EllipticGaussianOrtho (ImgLib2 Javadocs 0-SNAPSHOT API)

java.lang.Object
- net.imglib2.algorithm.localization.EllipticGaussianOrtho

All Implemented Interfaces:

FitFunction
```
public class EllipticGaussianOrtho
extends Object
implements FitFunction
```
A n-dimensional Gaussian peak function, representing an elliptical Gaussian, with axis constrained to be aligned with the main axis.
This fitting target function is defined over dimension n, by the following 2n+1 parameters:
```
k = 0..n-1  - x₀ᵢ (with i = k)
k = n       - A
k = n+1..2n - bᵢ (with i = k-n-1)
```
with
```
f(x) = A × exp( - S )
```
and
```
S = ∑ bᵢ × (xᵢ - x₀ᵢ)² 
```
Author:

Jean-Yves Tinevez 2012

Constructor Summary

Constructors
Constructor and Description

EllipticGaussianOrtho()

Constructors
Constructor and Description
`EllipticGaussianOrtho()`

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`double`	`grad(double[] x, double[] a, int k)` Returns the gradient value of this function, with respect to the variable specified by its index: Partial derivatives indices are ordered as follow:
`double`	`hessian(double[] x, double[] a, int r, int c)` Returns the hessian value of this function, with respect to the variable specified by its index: Partial derivatives indices are ordered as follow:
`String`	`toString()`
`double`	`val(double[] x, double[] a)` Evaluates this function at point `x`.

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

- Constructor Detail
  - EllipticGaussianOrtho
```
public EllipticGaussianOrtho()
```
- Method Detail
  - toString
```
public String toString()
```
    Overrides:
    
    toString in class Object
  - val
```
public final double val(double[] x,
                        double[] a)
```
    Description copied from interface: FitFunction
    
    Evaluates this function at point x. The function is otherwise defined over an array of parameters a, that is the target of the fitting procedure.
    
    Specified by:
    
    val in interface FitFunction
    
    Parameters:
    
    x - the multidimensional to evaluate the function at
    
    a - the set of parameters that defines the function
    
    Returns:
    
    a double value, the function evaluated at x
  - grad
```
public final double grad(double[] x,
                         double[] a,
                         int k)
```
    Returns the gradient value of this function, with respect to the variable specified by its index: Partial derivatives indices are ordered as follow:
```
k = 0..n-1  - x_i (with i = k-1)
k = n       - A
k = n+1..2n - b_i (with i = k-n-1)
```
    Specified by:
    
    grad in interface FitFunction
    
    Parameters:
    
    x - the position array to compute the gradient at.
    
    a - the parameters array that specified the gaussian shape.
    
    k - the parameter index for derivation.
    
    Returns:
    
    the value of the gradient computed with respect to parameter k for the gaussian with parameters a, calculated at position x.
    
    See Also:
    
    FitFunction.val(double[], double[])
  - hessian
```
public final double hessian(double[] x,
                            double[] a,
                            int r,
                            int c)
```
    Returns the hessian value of this function, with respect to the variable specified by its index: Partial derivatives indices are ordered as follow:
```
k = 0..n-1  - x_i (with i = k-1)
k = n       - A
k = n+1..2n - b_i (with i = k-n-1)
```
    Specified by:
    
    hessian in interface FitFunction
    
    Parameters:
    
    x - the position array to compute the gradient at.
    
    a - the parameters array that specified the gaussian shape.
    
    r - the parameter index for the first derivation.
    
    c - the parameter index for the second derivation.
    
    Returns:
    
    the value of the gradient computed with respect to parameters r, c for the elliptic gaussian with parameters a, calculated at position x.
    
    See Also:
    
    FitFunction.val(double[], double[])

Class EllipticGaussianOrtho

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

EllipticGaussianOrtho

Method Detail

toString

val

grad

hessian