Assignment 4
Computational Vision
U. Minn. Psy 5036
Daniel Kersten

Off[General::spell1];
<< 
      Graphics`
<< 
      Graphics`Graphics3D`
<< Geometry`Rotations`

Themes

Modeling image variation: Scene-based vs. image-based

Geometric vs. photometric variation

Different generative models make different predictions for recognition inference

Humans easily recognize familiar 3D objects from unfamiliar views. Humans can also recognize a familiar object under an unfamiliar illumination. How is this done? There are many possible models, too many to experimentally test them all. However, thinking about how to model image variation--i.e. the generative process, suggests some basic hypotheses to test.  One can model viewpoint and illumination change  using scene-based models of image formation--i.e. the visual system in effect "knows" the 3D structure of the object and/or illumination, and uses this knowledge to allow for variation. (Exactly how this is done is another matter, requiring theories, such as Bayes, for how to solve the inverse problem). Alternatively, image variation can be modeled using image-based knowledge. Here one has 2D knowledge of a few instances, and then interpolates between them to allow for variation (Ullman & Basri, 1991). Alternatively, one has 2D operations that are not perfect, but still reasonable approximations (Liu & Kersten, 1998).
In the first two exercises, you are going to see how to model viewpoint change using 3D and 2D manipulations. You will be modeling geometrical variation.
In the second two exercises, you will model illumination change using 3D and 2D manipulations. You will be modeling photometric variation.

3D Scene-based modeling of viewpoint change

Generate an n-segmented 3D wire object--"bent paper clip"

s = Table[{Random[]-0.5,Random[]-0.5,Random[]-0.5},{6}];

s

Use ScatterPlot3D[ ] to make perspective plot of the paper clip

g2 = 
        ScatterPlot3D[s, AxesLabel -> {"x", "y", "z"}, 
          ViewPoint -> {0, 0, 3}, PlotJoined -> True, 
          PlotStyle -> {PointSize[1], {RGBColor[1, 0, 0]}}, 
          AspectRatio -> 1];

Make an orthographic projection of paper clip by setting the z-coordinate to 0, and using ListPlot[ ]

orthographic[x_]:= Drop[#,-1]&/@x

ListPlot[orthographic[s],PlotJoined->True,PlotRange->{{-1,1},{-1,1}}];

Define a rotation matrix to apply to each vertex of the paper clip

RotationMatrix3D[ψ, θ, ϕ] // MatrixForm

For simplicity, let the first two euler angles equal each other and set the third to zero

RotationMatrix3D[θ,θ,0]

Rotate the paper clip by θ = Pi/8, and then make an orthographic projection again using ListPlot[ ]

ListPlot[orthographic[Dot[RotationMatrix3D[Pi/16,Pi/8,0],#]&/@s],PlotJoined->True,PlotRange->{{-1,1},{-1,1}}];

Now make a series of plots from  θ = Pi/8 to 3*Pi/4 in steps of Pi/16. (i.e. iterate {θ,Pi/4,3*Pi/4,Pi/16}).

Table[ListPlot[orthographic[Dot[RotationMatrix3D[θ,θ,0],#]&/@s],PlotJoined->True,PlotRange->{{-1,1},{-1,1}}],{θ,Pi/4,3*Pi/4,Pi/16}];

2D Image-based modeling of viewpoint change

Make a list of the first view of the above animation, i.e.  θ = Pi/4. Call it firstview.

firstview = orthographic[Dot[RotationMatrix3D[Pi/4,Pi/4,0],#]&/@s]

Make a list of the last view of the above animation, i.e.  θ = 3*Pi/4. Call it lastview.

lastview = orthographic[Dot[RotationMatrix3D[3*Pi/4,3*Pi/4,0],#]&/@s];

Define a function of t that interpolates between the 2D vertices of firstview (t=0) and lastview (t=1)

interview[t_]:= t*firstview + (1-t)*lastview;

Make an animation using ListPlot[], for t=0 to 1, in steps of 0.1 (i.e. iterate {t,0,1,.1}).

Table[ListPlot[interview[t],PlotJoined->True, PlotRange->{{-1,1},{-1,1}}],{t,0,1,.1}];

3D scene-based modeling of illumination change

In this section, we will make use of Mathematica's in-built 3D rendering model as used in ListPlot3D.

Range data defines surface list

Range data to define rface list -- BIG 64x64 file. 
Just initialize this cell--don't bother opening cell (from: http://sampl.eng.ohio-state.edu/)
If you want to read in a different file, use the Import[ ] function in the Appendix

