--- title: "GaborFilter" language: "en" type: "Symbol" summary: "GaborFilter[data, r, k] filters data by convolving with a Gabor kernel of pixel radius r and wave vector k. GaborFilter[data, r, k, \\[Phi]] uses a Gabor kernel with phase shift \\[Phi]. GaborFilter[data, {r, \\[Sigma]}, ...] uses a Gabor kernel with radius r and standard deviation \\[Sigma]." keywords: - image processing - Gabor filter - Gabor matrix - Gabor structure - Gabor transform - Fourier - filter canonical_url: "https://reference.wolfram.com/language/ref/GaborFilter.html" source: "Wolfram Language Documentation" related_guides: - title: "Image Filtering & Neighborhood Processing" link: "https://reference.wolfram.com/language/guide/ImageFilteringAndNeighborhoodProcessing.en.md" - title: "Video Computation: Update History" link: "https://reference.wolfram.com/language/guide/VideoComputation-UpdateHistory.en.md" related_functions: - title: "GaborMatrix" link: "https://reference.wolfram.com/language/ref/GaborMatrix.en.md" - title: "GaussianFilter" link: "https://reference.wolfram.com/language/ref/GaussianFilter.en.md" - title: "GradientFilter" link: "https://reference.wolfram.com/language/ref/GradientFilter.en.md" - title: "LaplacianFilter" link: "https://reference.wolfram.com/language/ref/LaplacianFilter.en.md" - title: "ImageConvolve" link: "https://reference.wolfram.com/language/ref/ImageConvolve.en.md" - title: "ListConvolve" link: "https://reference.wolfram.com/language/ref/ListConvolve.en.md" --- # GaborFilter GaborFilter[data, r, k] filters data by convolving with a Gabor kernel of pixel radius r and wave vector k. GaborFilter[data, r, k, ϕ] uses a Gabor kernel with phase shift ϕ. GaborFilter[data, {r, σ}, …] uses a Gabor kernel with radius r and standard deviation σ. ## Details and Options * ``GaborFilter`` is a linear, spatially directional and frequency-selective filter commonly used in image processing for texture analysis and segmentation. In the spatial domain, a 2D Gabor filter kernel is a Gaussian function modulated by a sinusoidal plane wave. [image] * 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 | | video | a Video object | * ``GaborFilter[data, r, k]`` is equivalent to ``GaborFilter[data, {r, r / 2}, k, 0]``. * Either of the ``r`` or ``σ`` can be lists, specifying different values for different directions. * ``GaborFilter[image, …]`` by default gives an image of a real type of the same dimensions as ``image``. * The following options can be specified: | | | | | ----------------- | --------- | ------------------------------------------------------------- | | Padding | "Fixed" | padding method | | Standardized | True | whether to rescale the Gabor kernel to account for truncation | | WorkingPrecision | Automatic | the precision to use | * With a setting ``Padding -> None``, ``GaborFilter[data, …]`` normally gives a result smaller than ``data``. --- ## Examples (25) ### Basic Examples (3) Filter an image: ```wl In[1]:= GaborFilter[[image], 