An Image Processing Example

Description

Mathematica uses a specially written package to operate on scanned images converted to PostScript.

By:   Mark A. Yoder
Rose-Hulman Institute of Technology

The Original Image

An image of the sign and surroundings to the left of the main entrance to Rose-Hulman.

The sign from above.

The word "ROSE"  from above.

The letter "R" from above.

A Small Image of "R"

The Image

The Density Plot

The raw input data is conatined in the following cell.

smallR = ReGrey[{
{0.3242, 0.3242, 0.2461, 0.2539, 0.2461, 0.2500, 0.2461, 0.2773, 0.2813, 
0.2852, 0.3086, 0.2813, 0.2461, 0.2500, 0.2461, 0.2695, 0.2695, 0.3086, 
0.3086},
{0.3242, 0.3086, 0.2773, 0.2344, 0.1875, 0.1992, 0.1836, 0.1797, 0.1680, 
0.2031, 0.2578, 0.2461, 0.1914, 0.1680, 0.1797, 0.1992, 0.2617, 0.2930, 
0.2969},
{0.3242, 0.3242, 0.3086, 0.4609, 0.6172, 0.6445, 0.6602, 0.6445, 0.6445, 
0.4023, 0.2773, 0.2539, 0.4375, 0.6172, 0.6289, 0.4766, 0.3398, 0.3086, 
0.2344},
{0.3242, 0.2969, 0.2969, 0.2539, 0.2539, 0.6758, 0.7774, 0.5820, 0.3320, 
0.2852, 0.2539, 0.4375, 0.7852, 0.7383, 0.3555, 0.3242, 0.2852, 0.2656, 
0.2305},
{0.3086, 0.3086, 0.2930, 0.2852, 0.2656, 0.6602, 0.7617, 0.4922, 0.3242, 
0.2461, 0.2578, 0.6055, 0.7617, 0.4453, 0.3320, 0.2930, 0.2773, 0.2539, 
0.2305},
{0.3086, 0.3242, 0.3086, 0.2852, 0.2852, 0.6680, 0.7930, 0.4766, 0.2734, 
0.2656, 0.2734, 0.7734, 0.5899, 0.3711, 0.3086, 0.3086, 0.2578, 0.2461, 
0.5078},
{0.3242, 0.3086, 0.2969, 0.2852, 0.2656, 0.6914, 0.8008, 0.4375, 0.2539, 
0.2813, 0.5547, 0.8086, 0.4063, 0.3320, 0.3086, 0.2891, 0.2578, 0.4453, 
0.7344},
{0.3320, 0.3242, 0.3086, 0.2852, 0.2773, 0.7344, 0.7969, 0.4336, 0.2734, 
0.3945, 0.7422, 0.8125, 0.3398, 0.2969, 0.2773, 0.2813, 0.2656, 0.5899, 
0.7695},
{0.3242, 0.3242, 0.2969, 0.2852, 0.2813, 0.7266, 0.7813, 0.4258, 0.3711, 
0.6172, 0.7813, 0.5547, 0.2734, 0.2656, 0.2656, 0.2852, 0.2617, 0.6758, 
0.7774},
{0.3320, 0.3320, 0.2891, 0.2852, 0.2930, 0.7383, 0.8125, 0.4375, 0.3398, 
0.2969, 0.2930, 0.6914, 0.3086, 0.2695, 0.2656, 0.2656, 0.2656, 0.7188, 
0.7656},
{0.3242, 0.3242, 0.2969, 0.2773, 0.3242, 0.7266, 0.7930, 0.4180, 0.3242, 
0.3398, 0.2617, 0.3555, 0.7227, 0.5859, 0.3242, 0.3086, 0.2930, 0.6758, 
0.7813},
{0.3242, 0.3242, 0.2852, 0.2578, 0.2969, 0.7188, 0.7734, 0.4219, 0.3320, 
0.3242, 0.2695, 0.2734, 0.6602, 0.7656, 0.3711, 0.3242, 0.3086, 0.6680, 
0.7852},
{0.3242, 0.3242, 0.2813, 0.2656, 0.2969, 0.7617, 0.7617, 0.4258, 0.3242, 
0.3086, 0.2422, 0.2578, 0.6055, 0.8203, 0.4023, 0.3555, 0.3242, 0.5078, 
0.7734},
{0.3242, 0.3242, 0.2617, 0.2500, 0.2852, 0.7422, 0.7305, 0.3945, 0.2969, 
0.2578, 0.2227, 0.2891, 0.6914, 0.6602, 0.3750, 0.3086, 0.3086, 0.3086, 
0.6602},
{0.3320, 0.3242, 0.2344, 0.2031, 0.2539, 0.7305, 0.7109, 0.3320, 0.2188, 
0.2070, 0.2266, 0.6016, 0.7734, 0.4375, 0.3398, 0.3086, 0.2969, 0.2969, 
0.4609},
{0.3242, 0.3242, 0.3242, 0.4219, 0.6172, 0.8086, 0.7031, 0.5078, 0.4453, 
0.5391, 0.7188, 0.5234, 0.3086, 0.2969, 0.2969, 0.2969, 0.3242, 0.3242, 
0.3086},
{0.3398, 0.3242, 0.3242, 0.3242, 0.3086, 0.2969, 0.2773, 0.2813, 0.2695, 
0.2695, 0.2383, 0.2383, 0.2813, 0.2969, 0.3086, 0.3086, 0.3086, 0.3242, 
0.3242},
{0.3242, 0.3398, 0.3242, 0.3242, 0.3242, 0.3086, 0.2969, 0.2969, 0.2852, 
0.2695, 0.2773, 0.2852, 0.2969, 0.2969, 0.2969, 0.3086, 0.3086, 0.3398, 
0.3398},
{0.3398, 0.3398, 0.3398, 0.3398, 0.3242, 0.3242, 0.3086, 0.2813, 0.2813, 
0.2695, 0.2813, 0.2969, 0.2969, 0.2969, 0.2969, 0.2969, 0.3242, 0.3242, 
0.3398}}, 1, 32];

