# Sigmoid

Computes the sigmoid function element-wise. A linear transformation is applied first on the argument of the sigmoid function. The resulting total transform is given by

$$f(x) = (Max-Min) * \dfrac{1}{1+e^{-(x - \beta) / \alpha }} + Min$$

Every output element is equal to f(x), where x is the intensity of the homologous input element, and alpha and beta are user-provided constants.

Consider an exampel of an image. The $$\beta$$ value can be thought of the offset on the pixel value that you are trying to isolate. E.g., if the object you are trying to isolate is at a pixel intensity above 150, you would choose a $$\beta$$ value that is around that value. The $$\alpha$$ value can be thought of as the scaling or variance of the sigmoid. Lower $$\alpha$$ values will make the pixel range of your intensity sharper. Your $$\alpha$$ value would decide how much of the noise you would want to include in your transformation. Smaller $$\alpha$$ values (0.25, 0.5) would zero out most of the noise, but it might make your actual signal thicker and not specific enough. Conversely, larger alpha values (e.g. 3+) might have a smoother signal but might include more noise. Negative alpha values can be thought of as using a positive alpha value and then inverting the image.

## Inputs

#### Input

Input.

Type: Column, Image, Numeric Array, List, Required, Single

## Outputs

#### Output

Output.

Type: Column, Image, Numeric Array, List

## Settings

### Configure

#### Alpha Float

Alpha parameter. Low values cancel noise, but makes signal thicker. Negative values inverts image.

#### Beta Float

Beta parameter. Set to ~the pixel value you want to isolate.

#### Min Float

Output min value.

#### Max Float

Output max value.