20, {.5, .5}]//ImageAdjust Out[1]= [image] ``` --- Gabor filtering of a 3D image: ```wl In[1]:= 10GaborFilter[[image], 5, {0, 0, 1}] Out[1]= [image] ``` --- Apply a Gabor filter to a list of values: ```wl In[1]:= list = N@Table[Sin[ π t^2 + 2π], {t, 0, 5, (1/30)}]; ListLinePlot[{list, GaborFilter[ list, 20, {.5}]}] Out[1]= [image] ``` ### Scope (8) #### Data (5) Gabor filtering of a 2D array: ```wl In[1]:= mat = Array[KroneckerDelta, {20, 20}]; res = GaborFilter[mat, 10, {.5, -.5}]; ArrayPlot /@ {mat, res} Out[1]= {[image], [image]} ``` --- Filter a ``TimeSeries`` object: ```wl In[1]:= ts = TemporalData[TimeSeries, {CompressedData["«1188»"], {{0, 1., 0.01}}, 1, {"Continuous", 1}, {"Continuous", 1}, 1, {ValueDimensions -> 1, ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, False, 10.1]; In[2]:= filtered = GaborFilter[ts, 10, {.1}] Out[2]= TemporalData[TimeSeries, {CompressedData["«1186»"], {{0, 1., 0.01}}, 1, {"Continuous", 1}, {"Continuous", 1}, 1, {ValueDimensions -> 1, ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, False, 14.3] In[3]:= ListLinePlot[{ts, filtered}, PlotLegends -> {"original data", "filtered"}] Out[3]= [image] ``` --- Filter an ``Audio`` signal: ```wl In[1]:= a = Import["ExampleData/rule30.wav"]; b = AudioNormalize[GaborFilter[a, 20, {1}]] Out[1]= [image] In[2]:= AudioPlot[{a, b}] Out[2]= [image] ``` --- Filter a color image: ```wl In[1]:= GaborFilter[[image], 20, {0.3, 0.3}]//ImageAdjust Out[1]= [image] ``` --- Filter video frames: ```wl In[1]:= GaborFilter[Video["ExampleData/fish.mp4"], 10, {0.3, 0.3}] Out[1]= \!\(\*VideoBox["![Embedded Video Player](video://content-jh7uf)"]\) ``` #### Parameters (3) Gabor filtering of a noisy signal using different kernel radii: ```wl In[1]:= ts = TemporalData[TimeSeries, {CompressedData["«1188»"], {{0, 1., 0.01}}, 1, {"Continuous", 1}, {"Continuous", 1}, 1, {ValueDimensions -> 1, ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, False, 10.1]; In[2]:= filtered = GaborFilter[ts, #, {0}]& /@ {1, 3, 9}; ListLinePlot[filtered, PlotLegends -> {"r=1", "r=3", "r=9"}] Out[2]= [image] ``` Use different standard deviations: ```wl In[3]:= filtered = GaborFilter[ts, {9, #}, {0}]& /@ {1, 5}; ListLinePlot[filtered, PlotLegends -> {"σ=1", "σ=5"}] Out[3]= [image] ``` Use different wave vectors: ```wl In[4]:= filtered = Table[GaborFilter[ts, 3, {k}], {k, {0., π / 3., 2π / 3.}}]; ListLinePlot[filtered, PlotLegends -> {"k={0}", "k={π/3}", "k={2π/3}"}] Out[4]= [image] ``` --- Gabor filtering in the vertical direction: ```wl In[1]:= GaborFilter[[image], 6, {π / 3, 0}]//ImageAdjust Out[1]= [image] ``` Filtering in the horizontal direction: ```wl In[2]:= GaborFilter[[image], 6, {0, π / 3}]//ImageAdjust Out[2]= [image] ``` Filtering in a diagonal direction: ```wl In[3]:= GaborFilter[[image], 6, {π, π} / 4]//ImageAdjust Out[3]= [image] ``` --- The cosine part of a Gabor filter is computed when $\phi =0$ : ```wl In[1]:= GaborFilter[[image], 3, {1, 1}, 0]//ImageAdjust