ListDensityPlot[smallR, Mesh->False]

How big is smallR?

Dimensions[smallR]

What are the largest and smallest values?

{Min[smallR], Max[smallR]}

The Histogram

How are its values distributed?

hist = Histogram[smallR, 0, 32, 32]

ListPlot[hist, PlotJoined->True, PlotRange->{0,70},
		AxesLabel->{"  Grey Level", "Count"}]

Making a Binary Image

Make all values below 12 black and those 12 and above white.

binary = Map[If[#<12, 0, 1]&, smallR, {2}];

ListDensityPlot[binary, Mesh->False]

Finding the Edges

Find the edges.

s = Sobel[smallR];

ListDensityPlot[s, Mesh->False]

What are the strongest and weakest edges?

{Min[s], Max[s]}

Find a histogram of the edge strengths.

hist = Histogram[s, Min[s], Max[s], 32];

ListPlot[hist, PlotJoined->True,
		AxesLabel->{"Edge Strength", "Count"}]

Make a binary image.

Map[If[#<50, 0, 1]&, s, {2}];

ListDensityPlot[%, Mesh->False]

A Big Image of "R"

The Image

The Density Plot

The raw input data is conatined in the following cell.

bigR = ReGrey[{
{0.3412, 0.3294, 0.3294, 0.3098, 0.3294, 0.3176, 0.2980, 0.2824, 0.2706, 
0.2667, 0.2510, 0.2588, 0.2784, 0.2784, 0.2706, 0.2941, 0.2863, 0.3059, 
0.2980, 0.3059, 0.3098, 0.2980, 0.3059, 0.3098, 0.2980, 0.3098, 0.3294, 
0.3294, 0.3098, 0.2980, 0.2980, 0.2706, 0.2706, 0.2706, 0.2706, 0.2706, 
0.2706, 0.2706, 0.2784, 0.2824, 0.2706, 0.2980, 0.3098, 0.3176, 0.3255, 
0.3098, 0.3294, 0.3098},
{0.3412, 0.3412, 0.3294, 0.3373, 0.3412, 0.2980, 0.2980, 0.2824, 0.2706, 
0.2706, 0.2706, 0.2588, 0.2667, 0.2824, 0.2824, 0.2667, 0.2784, 0.2980, 
0.2980, 0.2980, 0.2863, 0.2824, 0.2824, 0.3137, 0.3294, 0.3294, 0.3137, 
0.3294, 0.3098, 0.3098, 0.2863, 0.2706, 0.2824, 0.2863, 0.2706, 0.2706, 
0.2824, 0.2706, 0.2784, 0.2824, 0.2980, 0.3059, 0.3098, 0.3294, 0.3294, 
0.3373, 0.3412, 0.3294},
{0.3294, 0.3373, 0.3412, 0.3294, 0.3294, 0.3098, 0.2980, 0.2706, 0.2706, 
0.2706, 0.2706, 0.2471, 0.2706, 0.2706, 0.2784, 0.2784, 0.2706, 0.2941, 
0.3059, 0.2980, 0.2824, 0.2824, 0.2863, 0.3098, 0.3098, 0.3137, 0.3098, 
0.3098, 0.3137, 0.2980, 0.2824, 0.2824, 0.2706, 0.2784, 0.2824, 0.2706, 
0.2706, 0.2627, 0.2706, 0.2824, 0.2824, 0.3098, 0.3098, 0.3098, 0.3412, 
0.3294, 0.3373, 0.3216},
{0.3294, 0.3373, 0.3412, 0.3294, 0.3373, 0.3412, 0.2980, 0.2471, 0.2588, 
0.2588, 0.2471, 0.2588, 0.2824, 0.2784, 0.2549, 0.2588, 0.2588, 0.2588, 
0.2863, 0.2824, 0.2863, 0.2863, 0.2863, 0.2863, 0.3176, 0.3216, 0.3373, 
