## Correlation

Correlation — Correlation and cross-correlation

## Functions

gdouble | gwy_field_get_correlation_score ()
gdouble | gwy_field_get_weighted_correlation_score ()
GwyComputationState * | gwy_field_crosscorrelate_init ()
void | gwy_field_crosscorrelate_set_weights ()
void | gwy_field_crosscorrelate_iteration ()
void | gwy_field_crosscorrelate_finalize ()
void | gwy_field_correlate ()
GwyComputationState * | gwy_field_correlate_init ()
void | gwy_field_correlate_iteration ()
void | gwy_field_correlate_finalize ()
void | gwy_field_correlation_search ()

## Types and Values

enum | GwyCorrelationType

## Includes

    #include <libgwyddion/gwyddion.h>

## Description

## Functions

### gwy_field_get_correlation_score()

    gdouble
    gwy_field_get_correlation_score (GwyField *field,
                                     GwyField *kernel_field,
                                     gint col,
                                     gint row,
                                     gint kernel_col,
                                     gint kernel_row,
                                     gint kernel_width,
                                     gint kernel_height);

Calculates a correlation score in one point.

Correlation window size is given by `kernel_col` , `kernel_row` , `kernel_width` , `kernel_height` , postion of the correlation window on data is given by `col` , `row` .

If anything fails (data too close to boundary, etc.), function returns -1.0 (none correlation)..

#### Parameters

field | A data field. |
kernel_field | Kernel to correlate data field with. |
col | Upper-left column position in the data field. |
row | Upper-left row position in the data field. |
kernel_col | Upper-left column position in kernel field. |
kernel_row | Upper-left row position in kernel field. |
kernel_width | Width of kernel field area. |
kernel_height | Heigh of kernel field area. |

#### Returns

Correlation score (between -1.0 and 1.0). Value 1.0 denotes maximum correlation, -1.0 none correlation.

### gwy_field_get_weighted_correlation_score()

    gdouble
    gwy_field_get_weighted_correlation_score
                                   (GwyField *field,
                                    GwyField *kernel_field,
                                    GwyField *weight_field,
                                    gint col,
                                    gint row,
                                    gint kernel_col,
                                    gint kernel_row,
                                    gint kernel_width,
                                    gint kernel_height);

Calculates a correlation score in one point using weights to center the used information to the center of kernel.

Correlation window size is given by `kernel_col` , `kernel_row` , `kernel_width` , `kernel_height` , postion of the correlation window on data is given by `col` , `row` .

If anything fails (data too close to boundary, etc.), function returns -1.0 (none correlation)..

#### Parameters

field | A data field. |
kernel_field | Kernel to correlate data field with. |
weight_field | data field of same size as kernel window size |
col | Upper-left column position in the data field. |
row | Upper-left row position in the data field. |
kernel_col | Upper-left column position in kernel field. |
kernel_row | Upper-left row position in kernel field. |
kernel_width | Width of kernel field area. |
kernel_height | Heigh of kernel field area. |

#### Returns

Correlation score (between -1.0 and 1.0). Value 1.0 denotes maximum correlation, -1.0 none correlation.

### gwy_field_crosscorrelate_init()

    GwyComputationState *
    gwy_field_crosscorrelate_init (GwyField *field1,
                                   GwyField *field2,
                                   GwyField *x_dist,
                                   GwyField *y_dist,
                                   GwyField *score,
                                   gint search_width,
                                   gint search_height,
                                   gint window_width,
                                   gint window_height);

Initializes a cross-correlation iterator.

This iterator reports its state as GwyComputationStateType.

#### Parameters

field1 | A data field. |
field2 | A data field. |
x_dist | A data field to store x-distances to, or `NULL`. | [nullable]
y_dist | A data field to store y-distances to, or `NULL`. | [nullable]
score | Data field to store correlation scores to, or `NULL`. | [nullable]
search_width | Search area width. |
search_height | Search area height. |
window_width | Correlation window width. |
window_height | Correlation window height. |

#### Returns

A new cross-correlation iterator.

### gwy_field_crosscorrelate_set_weights()

    void
    gwy_field_crosscorrelate_set_weights (GwyComputationState *state,
                                          GwyWindowingType type);

Sets the weight function to be used within iterative cross-correlation algorithm.

By default (not setting it), rectangular windowing is used. This function should be called before running first iteration to get consistent results.

#### Parameters

state | Cross-correlation iterator. |
type | Set windowing type to be set as correlation weight, see GwyWindowingType for details. |

### gwy_field_crosscorrelate_iteration()

    void
    gwy_field_crosscorrelate_iteration (GwyComputationState *state);

Performs one iteration of cross-correlation.

Cross-correlation matches two different images of the same object under changes.

It does not use any special features for matching. It simply searches for all points (with their neighbourhood) of `field1` within `field2` . Parameters `search_width` and `search_height` determine maimum area where to search for points. The area is cenetered in the `field2` at former position of points at `field1` .