rface  =  {{2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 3, 7, 54, 89, 99, 110, 
            121, 128, 136, 143, 149, 156, 164, 171, 177, 183, 187, 191, 194, 
            194, 197, 198, 198, 197, 196, 194, 192, 188, 184, 178, 172, 165, 
            157, 152, 145, 139, 132, 126, 118, 112, 103, 94, 81, 62, 7, 2, 2, 
            2, 2, 2, 3, 2, 4, 9}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 57, 
            98, 109, 122, 133, 141, 150, 158, 165, 172, 180, 188, 194, 200, 
            205, 208, 211, 213, 215, 216, 216, 216, 215, 214, 210, 206, 202, 
            198, 192, 183, 175, 168, 160, 152, 144, 138, 128, 120, 111, 101, 
            86, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 7, 67, 108, 118, 128, 141, 149, 157, 165, 172, 179, 186, 
            194, 200, 205, 211, 214, 217, 220, 220, 219, 220, 220, 220, 219, 
            216, 212, 209, 205, 199, 191, 183, 174, 166, 158, 150, 141, 132, 
            125, 114, 103, 90, 45, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 
            0, 0, 0, 0, 0, 1, 0, 1, 3, 49, 97, 120, 140, 150, 158, 165, 172, 
            180, 187, 194, 201, 208, 213, 220, 222, 224, 226, 226, 226, 226, 
            226, 226, 225, 224, 222, 218, 214, 208, 201, 192, 182, 174, 166, 
            157, 148, 139, 131, 120, 109, 95, 42, 2, 0, 0, 0, 0, 0, 0, 0, 0, 
            0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 60, 139, 150, 158, 
            165, 172, 179, 187, 194, 200, 207, 215, 220, 226, 229, 231, 232, 
            232, 231, 229, 230, 230, 230, 230, 229, 225, 222, 217, 210, 200, 
            191, 182, 174, 164, 157, 147, 137, 127, 116, 103, 24, 0, 0, 0, 0, 
            0, 1, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 5, 86, 
            159, 157, 165, 172, 178, 185, 192, 199, 206, 213, 220, 225, 230, 
            233, 235, 235, 235, 234, 233, 233, 234, 235, 235, 233, 231, 228, 
            223, 217, 207, 198, 189, 181, 171, 165, 155, 145, 134, 122, 110, 
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            0, 0, 59, 148, 157, 165, 172, 178, 184, 190, 196, 203, 210, 218, 
            223, 228, 233, 236, 236, 236, 237, 237, 236, 236, 237, 238, 238, 
            237, 235, 232, 227, 223, 215, 204, 195, 188, 179, 171, 163, 154, 
            144, 131, 118, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 
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            185, 177, 171, 162, 151, 140, 127, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 117, 159, 160, 167, 175, 
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            241, 240, 239, 237, 236, 239, 240, 241, 240, 238, 235, 230, 226, 
            219, 212, 204, 196, 189, 182, 177, 168, 160, 150, 139, 24, 0, 0, 
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            155, 164, 172, 177, 183, 189, 193, 199, 205, 210, 215, 219, 226, 
            230, 234, 236, 239, 240, 240, 240, 238, 237, 240, 242, 241, 240, 
            238, 234, 230, 226, 220, 213, 206, 199, 192, 186, 179, 173, 166, 
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            0, 0, 0, 21, 141, 153, 160, 167, 173, 180, 186, 191, 196, 200, 
            205, 210, 215, 220, 224, 229, 233, 236, 238, 240, 240, 239, 237, 
            236, 238, 241, 241, 240, 237, 233, 229, 225, 220, 213, 207, 201, 
            195, 189, 183, 176, 169, 162, 153, 117, 11, 0, 0, 0, 0, 0, 0, 0, 
            0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 87, 146, 155, 164, 170, 178, 
            183, 188, 193, 197, 201, 206, 210, 215, 219, 223, 226, 230, 234, 
            237, 238, 238, 238, 235, 237, 238, 239, 239, 236, 232, 230, 228, 
            223, 218, 213, 207, 202, 197, 192, 185, 178, 173, 166, 156, 148, 
            57, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 14, 132, 
            151, 159, 165, 170, 178, 184, 189, 193, 198, 201, 206, 210, 214, 
            218, 223, 225, 227, 229, 232, 234, 235, 236, 236, 237, 236, 235, 
            233, 230, 228, 227, 224, 219, 215, 211, 207, 202, 198, 193, 188, 
            182, 175, 169, 160, 151, 114, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 
            0, 0, 0, 0, 0, 0, 43, 135, 154, 161, 167, 173, 179, 185, 189, 
            194, 199, 202, 205, 208, 213, 217, 221, 224, 226, 225, 227, 230, 
            233, 233, 235, 233, 231, 229, 228, 227, 226, 224, 221, 217, 214, 
            211, 208, 203, 199, 195, 190, 185, 177, 171, 162, 156, 138, 28, 
            0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 94, 144, 154, 
            163, 169, 175, 181, 187, 191, 195, 198, 201, 205, 208, 212, 215, 
            219, 222, 225, 226, 228, 229, 230, 232, 231, 232, 231, 230, 228, 
            227, 225, 223, 220, 216, 213, 210, 207, 202, 199, 193, 190, 185, 
            178, 171, 165, 158, 145, 81, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 
            0, 0, 0, 0, 0, 120, 150, 156, 165, 171, 175, 180, 187, 192, 195, 
            198, 200, 203, 205, 209, 213, 218, 221, 225, 228, 230, 230, 231, 
            231, 231, 233, 231, 231, 230, 228, 224, 221, 218, 214, 212, 208, 
            206, 202, 200, 195, 191, 186, 179, 173, 166, 160, 153, 112, 0, 0, 
            0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 17, 121, 152, 159, 165, 
            171, 175, 180, 184, 191, 195, 198, 200, 201, 204, 207, 211, 216, 
            222, 226, 229, 231, 231, 232, 232, 232, 232, 231, 231, 230, 228, 
            224, 221, 216, 212, 208, 207, 204, 202, 199, 196, 192, 186, 179, 
            174, 167, 162, 154, 127, 17, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 
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            202, 200, 198, 197, 190, 185, 179, 174, 167, 162, 155, 133, 46, 
            0, 1, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 7, 28, 47, 94, 134, 150, 160, 
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            212, 218, 223, 226, 229, 231, 232, 232, 232, 231, 230, 230, 228, 
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            179, 174, 170, 164, 155, 137, 55, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 2, 
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            195, 197, 198, 200, 200, 200, 204, 211, 218, 223, 226, 229, 231, 
