
-#### `plot_fit_plane`
-
-`[ hf, ax1, ax2, ax3 ] = plot_fit_plane( obj, scale_bar_length )`
-
-Generate a figure with the local plane orientation for each cell. This orientation is given as 3 Euler angles in the [ZX'Z'' convention](https://en.wikipedia.org/wiki/Euler_angles#Chained_rotations_equivalence).
-
-- The first one, `alpha` is the orientation of the cell plane (top panel below). 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`. On these figures we wrap the angle between 0º and 180º to and because of MATLAB convention, this angle is measured counterclockwise from the Y axis (so 90º corresponds to a slope going up in the east-west direction).
-- 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.
-- 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.
-
-```matlab
->> dpr.plot_fit_plane
-```
-
-
-
-### Secondary `deproj` methods.
\ No newline at end of file