A cross-correlation iterator can be created with `gwy_field_crosscorrelate_init()`. When iteration ends, either by finishing or being aborted, `gwy_field_crosscorrelate_finalize()` must be called to release allocated resources.

#### Parameters

state | Cross-correlation iterator. |

### gwy_field_crosscorrelate_finalize()

    void
    gwy_field_crosscorrelate_finalize (GwyComputationState *state);

Destroys a cross-correlation iterator, freeing all resources.

#### Parameters

state | Cross-correlation iterator. |

### gwy_field_correlate()

    void
    gwy_field_correlate (GwyField *field,
                         GwyField *kernel_field,
                         GwyField *score,
                         GwyCorrelationType method);

Computes correlation score for all positions in a data field.

Correlation score is compute for all points in data field `field` and full size of correlation kernel `kernel_field` .

The points in `score` correspond to centers of kernel. More precisely, the point ((`kxres` -1)/2, (`kyres` -1)/2) in `score` corresponds to kernel field top left corner coincident with data field top left corner. Points outside the area where the kernel field fits into the data field completely are set to -1 for `GWY_CORRELATION_NORMAL`.

This function is mostly made obsolete by `gwy_field_correlation_search()` which offers, beside the plain FFT-based correlation, a method equivalent to `GWY_CORRELATION_NORMAL` as well as several others, all computed efficiently using FFT.

#### Parameters

field | A data field. |
kernel_field | Correlation kernel. |
score | Data field to store correlation scores to. |
method | Correlation score calculation method. |

### gwy_field_correlate_init()

    GwyComputationState *
    gwy_field_correlate_init (GwyField *field,
                              GwyField *kernel_field,
                              GwyField *score);

Creates a new correlation iterator.

This iterator reports its state as GwyComputationStateType.

This function is mostly made obsolete by `gwy_field_correlation_search()` which offers, beside the plain FFT-based correlation, a method equivalent to `GWY_CORRELATION_NORMAL` as well as several others, all computed efficiently using FFT.

#### Parameters

field | A data field. |
kernel_field | Kernel to correlate data field with. |
score | Data field to store correlation scores to. |

#### Returns

A new correlation iterator.

### gwy_field_correlate_iteration()

    void
    gwy_field_correlate_iteration (GwyComputationState *state);

Performs one iteration of correlation.

An iterator can be created with `gwy_field_correlate_init()`. When iteration ends, either by finishing or being aborted, `gwy_field_correlate_finalize()` must be called to release allocated resources.

#### Parameters

state | Correlation iterator. |

### gwy_field_correlate_finalize()

    void
    gwy_field_correlate_finalize (GwyComputationState *state);

Destroys a correlation iterator, freeing all resources.

#### Parameters

state | Correlation iterator. |

### gwy_field_correlation_search()

    void
    gwy_field_correlation_search (GwyField *dfield,
                                  GwyField *kernel,
                                  GwyField *kernel_weight,
                                  GwyField *target,
                                  GwyCorrSearchType method,
                                  gdouble regcoeff,
                                  GwyExteriorType exterior,
                                  gdouble fill_value);

Performs correlation search of a detail in a larger data field.

There are two basic classes of methods: Covariance (products of kernel and data values are summed) and height difference (squared differences between kernel and data values are summed). For the second class, the sign of the output is inverted. So in both cases higher values mean better match. All methods are implemented efficiently using FFT.

Usually you want to use `GWY_CORR_SEARCH_COVARIANCE` or `GWY_CORR_SEARCH_HEIGHT_DIFF`, in which the absolute data offsets play no role (only the differences).

If the detail can also occur with different height scales, use `GWY_CORR_SEARCH_COVARIANCE_SCORE` or `GWY_CORR_SEARCH_HEIGHT_DIFF_SCORE` in which the local data variance is normalised. In this case `dfield` regions with very small (or zero) variance can lead to odd results and spurious maxima. Use `regcoeff` to suppress them: Score of image details is suppressed if their variance is `regcoeff` times the mean local variance.

If `kernel_weight` is non-`NULL` is allows specify masking/weighting of kernel. The simplest use is masking when searching for a non-rectangular detail. Fill `kernel_weight` with 1s for important kernel pixels and with 0s for irrelevant pixels. However, you can use arbitrary non-negative weights.

#### Parameters

dfield | A data field to search. |
kernel | Detail to find (kernel). |
kernel_weight | Kernel weight, or `NULL`. If given, its dimensions must match `kernel` . | [nullable]
target | Data field to fill with the score. It will be resampled to match `dfield` . |
method | Method, determining the type of output to put into `target` . |
regcoeff | Regularisation coefficient, any positive number. Pass something like 0.1 if unsure. You can also pass zero, it means the same as `G_MINDOUBLE`. |
exterior | Exterior pixels handling. |
fill_value | The value to use with `GWY_EXTERIOR_FIXED_VALUE` exterior. |

## Types and Values

### enum GwyCorrelationType

#### Members

GWY_CORRELATION_NORMAL |  |
GWY_CORRELATION_FFT |  |
GWY_CORRELATION_POC |  |