            232, 232, 233, 232, 230, 229, 228, 227, 222, 217, 209, 202, 201, 
            200, 201, 200, 199, 195, 189, 184, 180, 175, 170, 163, 155, 143, 
            97, 10, 6, 0, 0, 0, 1, 0}, {0, 1, 21, 43, 54, 63, 70, 102, 133, 
            150, 161, 168, 174, 178, 183, 186, 189, 194, 196, 198, 201, 203, 
            205, 209, 212, 217, 223, 227, 230, 232, 234, 233, 233, 234, 234, 
            232, 229, 227, 221, 215, 209, 204, 204, 202, 201, 200, 199, 195, 
            190, 182, 177, 174, 170, 164, 154, 141, 106, 64, 50, 21, 2, 0, 0, 
            0}, {1, 14, 35, 46, 48, 55, 68, 105, 133, 151, 161, 168, 175, 
            179, 184, 187, 190, 193, 195, 198, 201, 202, 205, 210, 216, 219, 
            222, 226, 228, 229, 230, 230, 229, 230, 230, 230, 227, 224, 219, 
            214, 211, 207, 205, 203, 202, 200, 198, 193, 188, 182, 179, 175, 
            170, 164, 154, 139, 107, 67, 65, 58, 30, 5, 1, 0}, {4, 22, 29, 
            38, 47, 49, 56, 102, 132, 149, 161, 169, 176, 180, 184, 188, 189, 
            191, 193, 196, 199, 202, 206, 211, 217, 222, 226, 227, 228, 229, 
            230, 232, 230, 229, 228, 227, 226, 223, 219, 216, 213, 209, 205, 
            203, 202, 200, 197, 192, 187, 183, 179, 176, 170, 163, 153, 137, 
            107, 75, 71, 61, 50, 34, 1, 0}, {12, 21, 18, 20, 27, 37, 49, 99, 
            130, 146, 162, 171, 177, 180, 184, 188, 190, 191, 192, 193, 196, 
            200, 206, 211, 216, 221, 227, 230, 231, 232, 232, 231, 232, 232, 
            231, 230, 228, 226, 222, 218, 213, 210, 204, 202, 199, 198, 196, 
            192, 187, 184, 179, 176, 171, 164, 153, 134, 107, 73, 60, 53, 53, 
            50, 21, 1}, {15, 14, 14, 13, 13, 16, 26, 95, 131, 146, 161, 169, 
            178, 182, 186, 190, 192, 193, 193, 193, 193, 195, 200, 208, 214, 
            219, 223, 227, 229, 230, 228, 226, 228, 230, 230, 231, 228, 225, 
            221, 217, 212, 206, 202, 199, 198, 197, 195, 190, 187, 184, 180, 
            177, 171, 164, 151, 132, 104, 61, 51, 56, 53, 47, 35, 7}, {13, 
            11, 13, 16, 15, 10, 22, 94, 129, 143, 160, 170, 177, 182, 188, 
            190, 192, 193, 194, 194, 193, 192, 194, 200, 209, 215, 220, 224, 
            226, 226, 225, 225, 225, 227, 227, 227, 225, 222, 217, 212, 205, 
            199, 197, 196, 196, 195, 194, 191, 188, 185, 181, 178, 172, 164, 
            149, 128, 101, 59, 54, 46, 37, 35, 32, 15}, {12, 10, 14, 15, 14, 
            12, 30, 96, 126, 143, 159, 168, 177, 182, 188, 191, 193, 194, 
            195, 196, 196, 194, 192, 195, 201, 209, 217, 221, 225, 225, 225, 
            224, 224, 225, 224, 224, 221, 217, 212, 205, 197, 195, 195, 196, 
            197, 195, 194, 192, 190, 187, 182, 179, 171, 162, 147, 127, 91, 
            32, 29, 26, 27, 30, 28, 20}, {11, 10, 14, 15, 16, 16, 36, 97, 
            126, 144, 157, 166, 177, 182, 186, 192, 193, 194, 196, 196, 197, 
            196, 194, 194, 199, 208, 214, 217, 223, 224, 227, 228, 226, 225, 
            224, 221, 216, 211, 204, 198, 196, 195, 195, 196, 197, 196, 195, 
            192, 189, 187, 182, 178, 170, 160, 143, 124, 86, 21, 21, 24, 28, 
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            215, 216, 215, 222, 228, 238, 242, 235, 226, 221, 214, 212, 212, 
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            177, 169, 160, 140, 121, 84, 21, 19, 24, 26, 23, 20, 18}, {6, 2, 
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            236, 243, 243, 241, 233, 224, 220, 220, 219, 206, 197, 198, 198, 
            198, 198, 198, 197, 195, 192, 190, 187, 183, 174, 165, 156, 137, 
            119, 76, 22, 22, 24, 25, 20, 18, 20}, {5, 1, 4, 12, 24, 22, 45, 
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            197, 196, 197, 195, 209, 226, 233, 236, 241, 243, 244, 244, 244, 
            242, 233, 232, 229, 223, 207, 198, 197, 198, 198, 198, 197, 195, 
            194, 192, 189, 186, 181, 172, 162, 151, 134, 117, 70, 25, 24, 24, 
            26, 18, 15, 16}, {6, 1, 3, 10, 18, 2, 29, 103, 129, 140, 149, 
            157, 165, 172, 179, 185, 190, 194, 195, 196, 197, 196, 198, 197, 
            202, 224, 236, 240, 243, 248, 248, 249, 249, 246, 239, 235, 231, 
            225, 202, 196, 198, 198, 197, 198, 197, 195, 194, 191, 187, 184, 
            176, 168, 159, 147, 132, 115, 80, 36, 29, 26, 26, 12, 10, 
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            244, 249, 251, 251, 252, 252, 249, 244, 240, 233, 213, 199, 199, 
            199, 199, 198, 197, 195, 193, 192, 189, 185, 179, 171, 164, 156, 
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            188, 189, 192, 194, 195, 197, 199, 204, 221, 241, 250, 252, 254, 
            254, 254, 252, 246, 240, 216, 201, 199, 200, 199, 198, 194, 194, 
            193, 190, 188, 184, 180, 174, 167, 161, 154, 144, 130, 109, 36, 
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            226, 206, 201, 199, 196, 194, 194, 192, 191, 189, 186, 184, 179, 
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            174, 175, 173, 173, 169, 166, 160, 156, 147, 137, 129, 110, 39, 
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            144, 148, 151, 156, 161, 167, 171, 176, 179, 183, 184, 184, 183, 
            181, 178, 175, 176, 191, 220, 232, 236, 234, 232, 223, 203, 184, 
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            162, 157, 152, 145, 137, 128, 109, 40, 0, 8, 30, 27, 20, 12, 
            1}, {0, 1, 0, 0, 0, 0, 70, 121, 129, 138, 146, 151, 156, 160, 
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            158, 148, 136, 128, 113, 55, 0, 1, 0, 0, 1, 0, 0, 1}, {0, 1, 0, 
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            144, 153, 162, 168, 175, 183, 186, 189, 189, 189, 192, 195, 194, 
            194, 195, 197, 198, 200, 200, 204, 204, 203, 202, 200, 198, 197, 
            197, 197, 198, 198, 197, 197, 194, 192, 189, 187, 184, 179, 172, 
            165, 155, 144, 133, 124, 96, 2, 0, 0, 1, 0, 0, 0, 0, 1}, {0, 0, 
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            203, 201, 203, 202, 201, 199, 198, 196, 196, 196, 196, 198, 197, 
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            135, 144, 151, 159, 166, 173, 177, 181, 185, 188, 190, 192, 193, 
