--- title: "RegionImage" language: "en" type: "Symbol" summary: "RegionImage[reg] returns a rasterized grayscale 2D or 3D image of reg. RegionImage[reg, {{xmin, xmax}, ...}] restricts to the bounds [xmin, xmax]*\\[CenterEllipsis]." keywords: - rasterizing region - rasterizing mesh region - rasterizing 2D mesh - rasterizing 3D mesh - grid a region - numericalize region - discretize a region - sample a region - convert region to image - region to image canonical_url: "https://reference.wolfram.com/language/ref/RegionImage.html" source: "Wolfram Language Documentation" related_guides: - title: "Creating & Importing Images" link: "https://reference.wolfram.com/language/guide/CreatingAndImportingImages.en.md" - title: "Image Computation: Update History" link: "https://reference.wolfram.com/language/guide/ImageComputation-UpdateHistory.en.md" related_functions: - title: "DiscretizeRegion" link: "https://reference.wolfram.com/language/ref/DiscretizeRegion.en.md" - title: "DiscretizeGraphics" link: "https://reference.wolfram.com/language/ref/DiscretizeGraphics.en.md" - title: "Rasterize" link: "https://reference.wolfram.com/language/ref/Rasterize.en.md" - title: "ImageMesh" link: "https://reference.wolfram.com/language/ref/ImageMesh.en.md" - title: "MeshRegion" link: "https://reference.wolfram.com/language/ref/MeshRegion.en.md" --- # RegionImage RegionImage[reg] returns a rasterized grayscale 2D or 3D image of reg. RegionImage[reg, {{xmin, xmax}, …}] restricts to the bounds $\left[x_{\text{\textit{min}}},x_{\text{\textit{max}}}\right]\times \cdots$. ## Details and Options * ``RegionImage`` converts regions to 2D and 3D raster images. * The region ``reg`` can be anything that is ``ConstantRegionQ`` and a ``RegionEmbeddingDimension`` of 2 or 3. * The following options can be specified: | | | | | --------------- | --------- | ------------------------------------------------- | | ImageResolution | Automatic | image resolution in DPI for rasterization | | ImageSize | Automatic | final displayed image size in printer's points | | MetaInformation | <\|\|> | metainformation to be included in the image | | Method | Automatic | method parameters to use | | RasterSize | Automatic | raster size in pixels or voxels for rasterization | * By default, an automatic thickness is chosen to draw lower-dimensional regions. With ``Method -> {"Thickness" -> t}``, these regions are rasterized using the absolute thickness ``t``. --- ## Examples (25) ### Basic Examples (2) Rasterize a region in 2D: ```wl In[1]:= RegionImage[Annulus[]] Out[1]= [image] ``` --- Rasterize a region in 3D: ```wl In[1]:= RegionImage[Cone[]] Out[1]= [image] ``` ### Scope (7) #### Data (5) Rasterize a ``Region`` : ```wl In[1]:= RegionImage[Region[DiskSegment[{0, 0}, 1, {π / 6, π - π / 6}]]] Out[1]= [image] ``` --- Rasterize a ``MeshRegion`` : ```wl In[1]:= RegionImage[[image]] Out[1]= [image] ``` --- Rasterize a ``BoundaryMeshRegion`` : ```wl In[1]:= ℛ = BoundaryMeshRegion[ {{0, 0}, {3, 0}, {3, 3}, {0, 3}, {1, 1}, {2, 1}, {2, 2}, {1, 2}}, Line[{1, 2, 3, 4, 1}], Line[{5, 6, 7, 8, 5}] ] Out[1]= [image] In[2]:= RegionImage[ℛ] Out[2]= [image] ``` --- Rasterize a region in 2D with components of 0, 1, and 2 dimensions: ```wl In[1]:= region = Region@RegionUnion[Annulus[], Circle[{0, 0}, 4 / 3], Point[{0, 0}]] Out[1]= [image] In[2]:= RegionImage[region] Out[2]= [image] ``` --- Rasterize a region in 3D with mixed dimensional