0.3176, 0.3216, 0.2824, 0.2588, 0.2627, 0.2510, 0.2588, 0.2627, 0.2510, 
0.2471, 0.2627, 0.2706, 0.2784, 0.2824, 0.2863, 0.2980, 0.3373, 0.3412, 
0.3294, 0.3373, 0.3216},
{0.3176, 0.3412, 0.3294, 0.3373, 0.3412, 0.3294, 0.2863, 0.2510, 0.2706, 
0.2549, 0.2588, 0.2510, 0.2745, 0.2588, 0.2510, 0.2471, 0.2588, 0.2627, 
0.2784, 0.2863, 0.2863, 0.2824, 0.2863, 0.2902, 0.3098, 0.3137, 0.3216, 
0.3216, 0.3137, 0.2863, 0.2824, 0.2471, 0.2588, 0.2627, 0.2510, 0.2471, 
0.2510, 0.2706, 0.2784, 0.2824, 0.2706, 0.2784, 0.3098, 0.3294, 0.3059, 
0.3098, 0.3294, 0.3294},
{0.3373, 0.3373, 0.3333, 0.3333, 0.3137, 0.3098, 0.3098, 0.2824, 0.2510, 
0.2588, 0.2392, 0.2314, 0.2392, 0.2510, 0.2549, 0.2510, 0.2510, 0.2549, 
0.2392, 0.2549, 0.2431, 0.2431, 0.2392, 0.2667, 0.2863, 0.3137, 0.3216, 
0.3137, 0.2824, 0.2667, 0.2549, 0.2392, 0.2196, 0.2510, 0.2510, 0.2510, 
0.2549, 0.2549, 0.2549, 0.2588, 0.2784, 0.2863, 0.3098, 0.3098, 0.3059, 
0.3176, 0.3098, 0.3059},
{0.3373, 0.3333, 0.3176, 0.3373, 0.3098, 0.3137, 0.3098, 0.2784, 0.2627, 
0.2667, 0.2275, 0.2392, 0.2510, 0.2392, 0.2510, 0.2549, 0.2392, 0.2510, 
0.2549, 0.2667, 0.2392, 0.2431, 0.2431, 0.2549, 0.2784, 0.3255, 0.3137, 
0.3098, 0.2863, 0.2549, 0.2627, 0.2314, 0.2196, 0.2275, 0.2510, 0.2549, 
0.2510, 0.2549, 0.2588, 0.2549, 0.2863, 0.3059, 0.3059, 0.3059, 0.3176, 
0.3294, 0.3137, 0.3098},
{0.3373, 0.3294, 0.3333, 0.3333, 0.3098, 0.3098, 0.2863, 0.2863, 0.2627, 
0.2392, 0.2039, 0.1882, 0.2000, 0.2000, 0.2000, 0.2000, 0.2000, 0.2000, 
0.2039, 0.1961, 0.1765, 0.1686, 0.1922, 0.2039, 0.2353, 0.2627, 0.2784, 
0.2863, 0.2588, 0.2471, 0.2196, 0.2039, 0.1922, 0.1882, 0.1765, 0.1765, 
0.1765, 0.1804, 0.2000, 0.2275, 0.2627, 0.2706, 0.2863, 0.2941, 0.3137, 
0.3059, 0.3098, 0.3059},
{0.3333, 0.3333, 0.3294, 0.3373, 0.3373, 0.3059, 0.2863, 0.2941, 0.2627, 
0.2353, 0.2157, 0.1922, 0.2000, 0.2000, 0.2000, 0.2000, 0.1843, 0.2039, 
0.1922, 0.1804, 0.1961, 0.1647, 0.1882, 0.2157, 0.2235, 0.2588, 0.2706, 
0.2784, 0.2549, 0.2549, 0.2235, 0.1922, 0.1922, 0.1961, 0.1725, 0.1765, 
0.1804, 0.1804, 0.2039, 0.2392, 0.2627, 0.2627, 0.2941, 0.3059, 0.3098, 
0.2980, 0.3098, 0.3020},
{0.3255, 0.3255, 0.3216, 0.3294, 0.3294, 0.3255, 0.3137, 0.3451, 0.4627, 
0.5686, 0.6353, 0.6275, 0.6471, 0.6588, 0.6627, 0.6588, 0.6745, 0.6667, 
0.6549, 0.6667, 0.6706, 0.6824, 0.6471, 0.5294, 0.4078, 0.3608, 0.3333, 
0.2784, 0.2549, 0.3294, 0.4431, 0.5294, 0.5765, 0.6275, 0.6353, 0.6353, 