            195, 196, 198, 199, 202, 202, 202, 203, 204, 202, 202, 201, 199, 
            198, 197, 195, 194, 193, 193, 191, 190, 189, 187, 184, 180, 174, 
            166, 158, 149, 139, 128, 115, 98, 41, 0, 0, 0, 0, 0, 0, 1, 
            0}, {0, 0, 0, 0, 0, 36, 91, 109, 122, 133, 142, 151, 158, 164, 
            171, 176, 180, 184, 188, 190, 193, 196, 199, 198, 200, 201, 202, 
            203, 205, 203, 204, 204, 202, 202, 201, 199, 199, 198, 196, 194, 
            192, 189, 188, 186, 184, 180, 176, 170, 163, 155, 147, 137, 126, 
            113, 97, 43, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 38, 93, 
            106, 119, 131, 141, 149, 156, 163, 168, 173, 178, 182, 186, 189, 
            193, 196, 199, 200, 201, 203, 203, 204, 205, 204, 203, 203, 204, 
            203, 203, 201, 201, 200, 198, 197, 193, 191, 188, 185, 181, 177, 
            173, 167, 159, 152, 144, 135, 125, 112, 97, 42, 0, 0, 0, 0, 0, 0, 
            0, 0}, {0, 0, 0, 0, 1, 50, 98, 103, 116, 129, 141, 149, 155, 162, 
            166, 172, 176, 181, 185, 188, 192, 196, 198, 200, 201, 203, 204, 
            204, 204, 204, 204, 204, 204, 204, 204, 202, 201, 199, 198, 197, 
            194, 191, 187, 183, 178, 174, 170, 163, 156, 150, 142, 133, 121, 
            111, 96, 42, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 1, 0, 34, 86, 
            101, 113, 126, 138, 147, 154, 160, 164, 170, 174, 179, 183, 186, 
            191, 195, 196, 199, 201, 203, 204, 204, 203, 203, 202, 202, 203, 
            203, 202, 202, 201, 201, 197, 195, 193, 189, 185, 180, 176, 173, 
            168, 161, 155, 148, 140, 129, 120, 109, 95, 41, 0, 0, 0, 0, 0, 0, 
            0, 0}, {0, 0, 0, 0, 0, 17, 74, 99, 110, 123, 136, 145, 153, 160, 
            163, 169, 173, 178, 181, 184, 189, 193, 195, 198, 199, 200, 202, 
            202, 201, 201, 200, 200, 201, 202, 201, 202, 201, 199, 196, 194, 
            191, 186, 182, 179, 175, 171, 165, 159, 153, 147, 138, 128, 118, 
            105, 93, 39, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 20, 72, 94, 
            105, 120, 133, 142, 150, 158, 162, 167, 172, 177, 180, 183, 187, 
            190, 194, 196, 198, 198, 199, 199, 199, 199, 199, 198, 200, 200, 
            200, 200, 200, 197, 195, 192, 188, 183, 179, 176, 171, 167, 162, 
            157, 150, 144, 137, 125, 113, 104, 90, 41, 0, 0, 0, 0, 0, 0, 0, 
            0}, {0, 0, 0, 1, 0, 19, 71, 88, 101, 118, 131, 140, 148, 156, 
            162, 167, 171, 176, 178, 181, 185, 188, 192, 193, 196, 195, 196, 
            195, 195, 195, 195, 194, 196, 196, 196, 195, 195, 193, 191, 188, 
            184, 180, 177, 174, 169, 165, 160, 154, 148, 140, 132, 121, 110, 
            99, 82, 11, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 9, 63, 84, 
            94, 113, 128, 137, 146, 155, 160, 165, 170, 174, 176, 179, 183, 
            186, 189, 190, 193, 193, 193, 193, 193, 193, 193, 192, 192, 192, 
            193, 192, 190, 189, 187, 185, 181, 179, 175, 172, 168, 164, 159, 
            152, 145, 138, 128, 118, 103, 95, 77, 2, 0, 0, 0, 0, 0, 0, 0, 
            0}, {0, 0, 0, 0, 0, 0, 48, 82, 89, 109, 124, 135, 145, 153, 159, 
            165, 169, 174, 177, 178, 182, 184, 186, 188, 189, 190, 190, 190, 
            191, 191, 191, 190, 190, 189, 189, 189, 188, 188, 184, 181, 179, 
            176, 172, 169, 165, 161, 157, 150, 143, 135, 124, 112, 99, 89, 
            39, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 21, 69, 85, 
            102, 119, 133, 141, 150, 158, 163, 169, 171, 175, 178, 179, 182, 
            183, 186, 187, 187, 188, 188, 189, 189, 189, 189, 188, 187, 187, 
            187, 186, 185, 183, 180, 178, 175, 170, 166, 163, 159, 154, 148, 
            140, 131, 119, 105, 92, 85, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 
            0, 0, 0, 0, 7, 56, 80, 98, 115, 126, 140, 145, 156, 162, 166, 
            170, 174, 176, 178, 181, 182, 183, 185, 187, 187, 186, 186, 187, 
            187, 187, 188, 187, 186, 185, 183, 182, 181, 179, 176, 172, 168, 
            165, 161, 156, 151, 144, 136, 127, 112, 98, 87, 66, 6, 0, 0, 0, 
            0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 36, 75, 91, 109, 125, 
            136, 144, 150, 159, 164, 169, 172, 175, 177, 180, 182, 182, 184, 
            184, 185, 186, 186, 186, 186, 186, 185, 185, 184, 184, 182, 181, 
            179, 177, 174, 170, 167, 164, 160, 154, 148, 141, 131, 120, 107, 
            91, 76, 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 
            12, 67, 88, 104, 119, 132, 142, 149, 155, 162, 167, 170, 173, 
            176, 179, 181, 182, 183, 183, 183, 185, 186, 185, 185, 186, 183, 
            183, 182, 182, 181, 180, 178, 176, 173, 169, 166, 163, 158, 152, 
            145, 137, 128, 116, 100, 85, 60, 5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 
            0}, {0, 1, 0, 0, 1, 0, 1, 0, 42, 79, 98, 114, 128, 139, 146, 153, 
            159, 164, 167, 171, 174, 177, 179, 180, 181, 183, 183, 183, 183, 
            183, 183, 183, 182, 182, 181, 180, 179, 178, 176, 174, 170, 168, 
            165, 160, 155, 149, 141, 132, 121, 109, 90, 77, 25, 0, 0, 0, 0, 
            0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 10, 70, 91, 106, 
            123, 135, 142, 149, 156, 161, 164, 168, 172, 175, 177, 179, 179, 
            182, 182, 182, 181, 182, 182, 182, 181, 180, 180, 178, 178, 176, 
            174, 172, 169, 166, 161, 156, 151, 144, 136, 126, 114, 100, 86, 
            46, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0, 
            0, 28, 81, 99, 116, 129, 137, 146, 153, 159, 162, 167, 171, 174, 
            177, 179, 179, 181, 181, 182, 182, 183, 182, 183, 182, 181, 180, 
            178, 178, 176, 174, 172, 169, 164, 158, 153, 147, 140, 131, 122, 
            110, 92, 60, 12, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {2, 2, 3, 
            2, 2, 2, 2, 2, 2, 6, 61, 87, 103, 116, 126, 134, 141, 146, 151, 
            156, 160, 162, 164, 167, 168, 169, 170, 171, 171, 173, 172, 171, 
            170, 170, 169, 167, 166, 164, 161, 159, 155, 151, 146, 142, 136, 
            127, 118, 111, 97, 75, 26, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 
            2}};

