**Morphometer**

**, a 2D interactive online tool.**

Features:

• 2D online tool to calculate Minkowski functionals of 2D point patterns, single polygons and grayscale images.

• Minkowski synthesis, the inverse of the Minkowski analysis, that is, a convex body is constructed for a chosen set of irreducible Minkowski Tensors

## Link:

**Stable Version:** morphometer 20.10

## Different modes

The morphometer has four different analysis modes: Single Polygon, Point Pattern, Image Analysis and Minkowski Synthesis.

The different modes are described in the following.

You can change between the different modes in the top menu bar.

In each mode you can change the complexity of the interface on the left side between SIMPLE, ADVANCED or EXPERT.

## Single Polygon

### SIMPLE

Choose one of the examples by clicking on the image.

You can choose between two different analysis types, the polygon itself or the convex hull of the points.

### ADVANCED

Different polytope generators are implemented in the morphmeter, an overview is given here

### EXPERT

The parameters of the different polytope generators can be varied.

In the expert mode you have the option to upload point files using the following input file format:

`x1 y1`

x2 y2

x3 y3

....

## Point Pattern

### SIMPLE

You can choose between two examples, a poisson point process and a hard disk system with crystalline cluster. Click on the image to view the example.

On the right side you can choose the analysis type (None, Voronoi-Tessellation or Delaunay-Triangulation).

You can add points by clicking inside the image.

### ADVANCED

Different point pattern generators are implemented in the morphometer, an overview is given here.

### EXPERT

In the expert mode you have the option to upload point files using the following input file format:

`#boxL [boxsize]`

`x1 y1`

x2 y2

x3 y3

....

Furthermore, you can change the parameters of the different point pattern generators.

## Image Analysis

### SIMPLE

You can choose between four given examples.

### ADVANCED

In the advanced mode you have the option to upload your own images and analyzed them.

### EXPERT

More analysis options are available in the expert mode.

## Minkowski Synthesis

A description how the Minkowski synthesis works is given here.