0.6667, 0.6275, 0.5804, 0.4863, 0.4000, 0.3412, 0.3569, 0.3137, 0.3098, 
0.3098, 0.3098, 0.2784},
{0.3255, 0.3216, 0.3333, 0.3294, 0.3255, 0.3333, 0.3098, 0.3412, 0.4627, 
0.5725, 0.6275, 0.6196, 0.6510, 0.6510, 0.6588, 0.6745, 0.6627, 0.6627, 
0.6667, 0.6588, 0.6588, 0.6902, 0.6510, 0.5451, 0.4039, 0.3647, 0.3176, 
0.2863, 0.2588, 0.3137, 0.4392, 0.5137, 0.5765, 0.6196, 0.6353, 0.6392, 
0.6549, 0.6392, 0.6000, 0.4745, 0.4118, 0.3569, 0.3412, 0.3216, 0.3137, 
0.3098, 0.3098, 0.2941},
{0.3294, 0.3333, 0.3373, 0.3333, 0.3294, 0.3098, 0.3098, 0.3686, 0.5373, 
0.7176, 0.8392, 0.9020, 0.9059, 0.8863, 0.8863, 0.8863, 0.8706, 0.8706, 
0.9137, 0.9569, 0.9569, 0.9373, 0.8431, 0.6471, 0.4667, 0.4078, 0.3451, 
0.2824, 0.3725, 0.5412, 0.7059, 0.7961, 0.8275, 0.8471, 0.9098, 0.9373, 
0.9333, 0.9020, 0.7843, 0.6275, 0.5020, 0.3765, 0.3451, 0.3412, 0.3412, 
0.3098, 0.2627, 0.2392},
{0.3373, 0.3373, 0.3255, 0.3333, 0.3333, 0.3216, 0.3098, 0.3725, 0.5255, 
0.6980, 0.8431, 0.9059, 0.9020, 0.8863, 0.8863, 0.8863, 0.8706, 0.8863, 
0.9098, 0.9569, 0.9608, 0.9333, 0.8706, 0.6627, 0.4706, 0.4039, 0.3490, 
0.2863, 0.3647, 0.5294, 0.6745, 0.7961, 0.8275, 0.8510, 0.9059, 0.9333, 
0.9373, 0.9020, 0.7882, 0.6353, 0.5059, 0.4000, 0.3608, 0.3451, 0.3373, 
0.3098, 0.2824, 0.2353},
{0.3373, 0.3294, 0.3255, 0.3333, 0.3333, 0.3020, 0.3098, 0.3098, 0.2784, 
0.2549, 0.2941, 0.4549, 0.6745, 0.7804, 0.8000, 0.8078, 0.8431, 0.8706, 
0.8863, 0.7608, 0.5804, 0.4392, 0.3333, 0.3098, 0.3176, 0.2863, 0.2706, 
0.3176, 0.4392, 0.6627, 0.8039, 0.7882, 0.8157, 0.8902, 0.8588, 0.6902, 
0.5333, 0.3961, 0.3176, 0.3373, 0.3216, 0.3020, 0.3020, 0.2902, 0.2863, 
0.2706, 0.2392, 0.2431},
{0.3294, 0.3333, 0.3373, 0.3373, 0.3294, 0.3098, 0.3098, 0.3059, 0.2863, 
0.2667, 0.2863, 0.4510, 0.6471, 0.7686, 0.8078, 0.8196, 0.8431, 0.8667, 
0.8863, 0.7843, 0.5765, 0.4510, 0.3647, 0.3020, 0.3294, 0.3020, 0.2549, 
0.3176, 0.4431, 0.6471, 0.8000, 0.7882, 0.8039, 0.8863, 0.8745, 0.7176, 
0.5294, 0.4078, 0.3373, 0.3333, 0.3176, 0.3059, 0.2941, 0.2980, 0.2980, 
0.2706, 0.2431, 0.2549},
{0.3294, 0.3255, 0.3373, 0.3294, 0.3020, 0.3020, 0.3137, 0.3098, 0.3098, 
0.2863, 0.2549, 0.3255, 0.5137, 0.6784, 0.7647, 0.7804, 0.8314, 0.8588, 
0.7804, 0.5843, 0.4039, 0.3569, 0.3451, 0.3333, 0.2863, 0.2863, 0.2706, 
0.4039, 0.6235, 0.7333, 0.8039, 0.8314, 0.8667, 0.8627, 0.7412, 0.5569, 
0.4118, 0.3529, 0.3451, 0.3294, 0.3333, 0.3216, 0.2863, 0.2941, 0.2667, 
0.2314, 0.2902, 0.4588},