Intensity in a DensityPlot is proportional to the z (depth) from the camera

size = Dimensions[rface][[1]];  
    hsize = size/2;
ListDensityPlot[rface, Mesh -> False];

(Range data from: http://sampl.eng.ohio-state.edu/)

ListPlot3D[rface,PlotRange->{0,255}];

Define ShadedListPlot3D[ ]

ShadedListPlot3D[list_,ref_,illum_] := ListPlot3D[rface,PlotRange->{0,255},Mesh->False,
  LightSources->{{illum,RGBColor[ref,ref,ref]}},ViewPoint->{0,0,10},
    AspectRatio->1,Ticks->False,Axes->False];

theta = N[Pi/4];
s={Cos[theta],1,Sin[theta]};
ref = 0.9;
Table[ShadedListPlot3D[rface,ref,{Cos[theta],1,Sin[theta]}],{theta,Pi/4,3*Pi/4,Pi/8}];

2D image-based modeling of illumination change

leftillumface

leftillumface  = {{123, 107, 108, 108, 108, 108, 108, 108, 108, 108, 
            109, 125, 135, 135, 124, 127, 123, 122, 122, 120, 120, 122, 126, 
            122, 122, 123, 123, 120, 120, 119, 118, 120, 119, 118, 117, 114, 
            112, 111, 112, 110, 107, 105, 105, 106, 105, 107, 107, 110, 111, 
            113, 110, 111, 106, 88, 93, 111, 108, 108, 108, 108, 109, 107, 
            110, 111}, {130, 114, 116, 116, 116, 116, 116, 116, 116, 117, 
            116, 141, 153, 128, 118, 113, 106, 107, 109, 109, 108, 109, 109, 
            108, 106, 106, 103, 100, 103, 103, 101, 102, 103, 103, 102, 100, 
            97, 93, 91, 91, 89, 87, 86, 87, 91, 90, 90, 92, 94, 94, 90, 92, 
            84, 42, 80, 121, 116, 116, 116, 116, 115, 117, 117, 104}, {130, 
            114, 115, 115, 115, 115, 115, 115, 114, 114, 114, 144, 176, 180, 
            139, 106, 108, 109, 110, 111, 110, 111, 110, 111, 108, 110, 109, 
            105, 105, 105, 104, 105, 108, 109, 108, 106, 104, 100, 98, 98, 
            93, 90, 87, 88, 90, 90, 90, 90, 92, 92, 89, 91, 81, 47, 87, 117, 
            115, 114, 115, 116, 114, 115, 117, 106}, {130, 113, 115, 115, 
            115, 115, 115, 116, 116, 113, 112, 134, 184, 193, 114, 103, 111, 
            111, 112, 113, 112, 112, 112, 113, 110, 112, 112, 110, 109, 110, 
            110, 108, 108, 110, 109, 107, 106, 104, 102, 100, 97, 95, 88, 90, 
            90, 92, 90, 91, 88, 89, 89, 89, 78, 55, 105, 117, 115, 115, 114, 
            114, 113, 113, 115, 106}, {130, 113, 115, 115, 115, 115, 115, 
            115, 114, 115, 116, 115, 139, 132, 99, 109, 110, 111, 112, 114, 
            115, 114, 115, 113, 114, 114, 113, 112, 112, 113, 112, 109, 109, 
            110, 111, 111, 109, 106, 103, 102, 100, 98, 90, 90, 92, 94, 90, 
            93, 91, 88, 86, 87, 75, 51, 110, 115, 114, 115, 115, 116, 115, 
            115, 116, 106}, {130, 113, 115, 115, 115, 115, 115, 116, 115, 
            115, 115, 122, 90, 77, 114, 115, 113, 113, 114, 115, 117, 116, 
            117, 115, 114, 117, 116, 114, 112, 111, 111, 111, 110, 112, 112, 
            112, 110, 109, 107, 105, 104, 103, 98, 91, 94, 95, 93, 93, 93, 
            88, 86, 85, 72, 49, 107, 116, 115, 115, 116, 117, 116, 115, 116, 
            106}, {130, 113, 115, 115, 115, 115, 115, 116, 115, 114, 117, 
            103, 65, 109, 115, 114, 115, 114, 115, 115, 116, 118, 119, 119, 
            116, 117, 117, 116, 114, 112, 111, 112, 114, 116, 116, 113, 111, 
            111, 110, 108, 107, 107, 105, 98, 98, 98, 99, 95, 95, 91, 90, 87, 
            72, 44, 105, 117, 115, 116, 115, 115, 115, 116, 116, 105}, {130, 
            113, 115, 115, 115, 115, 114, 116, 115, 113, 126, 85, 95, 118, 
            115, 115, 116, 116, 118, 118, 117, 120, 120, 122, 119, 118, 116, 
            118, 117, 115, 113, 112, 112, 116, 116, 114, 111, 111, 111, 111, 
            109, 110, 107, 103, 101, 100, 100, 100, 102, 97, 93, 87, 70, 47, 
            107, 117, 115, 115, 115, 115, 115, 115, 116, 106}, {130, 113, 
            116, 115, 115, 115, 115, 116, 115, 119, 102, 91, 118, 117, 115, 
            117, 116, 116, 118, 120, 120, 120, 120, 121, 121, 121, 119, 117, 
            118, 117, 114, 113, 112, 116, 118, 115, 112, 112, 111, 112, 111, 
            111, 108, 104, 105, 103, 102, 102, 102, 101, 97, 94, 80, 24, 83, 
            120, 114, 116, 115, 115, 115, 114, 116, 106}, {130, 113, 115, 
            115, 115, 115, 115, 116, 115, 120, 61, 107, 118, 120, 117, 116, 
            116, 116, 116, 119, 120, 120, 118, 120, 123, 123, 122, 119, 118, 
            118, 117, 115, 114, 117, 119, 118, 115, 113, 115, 115, 114, 113, 
            111, 108, 107, 106, 104, 104, 101, 101, 101, 100, 89, 0, 51, 121, 
            116, 115, 115, 115, 115, 116, 115, 106}, {130, 113, 115, 114, 
            115, 115, 115, 115, 123, 110, 111, 119, 116, 117, 115, 116, 117, 
            117, 117, 119, 119, 120, 120, 121, 119, 121, 124, 124, 122, 121, 
            119, 116, 115, 115, 116, 119, 119, 119, 120, 119, 116, 114, 114, 
            111, 108, 108, 106, 105, 102, 103, 103, 100, 95, 50, 24, 85, 118, 
            115, 115, 115, 115, 115, 116, 106}, {130, 113, 115, 115, 114, 
            116, 115, 114, 125, 83, 112, 119, 121, 123, 120, 119, 119, 119, 
            119, 120, 119, 120, 121, 121, 118, 119, 122, 125, 125, 123, 121, 
            117, 114, 115, 117, 120, 122, 121, 119, 119, 117, 115, 115, 114, 
            110, 109, 109, 108, 104, 101, 102, 102, 101, 91, 0, 57, 125, 115, 
