Create a Maze from an Image

Source Notebook

Create a maze image by computing a shortest tour through a set of image points

Examples

Testing cell renumbering:

In[1]:=

$Line=1234

Out[1]=

1234

In[2]:=

Range[10000]//Short

Out[2]//Short=

{1,2,3,4,5,6,7,8,9,10,11,9978,9990,9991,9992,9993,9994,9995,9996,9997,9998,9999,10000}

Start with an image:

In[3]:=

img=

;

Convert to grayscale and apply dithering using the resource function FloydSteinbergDithering:

In[4]:=

dithered=

[◼]	FloydSteinbergDithering

[ColorConvert[img,"Grayscale"],2]

Out[4]=

Extract the set of coordinates corresponding to dark pixels with

PixelValuePositions

and add some slight noise:

In[5]:=

pts=PixelValuePositions[dithered,0];noisy=RandomReal[{-.15,.15},Dimensions[pts]]+pts

Out[5]=

{{0.983242,97.9591},{3.14381,98.0129},{4.88179,98.1228},{7.04649,97.9469},{9.14214,98.0841},{11.0581,97.8632},{12.9178,98.1276},

⋯3983⋯

,{117.126,1.0599},{119.981,1.0192},{122.889,1.02882},{133.011,1.14902},{141.005,1.08078},{146.109,0.946914}}

Full expression not available

(

original memory size:

65.6 kB)

Preview the points:

In[6]:=

Graphics[Point[noisy]]

Out[6]=

Use

FindShortestTour

to generate a single line that visits very point:

In[7]:=

tour=Last[FindShortestTour[noisy]]

Out[7]=

{1,2,3,4,5,79,126,80,6,7,8,81,133,82,9,10,83,11,12,13,14,85,138,192,259,193,194,139,86,15,16,17,87,140,195,196,197,141,88,18,19,20,89,142,198,199,262,263,321,380,440,439,438,379,349,296,261,320,378,437,490,547,

⋯3873⋯

,938,867,833,768,735,673,705,734,797,796,733,671,672,645,591,538,569,623,646,706,736,737,674,647,592,540,539,483,430,374,318,257,244,184,130,78,77,129,188,243,287,340,339,398,429,482,481,454,537,590,622,568,511,453,397,338,286,242,183,128,76,1}

Full expression not available

(

original memory size:

32.9 kB)

These numbers represent the order that points should be visited.

GraphicsComplex

is a convenient way to represent graphics primitives using a set of points and indices.

Create a

Line

that passes through the points in order:

In[8]:=

Graphics[GraphicsComplex[noisy,Line[tour]]]

Out[8]=

Use the original image to add some color:

In[9]:=

Graphics[GraphicsComplex[noisy,Line[tour,VertexColorsDarker[RGBColor/@PixelValue[img,pts〚tour〛]]]]]

Out[9]=

Adding More Detail
(2)

To add detail to the maze, all that's needed is to resize the image to a higher resolution. Similarly, the detail can be decreased by lowering the image resolution.

Double the resolution of the original image with

ImageResize

In[1]:=

large=ImageResize

,Scaled[2]

Out[1]=

Repeat the steps from above:

In[2]:=

dithered=

[◼]	FloydSteinbergDithering

[ColorConvert[large,"Grayscale"],2];pts=PixelValuePositions[dithered,0];noisy=RandomReal[{-.15,.15},Dimensions[pts]]+pts;tour=Last[FindShortestTour[noisy]];Graphics[GraphicsComplex[noisy,Line[tour,VertexColorsDarker[RGBColor/@PixelValue[large,pts〚tour〛]]]]]

Wolfram Cloud Resource Object

Create a Maze from an Image

Categories

Examples

Adding More Detail
(2)

Generalization
(6)



Source Metadata

See Also

Publisher Information

Create a Maze from an Image

Categories

Examples

Adding More Detail (2)

Generalization (6) 

Source Metadata

See Also

Publisher Information

Adding More Detail
(2)

Generalization
(6)