{0.3373, 0.3373, 0.3255, 0.3333, 0.3059, 0.2941, 0.3098, 0.3098, 0.3098, 
0.2863, 0.2667, 0.3176, 0.4863, 0.6784, 0.7608, 0.7647, 0.8392, 0.8627, 
0.7647, 0.5882, 0.4196, 0.3451, 0.3412, 0.3451, 0.3020, 0.2824, 0.2706, 
0.3922, 0.6078, 0.7412, 0.8000, 0.8275, 0.8627, 0.8863, 0.7373, 0.5647, 
0.4157, 0.3412, 0.3412, 0.3412, 0.3216, 0.3176, 0.2980, 0.2863, 0.2627, 
0.2314, 0.2902, 0.4235},
{0.3373, 0.3373, 0.3294, 0.3373, 0.3373, 0.3255, 0.3098, 0.3137, 0.3098, 
0.3098, 0.2902, 0.3529, 0.5373, 0.6706, 0.7647, 0.7922, 0.8549, 0.8588, 
0.7137, 0.5137, 0.3882, 0.3608, 0.3255, 0.2941, 0.2627, 0.2588, 0.3333, 
0.5333, 0.7529, 0.7882, 0.7882, 0.8510, 0.8980, 0.7922, 0.5725, 0.4118, 
0.3882, 0.3490, 0.2941, 0.3333, 0.3098, 0.3137, 0.3059, 0.2784, 0.2549, 
0.3412, 0.5098, 0.6627},
{0.3294, 0.3373, 0.3373, 0.3412, 0.3333, 0.3137, 0.3059, 0.3020, 0.3098, 
0.3098, 0.2784, 0.3490, 0.5176, 0.6588, 0.7608, 0.7961, 0.8431, 0.8549, 
0.7294, 0.5137, 0.3843, 0.3686, 0.3294, 0.2902, 0.2627, 0.2627, 0.3216, 
0.5098, 0.7569, 0.7765, 0.7647, 0.8510, 0.8980, 0.8000, 0.5843, 0.4157, 
0.3843, 0.3608, 0.2980, 0.3176, 0.3137, 0.3176, 0.2863, 0.2549, 0.2588, 
0.3137, 0.4784, 0.6627},
{0.3294, 0.3059, 0.3373, 0.3373, 0.3333, 0.3137, 0.3137, 0.3098, 0.3216, 
0.2941, 0.2863, 0.3333, 0.4980, 0.6706, 0.7961, 0.7961, 0.8588, 0.8588, 
0.7137, 0.4980, 0.4000, 0.3725, 0.3137, 0.2941, 0.2471, 0.2980, 0.4157, 
0.6353, 0.7961, 0.7804, 0.8235, 0.8863, 0.8471, 0.6706, 0.4549, 0.3569, 
0.3765, 0.3333, 0.3098, 0.3176, 0.3098, 0.3098, 0.2784, 0.2549, 0.3333, 
0.5020, 0.7020, 0.7961},
{0.3373, 0.3098, 0.3255, 0.3333, 0.3373, 0.3333, 0.3098, 0.3098, 0.3098, 
0.2863, 0.2902, 0.3333, 0.4863, 0.6706, 0.7961, 0.7961, 0.8588, 0.8588, 
0.7137, 0.5098, 0.4157, 0.3647, 0.3098, 0.3098, 0.2667, 0.2745, 0.4314, 
0.6392, 0.7765, 0.7922, 0.8157, 0.8863, 0.8588, 0.6941, 0.4706, 0.3647, 
0.3804, 0.3373, 0.3098, 0.3216, 0.3098, 0.3098, 0.2784, 0.2471, 0.3137, 
0.5020, 0.6941, 0.7804},
{0.3373, 0.3373, 0.3333, 0.3333, 0.3412, 0.3294, 0.3216, 0.3216, 0.3098, 
0.2941, 0.2941, 0.3882, 0.5490, 0.7098, 0.7843, 0.8078, 0.8627, 0.8431, 
0.6667, 0.4902, 0.3961, 0.3294, 0.3059, 0.2980, 0.2706, 0.4196, 0.6118, 
0.7216, 0.7843, 0.8157, 0.8902, 0.8863, 0.7176, 0.5333, 0.3804, 0.3647, 
0.3373, 0.3098, 0.3490, 0.3216, 0.3098, 0.2863, 0.2706, 0.3333, 0.5137, 
0.6824, 0.7647, 0.7725},
{0.3373, 0.3333, 0.3373, 0.3373, 0.3294, 0.3216, 0.3412, 0.3176, 0.3176, 
