# RidgeFilter

RidgeFilter[data]

computes a measure for the presence of a ridge at every position of data.

RidgeFilter[data,σ]

uses the specified ridge scale σ.

# Details and Options

• RidgeFilter is commonly used to find ridges in images by computing estimates of the main principal curvature at each sample point using Gaussian derivatives.
• The main principal curvature orthogonal to a ridge is given by the main negative eigenvalue of the Hessian matrix.
• The data can be any of the following:
•  list 2D or 3D numerical array image arbitrary Image or Image3D object
• In RidgeFilter[data,σ], σ is the scale of the Gaussian derivatives in the Hessian matrix. By default, is used.
• RidgeFilter[image,] returns a real image of the same dimensions as image.
• RidgeFilter takes the following options used in the computation of the Hessian matrix:
• Possible settings for the InterpolationOrder option are 3, 4, 5, , 9.
• The Padding option accepts the settings "Fixed", "Periodic", "Reversed", "Reflected", or a numeric value. A list of two settings can specify different paddings for each dimension.

# Examples

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## Basic Examples(2)

Find the mountain ridges in a terrain elevation raster:

Sketch the thin parts in an engine block:

## Scope(4)

### Data(3)

Ridge filtering of a numeric matrix:

RidgeFilter of a grayscale image:

Use a ridge scale of 3:

RidgeFilter of a 3D image:

### Parameters(1)

By default, σ1 is used:

Use a larger σ for detecting thick lines:

## Options(2)

### InterpolationOrder(1)

Filtering an array using different InterpolationOrder values:

By default, a "Fixed" padding is used:

## Applications(5)

Ridges in a two-dimensional array:

Enhance the strokes of handwritten characters:

Detect lines of a given width in a noisy image with uneven brightness:

Find the red ridges in a microscopic photo of a Yucca leaf:

Extract the walls:

Enhance trabecular bone structure:

Change the transfer function and background to further highlight the structure:

## Properties & Relations(2)

Ridge detection at scale σ=2 using DerivativeFilter:

Compare to the result of RidgeFilter:

Ridge filtering of an image gives a real-valued image:

Wolfram Research (2010), RidgeFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/RidgeFilter.html (updated 2014).

#### Text

Wolfram Research (2010), RidgeFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/RidgeFilter.html (updated 2014).

#### CMS

Wolfram Language. 2010. "RidgeFilter." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/RidgeFilter.html.

#### APA

Wolfram Language. (2010). RidgeFilter. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RidgeFilter.html

#### BibTeX

@misc{reference.wolfram_2024_ridgefilter, author="Wolfram Research", title="{RidgeFilter}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/RidgeFilter.html}", note=[Accessed: 13-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_ridgefilter, organization={Wolfram Research}, title={RidgeFilter}, year={2014}, url={https://reference.wolfram.com/language/ref/RidgeFilter.html}, note=[Accessed: 13-July-2024 ]}