# solutionset

##### Evaluate Logical Expression Involving Pixel Images and Return Region Where Expression is True

Given a logical expression involving one or more pixel images, find all pixels where the expression is true, and assemble these pixels into a window.

- Keywords
- manip, spatial, programming

##### Usage

`solutionset(..., envir)`

##### Arguments

- ...
- An expression in the Rlanguage, involving one or more pixel images.
- envir
- Optional. The environment in which to evaluate the expression.

##### Details

Given a logical expression involving one or more pixel images, this function will find all pixels where the expression is true, and assemble these pixels into a spatial window.

Pixel images in `spatstat`

are represented by objects of class `"im"`

(see `im.object`

). These are essentially matrices of
pixel values, with extra attributes recording the pixel dimensions,
etc.

Suppose `X`

is a pixel image. Then `solutionset(abs(X) > 3)`

will find all the pixels in `X`

for which the pixel value
is greater than 3 in absolute value, and return a window containing
all these pixels.

If `X`

and `Y`

are two pixel images,
`solutionset(X > Y)`

will find all pixels for which the
pixel value of `X`

is greater than the corresponding pixel value
of `Y`

, and return a window containing these pixels.
In general, `...`

can be any logical expression involving
pixel images.

The code first tries to evaluate the expression using
`eval.im`

.
This is successful if the expression involves only
(a) the *names* of pixel images, (b) scalar
constants, and (c) functions which are vectorised.
There must be at least one pixel image in the expression.
The expression `expr`

must be vectorised.
See the Examples.

If this is unsuccessful, the code then tries to evaluate the
expression using pixel arithmetic. This is successful if all the
arithmetic operations in the expression are listed
in `Math.im`

.

##### Value

- A spatial window
(object of class
`"owin"`

, see`owin.object`

).

##### See Also

##### Examples

```
# test images
X <- as.im(function(x,y) { x^2 - y^2 }, unit.square())
Y <- as.im(function(x,y) { 3 * x + y - 1}, unit.square())
W <- solutionset(abs(X) > 0.1)
W <- solutionset(X > Y)
W <- solutionset(X + Y >= 1)
area(solutionset(X < Y))
solutionset(density(cells) > 20)
```

*Documentation reproduced from package spatstat, version 1.41-1, License: GPL (>= 2)*