            115, 114, 115, 114, 116, 106}, {130, 113, 115, 115, 115, 115, 
            115, 120, 126, 125, 119, 118, 115, 120, 120, 118, 119, 118, 116, 
            119, 121, 122, 121, 122, 120, 119, 119, 121, 124, 123, 121, 118, 
            119, 119, 119, 120, 121, 119, 117, 118, 116, 114, 113, 112, 110, 
            107, 108, 107, 105, 104, 101, 104, 100, 99, 44, 48, 110, 117, 
            115, 116, 116, 115, 116, 106}, {130, 113, 115, 115, 115, 114, 
            114, 128, 93, 116, 123, 118, 119, 117, 117, 118, 117, 119, 119, 
            120, 119, 120, 120, 122, 121, 121, 117, 115, 116, 118, 120, 120, 
            119, 117, 113, 113, 113, 113, 115, 114, 113, 112, 112, 112, 114, 
            110, 112, 111, 111, 109, 105, 105, 104, 103, 80, 14, 72, 121, 
            115, 115, 115, 115, 116, 106}, {130, 113, 115, 115, 115, 114, 
            113, 131, 105, 116, 121, 118, 118, 121, 123, 119, 118, 118, 119, 
            121, 121, 124, 124, 122, 119, 121, 118, 115, 113, 113, 115, 115, 
            116, 114, 112, 112, 110, 110, 113, 114, 113, 113, 114, 114, 114, 
            110, 111, 110, 108, 107, 105, 103, 104, 105, 91, 0, 54, 124, 115, 
            115, 115, 115, 117, 106}, {130, 113, 116, 115, 115, 115, 113, 
            128, 138, 120, 120, 121, 119, 119, 124, 123, 119, 118, 117, 118, 
            120, 121, 121, 124, 121, 120, 117, 116, 114, 113, 114, 113, 114, 
            115, 115, 115, 113, 111, 110, 111, 111, 113, 116, 116, 115, 113, 
            112, 111, 108, 107, 105, 109, 103, 107, 100, 41, 53, 116, 116, 
            115, 115, 115, 116, 106}, {130, 113, 115, 115, 117, 116, 124, 
            127, 137, 122, 120, 118, 116, 117, 116, 118, 118, 119, 119, 119, 
            121, 123, 127, 127, 125, 124, 122, 118, 118, 117, 117, 114, 115, 
            115, 113, 113, 114, 113, 112, 113, 110, 112, 115, 117, 116, 116, 
            114, 113, 108, 112, 108, 109, 106, 108, 103, 58, 28, 89, 118, 
            114, 115, 114, 115, 107}, {130, 113, 115, 117, 113, 99, 89, 95, 
            128, 125, 123, 120, 119, 120, 119, 120, 119, 117, 116, 116, 118, 
            122, 129, 129, 125, 125, 124, 120, 117, 115, 116, 115, 115, 115, 
            116, 116, 114, 113, 113, 113, 112, 113, 118, 119, 116, 114, 112, 
            111, 106, 106, 108, 109, 106, 106, 104, 77, 0, 72, 121, 115, 116, 
            114, 116, 105}, {130, 112, 114, 101, 83, 78, 88, 106, 129, 127, 
            122, 120, 121, 122, 120, 121, 119, 117, 116, 116, 115, 116, 122, 
            127, 123, 124, 120, 118, 117, 117, 115, 116, 114, 112, 115, 116, 
            113, 110, 110, 112, 111, 112, 118, 118, 117, 113, 112, 112, 109, 
            109, 108, 107, 106, 107, 105, 83, 0, 58, 117, 113, 115, 115, 115, 
            107}, {130, 112, 108, 87, 85, 96, 134, 148, 133, 127, 122, 118, 
            117, 119, 118, 121, 120, 118, 118, 116, 112, 109, 112, 117, 122, 
            122, 119, 117, 117, 117, 113, 113, 114, 111, 109, 111, 112, 110, 
            109, 110, 108, 108, 113, 112, 115, 114, 113, 111, 110, 109, 110, 
            111, 110, 107, 105, 93, 20, 41, 92, 98, 112, 116, 115, 
            106}, {131, 111, 101, 110, 125, 127, 143, 142, 134, 126, 123, 
            121, 118, 119, 116, 118, 121, 119, 119, 118, 115, 114, 114, 113, 
            117, 119, 120, 119, 117, 117, 116, 116, 118, 117, 114, 112, 113, 
            113, 110, 111, 109, 105, 110, 111, 112, 112, 113, 112, 111, 107, 
            111, 111, 109, 106, 103, 99, 61, 32, 53, 40, 74, 110, 119, 
            107}, {134, 116, 124, 126, 129, 139, 162, 147, 135, 128, 123, 
            122, 118, 118, 117, 117, 120, 120, 121, 121, 119, 119, 119, 119, 
            115, 115, 115, 116, 117, 119, 117, 115, 115, 117, 118, 117, 115, 
            112, 109, 108, 109, 106, 109, 112, 113, 112, 112, 112, 111, 109, 
            110, 109, 107, 108, 104, 96, 73, 61, 95, 72, 45, 52, 85, 
            105}, {137, 123, 141, 140, 134, 141, 165, 151, 136, 132, 122, 
            119, 117, 120, 119, 116, 115, 117, 120, 123, 123, 122, 121, 120, 
            122, 122, 118, 112, 111, 111, 113, 114, 112, 109, 110, 110, 108, 
            107, 106, 106, 108, 110, 110, 113, 116, 118, 115, 112, 109, 110, 
            108, 111, 107, 104, 101, 94, 79, 71, 104, 111, 95, 62, 43, 
            91}, {135, 120, 134, 145, 149, 152, 178, 153, 133, 131, 126, 124, 
            117, 116, 115, 115, 113, 113, 114, 118, 123, 129, 130, 125, 124, 
            125, 125, 122, 119, 117, 120, 121, 122, 118, 116, 113, 111, 111, 
            112, 112, 110, 113, 113, 117, 115, 115, 114, 113, 112, 111, 109, 
            110, 107, 106, 101, 93, 80, 74, 116, 123, 115, 99, 55, 73}, {134, 
            117, 118, 119, 131, 150, 179, 154, 133, 134, 126, 123, 120, 119, 
            116, 117, 116, 115, 112, 112, 118, 126, 134, 134, 128, 127, 125, 
            123, 122, 119, 118, 119, 122, 121, 121, 121, 116, 115, 115, 115, 
            117, 119, 121, 119, 118, 117, 116, 113, 110, 110, 108, 111, 106, 
            106, 99, 92, 80, 66, 107, 117, 118, 122, 100, 77}, {131, 116, 
            115, 111, 110, 129, 154, 149, 136, 134, 126, 124, 121, 121, 116, 
            116, 115, 114, 113, 111, 113, 120, 130, 134, 132, 130, 126, 123, 