components: ```wl In[1]:= region = Region@ParametricRegion[{{x, y, z + y x}, x^2 + y^2 + z^2 <= 1 ∨ z == Sin[x + y] ∨ (x == 0 ∧ y == 0)}, {{x, -1, 1}, {y, -1, 1}, {z, -1, 1}} ] Out[1]= [image] In[2]:= RegionImage[region] Out[2]= [image] ``` #### Parameters (2) Rasterize the part of a region in 2D that is within specified bounds: ```wl In[1]:= RegionImage[Disk[], {{0, 1}, {0, 1}}] Out[1]= [image] ``` --- Rasterize the part of a region in 3D that is within specified bounds: ```wl In[1]:= RegionImage[Sphere[], {{-1, 1}, {-1 / 2, 1}, {-1, -1 / 3}}] Out[1]= [image] ``` ### Options (6) #### Method (4) ##### "Thickness" (4) --- Compare different settings for the thickness of components that are not full dimensional: ```wl In[1]:= mesh = DiscretizeRegion[ImplicitRegion[x == 0∧y == 0 ∨ 1 / 4 ≤ x^2 + y^2 ≤ 1 ∨ x^2 + y^2 == 16 / 9, {x, y}] ] Out[1]= [image] In[2]:= Table[ Labeled[ RegionImage[mesh, RasterSize -> 100, Method -> {"Thickness" -> t}], Text[t]], {t, {0.5, 1, 2, 4, 8, 16}} ] Out[2]= {Labeled[[image], Text[0.5]], Labeled[[image], Text[1]], Labeled[[image], Text[2]], Labeled[[image], Text[4]], Labeled[[image], Text[8]], Labeled[[image], Text[16]]} ``` --- The thickness is effectively the width of a feature in pixels: ```wl In[1]:= bounds = {{-1.2, 1.2}, {-1.2, 1.2}}; mesh = MeshRegion[ {{0, 0}, {-1, 0}, {0, -1}, {1, 0}, {0, 1}, {1 / 2, 1 / 2}}, {Line[{2, 1, 3, 4, 1, 5}], Point[{6}]}, BaseStyle -> Thick ] Out[1]= [image] In[2]:= Table[ Labeled[ RegionImage[mesh, bounds, RasterSize -> 24, ImageSize -> 100, Method -> {"Thickness" -> t}], Text[t] ], {t, 3} ] Out[2]= {Labeled[[image], Text[1]], Labeled[[image], Text[2]], Labeled[[image], Text[3]]} ``` --- The default ``"Thickness" -> Automatic`` renders one white pixel per ``Point`` : ```wl In[1]:= n = 50; mesh = MeshRegion[RandomPoint[Disk[], n], Point[Range[n]]]; In[2]:= Table[ Labeled[ RegionImage[mesh, {{-1, 1}, {-1, 1}}, Method -> {"Thickness" -> t}, RasterSize -> 100], Text[t] ], {t, {Automatic, 0, 1, 2, 4, 8}} ] Out[2]= {Labeled[[image], Text[Automatic]], Labeled[[image], Text[0]], Labeled[[image], Text[1]], Labeled[[image], Text[2]], Labeled[[image], Text[4]], Labeled[[image], Text[8]]} ``` --- Thicken a shell in 3D: ```wl In[1]:= RegionImage[ Sphere[], {{-1, 1}, {-1 / 2, 1}, {-1, -1 / 3}}, Method -> {"Thickness" -> 4} ] Out[1]= [image] ``` #### RasterSize (2) By default, regions are rasterized to the default graphics raster size: ```wl In[1]:= RegionImage[Annulus[]] Out[1]= [image] In[2]:= ImageDimensions[%] Out[2]= {360, 360} ``` Specify the raster size: ```wl In[3]:= RegionImage[Annulus[], RasterSize -> 100] Out[3]= [image] In[4]:= ImageDimensions[%] Out[4]= {100, 100} ``` --- Use ``ImageSize`` to specify the display size: ```wl In[1]:= RegionImage[Annulus[], ImageSize -> 100] Out[1]= [image] In[2]:= ImageDimensions[%] Out[2]= {360, 360} ``` ### Applications (6) Create the image of a Sierpiński mesh: ```wl In[1]:= RegionImage[SierpinskiMesh[6]] Out[1]= [image] ``` --- Rasterization of a 3D knot: ```wl In[1]:= i = RegionImage[KnotData["Trefoil", "Region"]] Out[1]= [image] In[2]:= ListAnimate[Image3DSlices[i]] Out[2]= DynamicModule[«8»] ``` --- Generate cylindric masks for a volume: ```wl In[1]:= vol = ExampleData[{"TestImage3D", "CTengine"}] dims = ImageDimensions[vol]; Out[1]= [image] In[2]:= mask = Blur[RegionImage[ Region@Cylinder[{{-100, 0, 0}, {100, 0, 0}}, 50], Outer[Times, dims, {-1, 1} / 2], RasterSize -> dims ]] Out[2]= [image] In[3]:= ImageMultiply[vol, mask] Out[3]= [image] ``` --- Construct a 3D image from elevation data around Mount Everest: ```wl In[1]:= everest = GeoElevationData[Entity["Mountain", "MountEverest"], Automatic, "Region"] Out[1]= [image] In[2]:= RegionImage[everest] Out[2]= [image] ``` --- Generate the volume of a polyhedron: ```wl In[1]:= ico = BoundaryMeshRegion@@First[PolyhedronData["Icosahedron"]] Out[1]= [image] In[2]:= RegionImage[ico] Out[2]= [image] ``` --- "Melting" a snowflake region via curvature flow: ```wl In[1]:= flake = RegionImage[[image]] Out[1]= [image] In[2]:= corn = CurvatureFlowFilter[flake, 16] Out[2]= [image] In[3]:= ImageMesh[corn] Out[3]= [image] ``` ### Possible Issues (2) Setting the thickness to zero effectively ignores the lower-dimensional components: ```wl In[1]:= RegionImage[Circle[], Method -> {"Thickness" -> 0}] Out[1]= [image] ``` Increase the thickness to get response for lower-dimensional components: ```wl In[2]:= RegionImage[Circle[], Method -> {"Thickness" -> 1}] Out[2]= [image] ``` --- 3D rasterization can show a moiré-like effect due to the partial volume computation and coloring: ```wl In[1]:= vol = RegionImage[Sphere[], {{-1, 1}, {-1 / 2, 1}, {-1, -1 / 3}}, Method -> {"Thickness" -> 2}] Out[1]= [image] ``` Use a color function that changes only opacities based on the voxel intensity, not the color: ```wl In[2]:= vol2 = Image3D[vol, ColorFunction -> (GrayLevel[1, #]&), Background -> Black] Out[2]= [image] ``` Antialiasing using blur: ```wl In[3]:= Blur[vol2] Out[3]= [image] ``` Antialiasing would even improve a color function that changes both color and opacity by voxel intensities: ```wl In[4]:= Blur[vol] Out[4]= [image] ``` ### Neat Examples (2) Estimate the area content of a rasterized disk: ```wl In[1]:= img = RegionImage[ BoundaryDiscretizeRegion[Disk[], PrecisionGoal -> 8], {{-1.2, 1.2}, {-1.2, 1.2}}, RasterSize -> 32 ] Out[1]= [image] In[2]:= pixelSize = 2.4 / 32; ``` Compare the area estimate with the disk area π: ```wl In[3]:= area = ImageMeasurements[img, "Total"] pixelSize^2 Out[3]= 3.13862 In[4]:= area / π Out[4]= 0.999054 ``` --- Nested conversion between a discretized and mesh representation of a disk: ```wl In[1]:= mesh = BoundaryDiscretizeRegion[Disk[]] Out[1]= [image] In[2]:= Nest[ ImageMesh[ RegionImage[#, {{-1, 1}, {-1, 1}}], DataRange -> {{-1, 1}, {-1, 1}} ]&, mesh, 100 ] Out[2]= [image] ``` Show the evaluation: ```wl In[3]:= NestList[ ImageMesh[ RegionImage[#, {{-1, 1}, {-1, 1}}], DataRange -> {{-1, 1}, {-1, 1}} ]&, mesh, 100 ][[1 ;; -1 ;; 25]] Out[3]= {[image], [image], [image], [image], [image]} ``` ## See Also * [`DiscretizeRegion`](https://reference.wolfram.com/language/ref/DiscretizeRegion.en.md) * [`DiscretizeGraphics`](https://reference.wolfram.com/language/ref/DiscretizeGraphics.en.md) * [`Rasterize`](https://reference.wolfram.com/language/ref/Rasterize.en.md) * [`ImageMesh`](https://reference.wolfram.com/language/ref/ImageMesh.en.md) * [`MeshRegion`](https://reference.wolfram.com/language/ref/MeshRegion.en.md) ## Related Guides * [Creating & Importing Images](https://reference.wolfram.com/language/guide/CreatingAndImportingImages.en.md) * [Image Computation: Update History](https://reference.wolfram.com/language/guide/ImageComputation-UpdateHistory.en.md) ## History * [Introduced in 2017 (11.2)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn112.en.md)