EulerCharacteristic26N (SciJava Ops Image 1.0.0 API)

java.lang.Object
- org.scijava.ops.image.topology.eulerCharacteristic.EulerCharacteristic26N<B>

All Implemented Interfaces:

BiConsumer<RandomAccessibleInterval<B>,DoubleType>, Computers.Arity1<RandomAccessibleInterval<B>,DoubleType>
```
public class EulerCharacteristic26N<B extends BooleanType<B>>
extends Object
implements Computers.Arity1<RandomAccessibleInterval<B>,DoubleType>
```
An Op which calculates the Euler characteristic (χ) of the given 3D binary image.
Here Euler characteristic is defined as χ = β_0 - β_1 + β_2, where β_i are so called Betti numbers
- β_0 = number of separate particles
- β_1 = number of handles
- β_2 = number enclosed cavities
The Op calculates χ by using the triangulation algorithm described by Toriwaki & Yonekura (see below).
There it's calculated X = ∑Δχ(V), where V is a 2x2x2 neighborhood around each point in the 3D space.
We are using the 26-neighborhood version of the algorithm. The Δχ(V) values here are predetermined.

For the algorithm see
Toriwaki J, Yonekura T (2002)
Euler Number and Connectivity Indexes of a Three Dimensional Digital Picture
Forma 17: 183-209
http://www.scipress.org/journals/forma/abstract/1703/17030183.html

For the Betti number definition of Euler characteristic see
Odgaard A, Gundersen HJG (1993)
Quantification of connectivity in cancellous bone, with special emphasis on 3-D reconstructions
Bone 14: 173-182
doi:10.1016/8756-3282(93)90245-6
Author:

Richard Domander (Royal Veterinary College, London), David Legland - original MatLab implementation

Implementation Note:

op names='topology.eulerCharacteristic26N'

Constructor Summary

Constructors
Constructor Description

EulerCharacteristic26N()

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`void`	`compute(RandomAccessibleInterval<B> interval, DoubleType output)`	TODO
`static <B extends BooleanType<B>> int`	`neighborhoodEulerIndex(RandomAccess<B> access, long x, long y, long z)`	Determines the LUT index for this 2x2x2 neighborhood

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface java.util.function.BiConsumer
andThen

Methods inherited from interface org.scijava.function.Computers.Arity1
accept

- Constructor Detail
  - EulerCharacteristic26N
```
public EulerCharacteristic26N()
```
- Method Detail
  - compute
```
public void compute(RandomAccessibleInterval<B> interval,
                    DoubleType output)
```
    TODO
    
    Specified by:
    
    compute in interface Computers.Arity1<RandomAccessibleInterval<B extends BooleanType<B>>,DoubleType>
    
    Parameters:
    
    interval -
    
    output -
  - neighborhoodEulerIndex
```
public static <B extends BooleanType<B>> int neighborhoodEulerIndex(RandomAccess<B> access,
                                                                    long x,
                                                                    long y,
                                                                    long z)
```
    Determines the LUT index for this 2x2x2 neighborhood
    
    Parameters:
    
    access - The space where the neighborhood is
    
    x - Location of the neighborhood in the 1st spatial dimension (x)
    
    y - Location of the neighborhood in the 2nd spatial dimension (y)
    
    z - Location of the neighborhood in the 3rd spatial dimension (z)
    
    Returns:
    
    the index of the Δχ value for this configuration of voxels