            120, 116, 116, 117, 120, 120, 120, 120, 118, 117, 115, 116, 118, 
            119, 120, 118, 116, 115, 115, 113, 110, 108, 107, 110, 106, 106, 
            98, 91, 80, 68, 122, 131, 132, 132, 120, 91}, {130, 116, 116, 
            114, 112, 126, 149, 145, 135, 132, 128, 127, 121, 122, 120, 115, 
            115, 114, 114, 112, 110, 111, 119, 128, 130, 130, 126, 125, 120, 
            116, 115, 112, 115, 116, 117, 117, 117, 119, 120, 119, 117, 117, 
            117, 117, 115, 113, 113, 112, 111, 112, 108, 110, 107, 106, 100, 
            92, 72, 59, 136, 135, 127, 122, 119, 101}, {132, 119, 117, 113, 
            112, 125, 143, 144, 132, 131, 128, 128, 121, 120, 121, 117, 115, 
            115, 113, 115, 112, 109, 112, 119, 123, 120, 118, 126, 124, 117, 
            108, 98, 99, 109, 115, 119, 119, 114, 113, 115, 115, 114, 113, 
            115, 115, 113, 114, 113, 110, 113, 110, 110, 107, 103, 98, 93, 
            63, 28, 115, 123, 118, 115, 118, 107}, {133, 124, 122, 114, 113, 
            120, 132, 138, 133, 133, 128, 129, 125, 121, 120, 119, 116, 117, 
            114, 114, 115, 113, 112, 117, 120, 110, 102, 111, 115, 112, 107, 
            98, 93, 100, 107, 111, 109, 102, 101, 106, 113, 113, 111, 113, 
            113, 112, 113, 113, 111, 109, 110, 108, 108, 106, 94, 94, 62, 29, 
            106, 118, 118, 114, 117, 107}, {130, 126, 127, 121, 123, 143, 
            156, 139, 131, 130, 129, 130, 129, 125, 121, 119, 117, 117, 116, 
            115, 115, 116, 114, 124, 126, 115, 100, 100, 103, 107, 113, 113, 
            103, 92, 93, 97, 97, 95, 96, 101, 113, 115, 114, 115, 114, 113, 
            114, 113, 113, 111, 111, 107, 109, 110, 98, 94, 59, 42, 107, 116, 
            116, 110, 115, 109}, {126, 119, 129, 131, 128, 169, 184, 143, 
            128, 128, 129, 130, 129, 129, 126, 122, 118, 116, 117, 116, 114, 
            115, 113, 127, 138, 130, 112, 106, 109, 110, 110, 110, 106, 96, 
            95, 100, 101, 95, 97, 110, 114, 115, 115, 116, 114, 114, 115, 
            114, 112, 114, 112, 109, 108, 106, 100, 94, 49, 37, 97, 112, 114, 
            108, 118, 112}, {125, 112, 123, 124, 107, 136, 172, 141, 126, 
            127, 126, 127, 128, 129, 128, 126, 124, 121, 119, 117, 114, 115, 
            112, 123, 143, 144, 129, 115, 114, 110, 109, 109, 106, 102, 100, 
            104, 105, 100, 104, 113, 114, 113, 112, 115, 114, 114, 115, 114, 
            113, 113, 113, 112, 110, 105, 99, 92, 59, 57, 102, 107, 111, 107, 
            121, 112}, {124, 109, 121, 116, 93, 119, 158, 139, 126, 128, 124, 
            125, 127, 129, 128, 127, 127, 123, 119, 118, 115, 115, 113, 118, 
            139, 149, 141, 117, 110, 110, 111, 111, 108, 103, 101, 102, 103, 
            105, 109, 113, 112, 113, 112, 114, 115, 116, 117, 115, 113, 113, 
            113, 114, 110, 105, 97, 92, 71, 87, 120, 106, 109, 108, 123, 
            112}, {112, 96, 107, 103, 83, 116, 145, 131, 127, 129, 127, 126, 
            125, 127, 128, 128, 126, 126, 125, 126, 122, 121, 120, 119, 125, 
            138, 147, 135, 120, 113, 112, 111, 110, 106, 105, 106, 109, 114, 
            115, 115, 113, 115, 115, 119, 117, 115, 118, 118, 118, 116, 113, 
            113, 110, 106, 100, 89, 45, 105, 145, 114, 111, 113, 120, 
            109}, {121, 92, 100, 93, 80, 118, 127, 118, 125, 127, 127, 126, 
            125, 126, 129, 131, 132, 130, 129, 129, 128, 124, 123, 125, 123, 
            130, 144, 144, 131, 121, 117, 113, 113, 110, 110, 108, 108, 112, 
            114, 116, 119, 122, 118, 118, 119, 118, 119, 116, 118, 116, 113, 
            112, 110, 108, 103, 82, 6, 102, 151, 129, 108, 115, 120, 
            106}, {139, 118, 121, 125, 108, 135, 152, 122, 122, 124, 125, 
            127, 129, 127, 126, 125, 123, 124, 125, 128, 133, 131, 127, 128, 
            130, 134, 145, 147, 136, 128, 125, 123, 122, 120, 115, 110, 111, 
            115, 118, 119, 120, 126, 126, 126, 128, 124, 120, 118, 116, 116, 
            112, 112, 107, 106, 106, 85, 7, 90, 138, 125, 103, 107, 111, 
            103}, {159, 141, 125, 122, 114, 140, 158, 123, 122, 121, 121, 
            122, 125, 125, 124, 119, 113, 109, 109, 108, 114, 121, 126, 130, 
            130, 138, 154, 159, 144, 131, 128, 126, 125, 121, 116, 117, 122, 
            124, 126, 126, 129, 127, 126, 125, 125, 124, 120, 119, 113, 114, 
            111, 112, 107, 104, 105, 85, 9, 85, 128, 118, 93, 99, 107, 
            99}, {142, 133, 126, 117, 110, 138, 157, 123, 123, 120, 116, 115, 
            117, 119, 122, 123, 124, 118, 116, 110, 106, 106, 110, 114, 118, 
            125, 145, 163, 153, 133, 127, 124, 122, 113, 113, 126, 134, 129, 
            122, 116, 112, 108, 106, 103, 106, 109, 111, 116, 118, 119, 114, 
            115, 110, 107, 105, 86, 8, 87, 131, 130, 102, 101, 111, 
            101}, {130, 112, 116, 117, 112, 139, 167, 127, 122, 121, 116, 
            114, 113, 114, 116, 119, 122, 123, 127, 125, 122, 117, 114, 113, 
            112, 112, 124, 149, 153, 134, 125, 123, 116, 108, 113, 125, 123, 
            115, 111, 108, 108, 109, 108, 109, 112, 111, 110, 112, 116, 119, 
            117, 115, 110, 107, 105, 86, 10, 86, 130, 124, 109, 106, 113, 
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rightillumface