0.2980, 0.2863, 0.3922, 0.5529, 0.6863, 0.7804, 0.8118, 0.8627, 0.8392, 
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{0.3333, 0.3373, 0.3490, 0.3373, 0.3137, 0.3137, 0.2902, 0.2353, 0.2157, 
0.2275, 0.2549, 0.4196, 0.6196, 0.7333, 0.7725, 0.8000, 0.8157, 0.7137, 
0.4824, 0.3451, 0.2588, 0.2314, 0.2235, 0.2078, 0.2235, 0.2784, 0.4510, 
0.6392, 0.7569, 0.7804, 0.8863, 0.9412, 0.8549, 0.6314, 0.4549, 0.3804, 
0.3765, 0.3490, 0.3412, 0.3059, 0.3059, 0.3059, 0.2980, 0.2980, 0.3176, 
0.4588, 0.6549, 0.8196},
{0.3333, 0.3412, 0.3373, 0.3333, 0.3176, 0.3098, 0.2863, 0.2471, 0.2039, 
0.2235, 0.2706, 0.4235, 0.6196, 0.7412, 0.7686, 0.7961, 0.8157, 0.7137, 
0.4588, 0.3333, 0.2627, 0.2314, 0.2196, 0.2235, 0.2118, 0.3059, 0.4941, 
0.6627, 0.7529, 0.7882, 0.8941, 0.9373, 0.8314, 0.6118, 0.4431, 0.3882, 
0.3804, 0.3412, 0.3373, 0.3098, 0.3137, 0.3020, 0.3020, 0.2980, 0.3059, 
0.4667, 0.6863, 0.8039},
{0.3412, 0.3412, 0.3294, 0.3333, 0.3176, 0.3137, 0.3412, 0.3843, 0.4235, 
0.4941, 0.6196, 0.7412, 0.8000, 0.8118, 0.8353, 0.8353, 0.8353, 0.7255, 
0.5961, 0.5176, 0.4863, 0.4471, 0.4784, 0.5412, 0.5961, 0.7216, 0.8431, 
0.8902, 0.9373, 0.9608, 0.8863, 0.6706, 0.5059, 0.4118, 0.3490, 0.3373, 
0.3451, 0.3294, 0.2980, 0.2980, 0.3137, 0.3216, 0.3333, 0.3529, 0.3255, 
0.3333, 0.4431, 0.6196},
{0.3333, 0.3373, 0.3412, 0.3373, 0.3137, 0.3255, 0.3451, 0.3804, 0.4314, 
0.4980, 0.6196, 0.7529, 0.8039, 0.8118, 0.8118, 0.8392, 0.8157, 0.7020, 
0.5804, 0.5098, 0.4745, 0.4549, 0.4824, 0.5412, 0.6118, 0.7529, 0.8392, 
0.8902, 0.9608, 0.9608, 0.8549, 0.6392, 0.4745, 0.4078, 0.3529, 0.3294, 
0.3412, 0.3294, 0.3176, 0.2980, 0.3255, 0.3255, 0.3216, 0.3294, 0.3294, 
0.3255, 0.4588, 0.6353},
{0.3373, 0.3373, 0.3451, 0.3373, 0.3294, 0.3725, 0.4863, 0.6471, 0.7843, 
0.8824, 0.9490, 0.9725, 0.9725, 0.9725, 0.9725, 0.9765, 0.9765, 0.9765, 
0.9765, 0.9765, 0.9765, 0.9765, 0.9765, 0.9765, 0.9765, 0.9765, 0.9765, 
0.9059, 0.7843, 0.5373, 0.3961, 0.3451, 0.3098, 0.2980, 0.3098, 0.3216, 
0.2980, 0.2980, 0.2980, 0.3137, 0.3294, 0.3294, 0.3255, 0.3333, 0.3451, 
0.3333, 0.3098, 0.3529},
{0.3373, 0.3412, 0.3333, 0.3333, 0.3333, 0.3647, 0.4941, 0.6627, 0.8000, 
0.8941, 0.9529, 0.9725, 0.9725, 0.9725, 0.9765, 0.9725, 0.9765, 0.9765, 
0.9765, 0.9765, 0.9765, 0.9765, 0.9765, 0.9765, 0.9765, 0.9765, 0.9765, 
0.8941, 0.7490, 0.5294, 0.3725, 0.3373, 0.3098, 0.2980, 0.2980, 0.3098, 
0.2980, 0.2980, 0.2980, 0.3098, 0.3176, 0.3255, 0.3294, 0.3294, 0.3333, 
0.3294, 0.3098, 0.3373},
{0.3412, 0.3412, 0.3412, 0.3373, 0.3412, 0.3294, 0.3373, 0.3412, 0.3608, 
0.3569, 0.3373, 0.3412, 0.3373, 0.3686, 0.3686, 0.3686, 0.3765, 0.3961, 
0.3804, 0.3961, 0.4000, 0.3686, 0.3686, 0.3529, 0.3294, 0.2980, 0.2824, 
0.2392, 0.2392, 0.2706, 0.2902, 0.2863, 0.2980, 0.2980, 0.3176, 0.3294, 
0.3294, 0.3176, 0.3098, 0.3412, 0.3294, 0.3294, 0.3412, 0.3294, 0.3373, 
0.3412, 0.3608, 0.3373},
{0.3412, 0.3373, 0.3412, 0.3294, 0.3294, 0.3373, 0.3412, 0.3373, 0.3373, 
0.3412, 0.3373, 0.3373, 0.3412, 0.3608, 0.3647, 0.3686, 0.3686, 0.3686, 
0.3765, 0.4000, 0.3961, 0.3765, 0.3686, 0.3608, 0.3373, 0.2980, 0.2706, 
0.2471, 0.2549, 0.2706, 0.2824, 0.2980, 0.2902, 0.2980, 0.3294, 0.3294, 
0.3294, 0.3098, 0.3294, 0.3294, 0.3294, 0.3294, 0.3294, 0.3373, 0.3412, 
0.3608, 0.3373, 0.3373},
{0.3412, 0.3373, 0.3412, 0.3412, 0.3373, 0.3412, 0.3412, 0.3294, 0.3373, 
0.3412, 0.3294, 0.3098, 0.3098, 0.2980, 0.3059, 0.3098, 0.2980, 0.2784, 
0.2824, 0.2980, 0.2941, 0.2824, 0.2706, 0.2706, 0.2706, 0.2706, 0.2863, 
0.2980, 0.2980, 0.2980, 0.2980, 0.3098, 0.2980, 0.3294, 0.3098, 0.3216, 
0.3294, 0.3098, 0.3294, 0.3294, 0.3098, 0.3137, 0.3294, 0.3373, 0.3451, 
0.3294, 0.3412, 0.3412},
{0.3490, 0.3412, 0.3373, 0.3412, 0.3412, 0.3294, 0.3373, 0.3412, 0.3294, 
0.3373, 0.3412, 0.3294, 0.3059, 0.3098, 0.3098, 0.3059, 0.2824, 0.2824, 
0.2980, 0.2824, 0.2980, 0.2706, 0.2784, 0.2824, 0.2863, 0.2706, 0.2824, 
0.2863, 0.2980, 0.3098, 0.2980, 0.2980, 0.3098, 0.3294, 0.3176, 0.3098, 
0.3294, 0.3176, 0.3294, 0.3412, 0.3294, 0.3098, 0.3412, 0.3412, 0.3412, 
0.3412, 0.3451, 0.3412},
{0.3412, 0.3412, 0.3373, 0.3373, 0.3412, 0.3294, 0.3373, 0.3412, 0.3294, 
0.3373, 0.3412, 0.3294, 0.3373, 0.3412, 0.3294, 0.3294, 0.3098, 0.3098, 
0.2980, 0.2980, 0.2980, 0.2980, 0.2941, 0.2824, 0.2863, 0.2784, 0.2980, 
0.2980, 0.2980, 0.3098, 0.3294, 0.3176, 0.3098, 0.3294, 0.3294, 0.3373, 
0.3412, 0.3294, 0.3294, 0.3176, 0.3098, 0.3176, 0.3412, 0.3412, 0.3373, 
0.3412, 0.3412, 0.3373},
{0.3294, 0.3373, 0.3412, 0.3412, 0.3373, 0.3412, 0.3412, 0.3294, 0.3373, 
0.3412, 0.3294, 0.3373, 0.3412, 0.3294, 0.3294, 0.3098, 0.3176, 0.3059, 
0.3098, 0.2980, 0.2980, 0.2980, 0.2863, 0.2706, 0.2824, 0.2824, 0.2980, 
0.2980, 0.3098, 0.2980, 0.3294, 0.3098, 0.2980, 0.3294, 0.3412, 0.3294, 
0.3373, 0.3373, 0.3294, 0.3294, 0.3098, 0.3412, 0.3294, 0.3373, 0.3412, 
0.3412, 0.3373, 0.3490},
