This is a software suite to analyze the shape of triangulated objects stored, into ply files.
This is mostly designed for rod-like cells, e.g. yeast, but any closed triangulated mesh stored in a ply file should work.
To segment shapes from microscopy images, we recommend Limeseg : https://imagej.net/LimeSeg

We provide a set of simple functions to analyze the shape of a single cell, or to compare cells at different stages. The simplest is to go through the interface of analyze_shape(shape) a function that takes as argument the shape of a cell (see below : I/O variables). This outputs results, a structure containing a set of results. To compare several stages for a set of cells, the function summary_experiments should be used. It takes for input experiments, a formated list of severall cell shape shapes for different stages (see below : I/O variables). Several simple examples of usage are provided.

See demo_single_cell.m

To compare the states of several cells of a number for a various number of stages (i.e. each cell has different states), see :

• demo_compare_2_stages.m
• demo_compare_4_stages.m

Shape is the input argument for analyze_shape. A shape is a structure containing points - an array of vertices -, faces - the array of triangles -, normals - an array of the normals to the faces-.

• shape.points : $ 3 \times N_v$ array with $N_v$ the number of vertices. Each element is a float representing a position.
• shape.faces : $ 3 \times N_f$ array with $N_f$ the number of faces. Each element is an float representing a vertex index.
• shape.normals : $ 3 \times N_f$ array. Each element is a float representing an element of the normal vector.
  A shape is the output from import_ply, itself a wrapper for ply_read.m, and external module.

An experiment is a structure containing several states. Each state is a structure containing a name (usually the filename) and a shape. E.g. :

• experiment.states(1).name='cell_1_stage_1.ply'
• experiment.states(1).shape=import_ply('cell_1_stage_1.ply')
• experiment.states(2).name='cell_1_stage_2.ply'
• experiment.states(2).shape=import_ply('cell_1_stage_2.ply')

Experiment can also store an analysis, the results of analyze_shape :

• experiment.states(1).analysis=analyze_shape(experiment.states(1).shape)

Experiments is the input argument for summary_experiments. Experiment is a list of several experiments :

• experiments(1).states(1).name='cell_1_stage_1.ply'
• experiments(1).states(1).shape=import_ply('cell_1_stage_1.ply')
• experiments(2).states(1).name='cell_2_stage_1.ply'
• experiments(2).states(1).shape=import_ply('cell_2_stage_1.ply')

Each element of experiments may also store an analysis, the result of analyze_shape :

• experiments(i).states(j).analysis=analyze_shape(experiments(i).states(j).shape)

An analysis is the results of analyze_shape analyzing a shape. It contains many derived quantities. See the code for the definition of these quantities. The most important quantities are :

• analysis.length : the length of the shape
• analysis.volume : the volume of the shape
• analysis.surface : the surface of the shape
• analysis.mean_circ : mean circularity of slices in the cell, weighted by surface area
• analysis.mean_pers : mean perimeter of slices in the cell, weighted by surface area
• analysis.mean_area : mean area of slices in the cell, weighted by surface area