ImageMomentsLayout

java.lang.Object
- stella.math.ImageMomentsLayout

All Implemented Interfaces:

Serializable
```
public class ImageMomentsLayout
extends Object
implements Serializable
```
Similar to one-dimension power sums or CentralMoments this class calculates image moments meaning statistic properties in a two-dimensional image. Suppose you have an array of pixel values I_ij = I(x,y) Sampled at integer x/y pixel values, thus representable as a two-dimensional double array ADU[y][x] like returned from fits.FitsTools (note the counter-intuitive indexing within the array; this stems from the FITS standard. Passing this to the constructor of this class immediately calculates I_0, x_c and y_c via the formulars:
```
 I_0=ΣADU_ij,

 xc=Σ(x_ij·ADU_ij)/I_0,

 yc=Σ(y_ij·ADU_ij)/I_0.
 
```
Further calls to #getImageMoment first check, if the moment to n,k has already been cached, otherwise it is calculated according to M_nk=Σ(x_ij-xc)n(y_ij-yc)k/I_0
See Also:

Serialized Form

Nested Class Summary

Nested Classes
Modifier and Type Class and Description

static class ImageMomentsLayout.Focus
This class reads an fits image and calculates the requested image moment.

Nested Classes
Modifier and Type	Class and Description
`static class`	`ImageMomentsLayout.Focus` This class reads an fits image and calculates the requested image moment.

Field Summary

Fields
Modifier and Type	Field and Description
`private double[]`	`adu` This is the image array, description from layout.
`private double`	`bias` If a bias is set, only adus above this are considered.
`private Map<Integer,Double>`	`cache` Cache is updated at each call to `#getImageMoment` with no hit.
`private LayoutImpl`	`dim2` How the image array is to be read as a 2-dim image.
`private double`	`high` The multiplicator to the RN for maximum ADU still considered BG.
`private double`	`low` The multiplicator to the RN for minimum ADU still considered BG.
`private double`	`readnoise` The standard deviation estimate for background rejection.
`private double`	`sum0` Once the image is set, this is the ADU-sum.
`private double`	`xc` Once the image is set, this is the center-of-gravity, x coordinate.
`private double`	`yc` Once the image is set, this is the center-of-gravity, y coordinate.

Constructor Summary

Constructors
Constructor and Description
`ImageMomentsLayout(double[] image, ArrayLayout d2)` Takes an image array and readily calculates the count sum plus the center of gravity.
`ImageMomentsLayout(double[] image, ArrayLayout d2, double bias, double rn)` Takes an image array and readily calculates the count sum plus the center of gravity.
`ImageMomentsLayout(double[] image, ArrayLayout d2, double bias, double rn, double hi, double lo)` Takes an image array and readily calculates the count sum plus the center of gravity.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`private double`	`calculateMnk(int n, int m)`
`Point2D`	`getCenter()` Returns xc yc as a Point2D object.
`double`	`getMoment(int x0, int y0)` If the queried moment has not been calculated, we evaluate it by `M_nk=Σ(x_ij-xc)n(y_ij-yc)k/I_0.`
`void`	`setImage(double[] image, ArrayLayout d2, double bs, double rn, double hisig, double losig)` Sets a new pixel array, erasing the cache, but immediately calculating the new count sum plus center of gravity.

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

- Field Detail
  - adu
```
private double[] adu
```
    This is the image array, description from layout.
  - dim2
```
private LayoutImpl dim2
```
    How the image array is to be read as a 2-dim image.
  - bias
```
private double bias
```
    If a bias is set, only adus above this are considered.
  - readnoise
```
private double readnoise
```
    The standard deviation estimate for background rejection.
  - high
```
private double high
```
    The multiplicator to the RN for maximum ADU still considered BG.
  - low
```
private double low
```
    The multiplicator to the RN for minimum ADU still considered BG.
  - sum0
```
private double sum0
```
    Once the image is set, this is the ADU-sum.
  - xc
```
private double xc
```
    Once the image is set, this is the center-of-gravity, x coordinate.
  - yc
```
private double yc
```
    Once the image is set, this is the center-of-gravity, y coordinate.
  - cache
```
private Map<Integer,Double> cache
```
    Cache is updated at each call to #getImageMoment with no hit.
- Constructor Detail
  - ImageMomentsLayout
```
public ImageMomentsLayout(double[] image,
                          ArrayLayout d2)
```
    Takes an image array and readily calculates the count sum plus the center of gravity.
  - ImageMomentsLayout
```
public ImageMomentsLayout(double[] image,
                          ArrayLayout d2,
                          double bias,
                          double rn)
```
    Takes an image array and readily calculates the count sum plus the center of gravity.
  - ImageMomentsLayout
```
public ImageMomentsLayout(double[] image,
                          ArrayLayout d2,
                          double bias,
                          double rn,
                          double hi,
                          double lo)
```
    Takes an image array and readily calculates the count sum plus the center of gravity.
- Method Detail
  - setImage
```
public void setImage(double[] image,
                     ArrayLayout d2,
                     double bs,
                     double rn,
                     double hisig,
                     double losig)
```
    Sets a new pixel array, erasing the cache, but immediately calculating the new count sum plus center of gravity.
  - getMoment
```
public double getMoment(int x0,
                        int y0)
```
    If the queried moment has not been calculated, we evaluate it by M_nk=Σ(x_ij-xc)n(y_ij-yc)k/I_0. The moment is also cached for further queries. The special case with x0=y0=0 returns the ADU-sum, I_0, while queries with x0=1,y0=0 or x0=0,y0=1 return the center of gravity coordinate.
    
    Parameters:
    
    x0 - The leading index in M_nk
    
    y0 - The trailing index in M_nk
  - getCenter
```
public Point2D getCenter()
```
    Returns xc yc as a Point2D object.
  - calculateMnk
```
private double calculateMnk(int n,
                            int m)
```

Class ImageMomentsLayout

Nested Class Summary

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

adu

dim2

bias

readnoise

high

low

sum0

xc

yc

cache

Constructor Detail

ImageMomentsLayout

ImageMomentsLayout

ImageMomentsLayout

Method Detail

setImage

getMoment

getCenter

calculateMnk