# DerivativeFilter

DerivativeFilter[data,{n1,n2,}]

computes the ni derivative of data at level i.

DerivativeFilter[data,{n1,n2,},σ]

computes the derivative at a Gaussian scale of standard deviation σ.

DerivativeFilter[data,{der1,der2,},]

computes several derivatives der1, der2, .

# Details and Options • DerivativeFilter is a linear filter that computes the derivatives of data based on a spline interpolation model. Regularization with a Gaussian kernel of standard deviation σ (defaults to 0) can be used to reduce susceptibility to noise.
• • The data can be any of the following:
•  list arbitrary-rank numerical array tseries temporal data such as TimeSeries, TemporalData, … image arbitrary Image or Image3D object audio an Audio object
• DerivativeFilter operates separately on each level of data.
• DerivativeFilter[image,] uses the array coordinate system, where the first coordinate runs from the top to the bottom of image, and the second coordinate increases from left to right.
• DerivativeFilter gives a result with the same dimensions as data.
• DerivativeFilter can take the following options:
•  InterpolationOrder Automatic interpolation order up to 9 Padding "Fixed" padding method
• The derivative order has to be smaller than the specified interpolation order.

# Examples

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## Basic Examples(3)

A horizontal derivative of an image:

A regularized horizontal derivative of an image:

Derivative of a numeric list:

## Scope(13)

### Data(5)

First-order derivatives of a 2D array:

Obtain the first derivative of a TimeSeries object:

Filter an Audio signal:

Vertical derivative of a color image:

Vertical derivative of a 3D image:

### Parameters(8)

Zeroth derivative of a list:

First, second and third derivatives of a step sequence:

Vertical derivative of an image:

Horizontal derivative:

Second-order derivative in both dimensions:

Compute several derivatives of an image:

Vertical derivative of a 3D image:

Horizontal derivatives only:

Regularize the derivative using Gaussian smoothing:

Horizontal derivative at different Gaussian scales:

## Options(3)

### InterpolationOrder(1)

Filtering an array using different InterpolationOrder values:

Derivative filtering using different padding schemes:

First derivatives of a grayscale image using different padding schemes:

Use different padding schemes in each spatial direction:

## Applications(5)

Compute the Laplacian of an image at scale σ=6:

Ridge detection at scale σ=2:

T-junction filter:

Get borders from a colored map:

## Properties & Relations(4)

For larger values of , the results of GaussianFilter and DerivativeFilter converge:

DerivativeFilter and the corresponding derivatives of a spline interpolation return the same values:

Plot the result of the filter on top of the derivative of the interpolating function:

Derivative filtering of a binary image gives a grayscale image of a real type:

DerivativeFilter is a linear filter: