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RidgeFilter
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RidgeFilter

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RidgeFilter[data]

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

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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:
  • list2D or 3D numerical array
    imagearbitrary 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:
  • InterpolationOrder Automaticinterpolation order
    Padding "Fixed"padding method
  • 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

open allclose all

Basic Examples  (2)Summary of the most common use cases

Find the mountain ridges in a terrain elevation raster:

In[3]:=3
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https://wolfram.com/xid/0fq7p8g33pd7e-pmfru1
Out[3]=3

Sketch the thin parts in an engine block:

In[1]:=1
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https://wolfram.com/xid/0fq7p8g33pd7e-07q8ym
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0fq7p8g33pd7e-02nh07
Out[2]=2

Scope  (4)Survey of the scope of standard use cases

Data  (3)

Ridge filtering of a numeric matrix:

In[1]:=1
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https://wolfram.com/xid/0fq7p8g33pd7e-dq7on4

RidgeFilter of a grayscale image:

In[1]:=1
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https://wolfram.com/xid/0fq7p8g33pd7e-op3qwr
Out[1]=1

Use a ridge scale of 3:

In[2]:=2
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https://wolfram.com/xid/0fq7p8g33pd7e-8ol86
Out[2]=2

RidgeFilter of a 3D image:

In[1]:=1
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https://wolfram.com/xid/0fq7p8g33pd7e-3n7xkb
Out[1]=1

Parameters  (1)

By default, σ1 is used:

In[11]:=11
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https://wolfram.com/xid/0fq7p8g33pd7e-dxuuh1
Out[11]=11

Use a larger σ for detecting thick lines:

In[12]:=12
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https://wolfram.com/xid/0fq7p8g33pd7e-xo5lrr
Out[12]=12

Options  (2)Common values & functionality for each option

InterpolationOrder  (1)

Filtering an array using different InterpolationOrder values:

✖
https://wolfram.com/xid/0fq7p8g33pd7e-3dj0x9
Out[2]=2

Padding  (1)

By default, a "Fixed" padding is used:

In[3]:=3
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https://wolfram.com/xid/0fq7p8g33pd7e-mrmivc
Out[3]=3

Specify a different padding:

In[4]:=4
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https://wolfram.com/xid/0fq7p8g33pd7e-5pdism
Out[4]=4

Applications  (5)Sample problems that can be solved with this function

Ridges in a two-dimensional array:

In[1]:=1
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https://wolfram.com/xid/0fq7p8g33pd7e-ih984t

Enhance the strokes of handwritten characters:

In[1]:=1
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https://wolfram.com/xid/0fq7p8g33pd7e-t5hdpt
Out[1]=1

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

In[1]:=1
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https://wolfram.com/xid/0fq7p8g33pd7e-34ed8c
Out[1]=1

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

In[1]:=1
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https://wolfram.com/xid/0fq7p8g33pd7e-w28fuv
Out[1]=1

Extract the walls:

In[2]:=2
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https://wolfram.com/xid/0fq7p8g33pd7e-esqj84
Out[2]=2

Enhance trabecular bone structure:

In[1]:=1
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https://wolfram.com/xid/0fq7p8g33pd7e-mbtgdp
Out[1]=1

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

In[2]:=2
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https://wolfram.com/xid/0fq7p8g33pd7e-np3lvk
Out[2]=2

Properties & Relations  (2)Properties of the function, and connections to other functions

Ridge detection at scale σ=2 using DerivativeFilter:

In[5]:=5
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https://wolfram.com/xid/0fq7p8g33pd7e-bixkja
Out[7]=7

Compare to the result of RidgeFilter:

In[8]:=8
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https://wolfram.com/xid/0fq7p8g33pd7e-h80sh7
Out[8]=8

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

In[1]:=1
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https://wolfram.com/xid/0fq7p8g33pd7e-hznxi1
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0fq7p8g33pd7e-cfnht8
Out[2]=2
Wolfram Research (2010), RidgeFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/RidgeFilter.html (updated 2014).
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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).

✖
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.

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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

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

BibTeX

@misc{reference.wolfram_2025_ridgefilter, author="Wolfram Research", title="{RidgeFilter}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/RidgeFilter.html}", note=[Accessed: 27-March-2025 ]}

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@misc{reference.wolfram_2025_ridgefilter, author="Wolfram Research", title="{RidgeFilter}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/RidgeFilter.html}", note=[Accessed: 27-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_ridgefilter, organization={Wolfram Research}, title={RidgeFilter}, year={2014}, url={https://reference.wolfram.com/language/ref/RidgeFilter.html}, note=[Accessed: 27-March-2025 ]}

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@online{reference.wolfram_2025_ridgefilter, organization={Wolfram Research}, title={RidgeFilter}, year={2014}, url={https://reference.wolfram.com/language/ref/RidgeFilter.html}, note=[Accessed: 27-March-2025 ]}