# graydist

Gray-weighted distance transform of grayscale image

## Syntax

``T = graydist(I,mask)``
``T = graydist(I,C,R)``
``T = graydist(I,ind)``
``T = graydist(___,method)``

## Description

````T = graydist(I,mask)` computes the gray-weighted distance transform of the grayscale image `I`. Locations where `mask` is `true` are seed locations.```

example

````T = graydist(I,C,R)` specifies the column and row coordinates of seed locations in vectors `C` and `R`.```
````T = graydist(I,ind)` specifies the linear indices of seed locations, `ind`.```
````T = graydist(___,method)` specifies an alternate distance metric, `method`.```

## Examples

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Create a magic square. Matrices generated by the magic function have equal row, column, and diagonal sums. The minimum path between the upper-left and lower-right corner is along the diagonal.

`A = magic(3)`
```A = 3×3 8 1 6 3 5 7 4 9 2 ```

Calculate the gray-weighted distance transform, specifying the upper left corner and the lower right corner of the square as seed locations.

```T1 = graydist(A,1,1); T2 = graydist(A,3,3);```

Sum the two transforms to find the minimum path between the seed locations. As expected, there is a constant-value minimum path along the diagonal.

`T = T1 + T2`
```T = 3×3 10 11 17 13 10 13 17 17 10 ```

## Input Arguments

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Grayscale image, specified as a numeric or logical array.

Binary mask that specifies seed locations, specified as a logical array the same size as `I`.

Column and row coordinates of seed locations, specified as a vector of positive integers. Coordinate values are valid `C`,`R` subscripts in `I`.

Indices of seed locations, specified as a vector of positive integers.

Distance metric, specified as one of these values.

Method

Description

`'chessboard'`

In 2-D, the chessboard distance between (x1,y1) and (x2,y2) is

max(│x1x2│,│y1y2│).

`'cityblock'`

In 2-D, the cityblock distance between (x1,y1) and (x2,y2) is

x1x2│ + │y1y2

`'quasi-euclidean'`

In 2-D, the quasi-Euclidean distance between (x1,y1) and (x2,y2) is

For more information, see Distance Transform of a Binary Image.

## Output Arguments

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Gray-weighted distance transform, returned as a numeric array of the same size as `I`. If the input numeric type of `I` is `double`, then the output numeric type of `T` is `double`. If the input is any other numeric type, then the output `T` is `single`.

Data Types: `single` | `double`

## Algorithms

`graydist` uses the geodesic time algorithm [1]. The basic equation for geodesic time along a path is:

`${\tau }_{f}\left(P\right)=\frac{f\left({p}_{o}\right)}{2}+\frac{f\left({p}_{l}\right)}{2}+\sum _{i=1}^{l-1}f\left({p}_{i}\right)$`

`method` determines the chamfer weights that are assigned to the local neighborhood during outward propagation. Each pixel's contribution to the geodesic time is based on the chamfer weight in a particular direction multiplied by the pixel intensity.

## References

[1] Soille, P. "Generalized geodesy via geodesic time." Pattern Recognition Letters. Vol.15, December 1994, pp. 1235–1240.