This function calculates the first and second order differential of a time series image according to the following formula and schematic:

First Order Differential:

Output[t] = Input[t+1] – Input[t-1]

The difference between consecutive pixels is not calculated so that the output is not directional. The first order differential represents the Speed.

Second Order Differential:

Output[t] = Input[t-1] + Input[t+1] – 2 x Input[t]

Second order differential is also known as the "Laplacian" and represents the Acceleration. It enhances the fine details in the image (including noise). The smoothing kernel helps reduce this noise.

Parameter

Description

Derivative

Selects which differential is calculated.

–

First

Calculates the first order differential (speed).

–

Second

Calculates the second order differential (acceleration).

Smoothing

Defines the iterative, binomial smoothing filter. This reduces noise in the differential images, whilst retaining maximums and minimums. Value range: 0 – 50

Normalization

Defines what to do with negative values resulting from the calculation.

–

Clip

Sets negative values to 0.

–

Absolute

Converts negative pixel values into positive values. Positive pixel values exceeding the maximum pixel value are set to the maximum pixel value.