Note that all the plots generated by DeProj are 3D plots following the tissue surface. This can be somewhat hidden by the default plot view (view orthogonal to the XY plane) so the ellipses have their major axis apparent to stress their angle with the XY plane:

![Ellipse_1](static/Ellipse_1.png)

If we now put back the axis, labels and rotate the view to make the angle appearing we get this:

![Ellipse_2](static/Ellipse_2.png)

Because we have access the Z-position of each location thanks to the height-map, we cam compute the [local curvature](https://en.wikipedia.org/wiki/Curvature#Curves_on_surfaces) of the tissue just at a cell position. This measure a form of 'stretch' on the cell. DeProj reports the Gaussian curvature, the mean curvature and the principal curvatures (Figure 4 below).

Finally we can also have a simplified plot of the cell contour, using the junctions. The following figure shows 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.

![FigureTopology](static/FigureTopology.png)

## Running DeProj from MATLAB prompt.

DeProj is mainly made of two classes, and running it from the MATLAB prompt should be convenient enough.

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@@ -347,9 +362,13 @@ It can also be used to generate customisable plots. Several convenience methods

## More documentation.

The file [DeProjProperties.md](DeProjProperties.md) documents the properties you can find in the analysis results.

The file [DeProjProperties.md](DeProjProperties.md) documents the properties you can find in the analysis results. They contain the metrics with which you can investigate the cells morphology.

The file [DeProjMethods.md](DeProjMethods.md) documents the methods you can run with the objects returned by the analysis. Mainly they fall into three categories:

The file [DeProjMethods.md](DeProjMethods.md) documents the methods you can run with the objects returned by the analysis.

- the methods that can generate a `deproj` object from various inputs (image + height-map, segmentation results + tissue mesh, any combination, *etc.*)

- the methods to generate the plot we exemplified above.

- the methods to export the analysis results to tables, files, ...