Out[1]= [image] ``` The sine part of a Gabor filter is computed when $\phi =\pi /2$ : ```wl In[2]:= GaborFilter[[image], 3, {1, 1}, π / 2]//ImageAdjust Out[2]= [image] ``` ### Options (6) #### Padding (3) Gabor filtering using different padding schemes: ```wl In[1]:= v = Table[SawtoothWave[(n/10)], {n, -10, 10}]; pad = {"Fixed", "Periodic", "Reversed"}; In[2]:= ListLinePlot[GaborFilter[v, 5, {0}, Padding -> #]& /@ pad, PlotRange -> All, PlotLegends -> pad] Out[2]= [image] ``` --- Gabor filtering of a grayscale image using different padding schemes: ```wl In[1]:= ImageAdjust[GaborFilter[[image], 20, {Pi, Pi} / 2, Padding -> #]]& /@ {"Fixed", "Periodic"} Out[1]= [image] ``` --- ``Padding -> None`` normally returns an image smaller than the input image: ```wl In[1]:= GaborFilter[[image], 20, {0, 0}, Padding -> None] Out[1]= [image] ``` #### WorkingPrecision (3) ``MachinePrecision`` is by default used with integer arrays: ```wl In[1]:= GaborFilter[{3, 4, 4, 3}, 1, {1}] Out[1]= {2.76378, 3.55077, 3.55077, 2.76378} ``` Perform exact computation instead: ```wl In[2]:= GaborFilter[{3, 4, 4, 3}, 1, {1}, WorkingPrecision -> ∞] Out[2]= {(3 Sqrt[(2/π)]/Sqrt[(2/π)] + (2 Sqrt[(2/π)]/E^2)) + (7 Sqrt[(2/π)] Cos[1]/E^2 (Sqrt[(2/π)] + (2 Sqrt[(2/π)]/E^2))), (4 Sqrt[(2/π)]/Sqrt[(2/π)] + (2 Sqrt[(2/π)]/E^2)) + (7 Sqrt[(2/π)] Cos[1]/E^2 (Sqrt[(2/π)] + (2 Sqrt[(2/π)]/E^2))), (4 Sqrt[(2/π)]/Sqrt[(2/π)] + (2 Sqrt[(2/π)]/E^2)) + (7 Sqrt[(2/π)] Cos[1]/E^2 (Sqrt[(2/π)] + (2 Sqrt[(2/π)]/E^2))), (3 Sqrt[(2/π)]/Sqrt[(2/π)] + (2 Sqrt[(2/π)]/E^2)) + (7 Sqrt[(2/π)] Cos[1]/E^2 (Sqrt[(2/π)] + (2 Sqrt[(2/π)]/E^2)))} ``` --- With real arrays, by default the precision of the input is used: ```wl In[1]:= GaborFilter[{1.0000000000000000000, 2.0000000000000000000, 3.0000000000000000000, 4.0000000000000000000}, 1, {1}] Out[1]= {0.9596239410648790375, 1.804155949527571049, 2.706233924291356574, 3.550765932754048586} ``` Specify the precision to use: ```wl In[2]:= GaborFilter[{1.0000000000000000000, 2.0000000000000000000, 3.0000000000000000000, 4.0000000000000000000}, 1, {1}, WorkingPrecision -> MachinePrecision] Out[2]= {0.959624, 1.80416, 2.70623, 3.55077} ``` --- ``WorkingPrecision`` is ignored when filtering images: ```wl In[1]:= GaborFilter[[image], 2, {1, 1}, WorkingPrecision -> Infinity] Out[1]= [image] ``` An image of a real type is always returned: ```wl In[2]:= ImageType[%] Out[2]= "Real32" ``` ### Applications (3) Gabor filtering of an image to detect vertical lines in an image: ```wl In[1]:= GaborFilter[[image], {9, {3, 1}}, {0, 2}]//ImageAdjust Out[1]= [image] ``` --- Detect edges in the specified direction in a noisy image: ```wl In[1]:= GaborFilter[[image], 6, {1, 1} / 2, Pi / 2]//ImageAdjust Out[1]= [image] ``` --- The magnitude of the Gabor filter is computed as the squared norm of the sine and cosine components: ```wl In[1]:= gaborMagnitude[image_, r_, k_] := With[{data = ImageData[image]}, Image[GaborFilter[image, r, k, 0] ^ 2 + GaborFilter[image, r, k, Pi / 2] ^ 2]] ``` Extract regions with the dominant direction parallel to $-45 {}^{\circ}$ and $45 {}^{\circ}$ : ```wl In[2]:= i = [image]; λ = .5;r = 10; {t1, t2} = Table[ImageAdjust[gaborMagnitude[i, r, λ k]], {k, {{1, -1}, {1, 1}}}] Out[2]= [image] ``` Highlight two texture segments on the image: ```wl In[3]:= ImageCompose[i, {ImageAdd@@MapThread[ImageMultiply[MorphologicalBinarize[#1], #2]&, {{t1, t2}, {Red, Green}}], .3}] Out[3]= [image] ``` ### Properties & Relations (5) ``GaborFilter`` is equivalent to a convolution with a ``GaborMatrix`` : ```wl In[1]:= i = [image]; g1 = GaborFilter[i, 10, .5{1, -1}]//ImageAdjust Out[1]= [image] In[2]:= g2 = ImageConvolve[i, GaborMatrix[10, .5{1, -1}]]//ImageAdjust Out[2]= [image] In[3]:= g1 === g2 Out[3]= True ``` --- Gabor filtering with a zero-valued wave vector is equivalent to Gaussian smoothing: ```wl In[1]:= GaborFilter[{1, 1, 1, 1, 1, 0, 0, 3, 12, 1, 0, 0, 0, 0, 0}, 1, {0}] == GaussianFilter[{1, 1, 1, 1, 1, 0, 0, 3, 12, 1, 0, 0, 0, 0, 0}, 1, Method -> "Gaussian"] Out[1]= True ``` --- Impulse response of a Gabor filter: ```wl In[1]:= h = GaborFilter[ArrayPad[{{1}}, 10], 10, .75{1, 1}]; ListPlot3D[h, Mesh -> False, PlotRange -> All] Out[1]= [image] ``` Magnitude spectrum of the filter: ```wl In[2]:= Plot3D[Evaluate[Abs@ListFourierSequenceTransform[h, {u, v}]], {u, 0, π}, {v, 0, π}, Mesh -> False, PlotRange -> All] Out[2]= [image] ``` --- Gabor filtering of an image gives a real-valued image: ```wl In[1]:= GaborFilter[[image], 5, {1, 1}]//ImageAdjust Out[1]= [image] ``` --- ``GaborFilter`` is a linear filter: ```wl In[1]:= list1 = {1, 1, 1, 1, 1, 0, 0, 3, 12, 1, 0, 0, 0, 0, 0}; list2 = {2, 2, 2, 2, 1, 5, 4, 6, 2, 2, 1, 1, 1, 1, 1}; GaborFilter[list1 + list2, 1, {1}] == GaborFilter[list1, 1, {1}] + GaborFilter[list2, 1, {1}] Out[1]= True ``` ## See Also * [`GaborMatrix`](https://reference.wolfram.com/language/ref/GaborMatrix.en.md) * [`GaussianFilter`](https://reference.wolfram.com/language/ref/GaussianFilter.en.md) * [`GradientFilter`](https://reference.wolfram.com/language/ref/GradientFilter.en.md) * [`LaplacianFilter`](https://reference.wolfram.com/language/ref/LaplacianFilter.en.md) * [`ImageConvolve`](https://reference.wolfram.com/language/ref/ImageConvolve.en.md) * [`ListConvolve`](https://reference.wolfram.com/language/ref/ListConvolve.en.md) ## Related Guides * [Image Filtering & Neighborhood Processing](https://reference.wolfram.com/language/guide/ImageFilteringAndNeighborhoodProcessing.en.md) * [Video Computation: Update History](https://reference.wolfram.com/language/guide/VideoComputation-UpdateHistory.en.md) ## History * [Introduced in 2012 (9.0)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn90.en.md) \| [Updated in 2014 (10.0)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn100.en.md) ▪ [2016 (11.0)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn110.en.md) ▪ [2025 (14.3)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn143.en.md)