{0.3412, 0.3373, 0.3412, 0.3412, 0.3373, 0.3373, 0.3412, 0.3294, 0.3373, 
0.3412, 0.3294, 0.3373, 0.3412, 0.3176, 0.3294, 0.3294, 0.2980, 0.2980, 
0.3098, 0.2980, 0.2980, 0.2980, 0.2902, 0.2863, 0.2824, 0.2863, 0.2863, 
0.2824, 0.2980, 0.2863, 0.2980, 0.2980, 0.2980, 0.2980, 0.3098, 0.2980, 
0.3255, 0.3098, 0.3294, 0.3059, 0.3059, 0.3373, 0.3294, 0.3373, 0.3412, 
0.3373, 0.3373, 0.3490},
{0.3412, 0.3412, 0.3373, 0.3373, 0.3412, 0.3294, 0.3373, 0.3412, 0.3294, 
0.3373, 0.3412, 0.3294, 0.3294, 0.3098, 0.3294, 0.3294, 0.3059, 0.2980, 
0.2980, 0.2980, 0.2980, 0.2863, 0.2980, 0.2863, 0.2863, 0.2980, 0.2863, 
0.2902, 0.2980, 0.2980, 0.2980, 0.2980, 0.2980, 0.2980, 0.2980, 0.3059, 
0.3294, 0.3176, 0.3059, 0.3294, 0.3294, 0.3333, 0.3373, 0.3373, 0.3373, 
0.3373, 0.3412, 0.3373},
{0.3412, 0.3412, 0.3373, 0.3373, 0.3412, 0.3608, 0.3373, 0.3412, 0.3490, 
0.3373, 0.3412, 0.3294, 0.3294, 0.3294, 0.3294, 0.3294, 0.3098, 0.3098, 
0.2980, 0.2824, 0.2863, 0.2980, 0.2980, 0.2863, 0.2706, 0.2824, 0.3098, 
0.2980, 0.2980, 0.3098, 0.2980, 0.2980, 0.2980, 0.3020, 0.2980, 0.2980, 
0.3098, 0.3176, 0.3255, 0.3294, 0.3294, 0.3255, 0.3373, 0.3294, 0.3333, 
0.3373, 0.3412, 0.3373},
{0.3412, 0.3373, 0.3412, 0.3412, 0.3373, 0.3412, 0.3412, 0.3373, 0.3412, 
0.3412, 0.3294, 0.3294, 0.3294, 0.3176, 0.3294, 0.3294, 0.3176, 0.3059, 
0.2980, 0.2980, 0.2824, 0.2863, 0.2980, 0.2824, 0.2824, 0.2863, 0.2980, 
0.3098, 0.3098, 0.2980, 0.2980, 0.2980, 0.2980, 0.2980, 0.2980, 0.2980, 
0.2980, 0.3098, 0.2980, 0.3255, 0.3294, 0.3412, 0.3294, 0.3333, 0.3373, 
0.3373, 0.3373, 0.3412}}, 1, 32];

ListDensityPlot[bigR, Mesh->False]

How big is bigR?

Dimensions[bigR]

What are the largest and smallest values?

{Min[bigR], Max[bigR]}

The Histogram

How are its values distributed?

hist = Histogram[bigR, 0, 32, 32];

{Min[hist], Max[hist]}

ListPlot[hist, PlotJoined->True, PlotRange->{0,737},
		AxesLabel->{"  Grey Level", "Count"}]

Making a Binary Image

Make all values below 12 black and those 12 and above white.

binary = Map[If[#<12, 0, 1]&, bigR, {2}];

ListDensityPlot[binary, Mesh->False]

Finding the Edges

Find the edges

s = Sobel[bigR];

ListDensityPlot[s, Mesh->False]

What is the strongest and weakest edge?

{Min[s], Max[s]}

Find a histogram of the edge strengths

hist2 = Histogram2[s];

ListPlot[hist2, PlotJoined->True,
		AxesLabel->{"Edge Strength", "Count"}]

Make a binary image.

Map[If[#<45, 0, 1]&, s, {2}];

ListDensityPlot[%, Mesh->False]