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            115, 116, 119, 120, 115, 116, 114, 114, 106, 90, 108, 122, 108, 
            100, 104, 110, 109, 110, 113, 117, 110, 110, 117, 151, 131, 117, 
            110, 114, 113, 117, 120, 119, 119, 123, 120, 125, 133, 131, 132, 
            133, 133, 141, 171, 160, 119, 106, 124, 134, 138}, {124, 101, 97, 
            98, 126, 97, 4, 69, 103, 107, 108, 110, 111, 112, 114, 116, 117, 
            118, 117, 119, 118, 117, 118, 111, 95, 100, 115, 115, 105, 108, 
            110, 109, 110, 114, 117, 113, 116, 140, 152, 124, 113, 111, 115, 
            118, 120, 120, 120, 123, 124, 125, 129, 132, 130, 132, 133, 133, 
            145, 179, 169, 123, 114, 135, 134, 131}, {121, 90, 80, 83, 125, 
            88, 3, 68, 107, 106, 109, 112, 112, 111, 116, 118, 119, 119, 123, 
            124, 123, 120, 120, 118, 110, 98, 100, 114, 117, 115, 113, 111, 
            111, 115, 116, 121, 143, 157, 133, 113, 114, 119, 121, 120, 121, 
            122, 122, 126, 126, 130, 131, 129, 128, 128, 131, 134, 152, 163, 
            126, 124, 139, 143, 124, 121}, {127, 100, 87, 118, 161, 89, 10, 
            86, 105, 105, 109, 112, 115, 114, 117, 117, 118, 122, 125, 124, 
            126, 126, 122, 119, 116, 110, 100, 107, 118, 117, 117, 119, 118, 
            121, 128, 142, 159, 134, 116, 117, 120, 124, 126, 125, 127, 129, 
            125, 128, 126, 129, 129, 125, 124, 126, 132, 134, 152, 150, 90, 
            116, 144, 131, 105, 119}, {138, 124, 129, 154, 164, 77, 29, 103, 
            105, 106, 108, 111, 117, 117, 114, 113, 111, 110, 112, 113, 114, 
            119, 124, 122, 120, 121, 113, 113, 118, 119, 122, 126, 128, 132, 
            143, 155, 146, 129, 127, 132, 133, 132, 132, 133, 133, 130, 127, 
            128, 127, 124, 123, 123, 124, 128, 130, 130, 151, 156, 102, 106, 
            119, 109, 91, 120}, {135, 130, 151, 141, 129, 59, 31, 103, 107, 
            105, 108, 110, 109, 109, 108, 108, 111, 111, 109, 107, 105, 105, 
            113, 116, 122, 122, 116, 117, 121, 121, 123, 128, 131, 134, 145, 
            153, 147, 143, 138, 136, 129, 128, 119, 117, 114, 115, 121, 118, 
            124, 124, 124, 124, 126, 130, 127, 128, 151, 157, 106, 102, 108, 
            101, 96, 132}, {126, 116, 129, 119, 121, 59, 36, 104, 105, 105, 
            107, 107, 102, 102, 103, 106, 110, 119, 120, 118, 119, 114, 111, 
            112, 118, 117, 108, 103, 112, 120, 124, 129, 128, 134, 150, 157, 
            149, 134, 126, 116, 108, 106, 103, 106, 107, 109, 115, 117, 123, 
            128, 128, 127, 126, 129, 124, 129, 154, 157, 110, 96, 99, 111, 
            112, 147}, {129, 112, 113, 114, 122, 61, 57, 114, 104, 105, 106, 
            104, 104, 105, 105, 108, 106, 109, 110, 112, 117, 120, 124, 124, 
            121, 118, 110, 92, 97, 118, 124, 125, 126, 136, 157, 156, 124, 
            114, 109, 108, 109, 113, 119, 122, 122, 126, 125, 125, 122, 120, 
            120, 123, 123, 124, 124, 130, 155, 157, 103, 93, 109, 139, 141, 
            151}, {129, 114, 115, 115, 121, 70, 50, 107, 105, 106, 108, 105, 
            105, 104, 104, 107, 105, 105, 105, 107, 108, 111, 116, 114, 115, 
            118, 114, 87, 92, 119, 122, 124, 127, 141, 157, 128, 108, 112, 
            111, 118, 120, 120, 121, 123, 121, 122, 123, 121, 117, 115, 114, 
            117, 118, 122, 127, 132, 156, 165, 105, 103, 133, 154, 145, 
            142}, {132, 114, 115, 114, 121, 83, 17, 87, 107, 106, 108, 104, 
            105, 100, 102, 105, 105, 108, 112, 112, 111, 108, 104, 103, 108, 
            114, 111, 85, 86, 115, 129, 128, 132, 154, 153, 115, 108, 109, 
            117, 118, 120, 115, 111, 114, 111, 113, 114, 114, 115, 116, 117, 
            116, 116, 123, 130, 133, 160, 178, 116, 110, 121, 130, 120, 
            130}, {131, 112, 116, 115, 120, 88, 7, 79, 108, 103, 104, 104, 
            101, 103, 102, 102, 102, 106, 108, 107, 108, 114, 113, 109, 106, 
            99, 92, 83, 89, 113, 125, 135, 144, 153, 132, 103, 99, 104, 110, 
            107, 108, 109, 112, 113, 114, 111, 113, 113, 114, 117, 113, 114, 
            121, 130, 130, 134, 171, 146, 115, 115, 114, 114, 111, 
            130}, {130, 112, 116, 114, 119, 73, 0, 70, 109, 102, 104, 107, 
            105, 107, 105, 102, 106, 106, 104, 103, 104, 105, 103, 102, 101, 
            95, 99, 109, 103, 104, 116, 125, 128, 125, 112, 101, 98, 96, 100, 
            105, 107, 110, 114, 114, 113, 112, 112, 112, 114, 111, 114, 120, 
            129, 132, 124, 147, 185, 118, 113, 117, 115, 114, 111, 
            131}, {130, 115, 115, 117, 102, 9, 17, 98, 108, 106, 104, 104, 
            109, 115, 116, 110, 115, 115, 114, 118, 118, 113, 111, 113, 114, 
            119, 121, 115, 109, 107, 112, 115, 116, 114, 107, 107, 113, 113, 
            109, 104, 103, 102, 104, 107, 109, 110, 111, 115, 114, 114, 120, 
            127, 131, 129, 129, 154, 151, 118, 114, 112, 114, 117, 114, 
            129}, {130, 113, 115, 115, 86, 7, 53, 105, 105, 105, 101, 103, 
            108, 112, 114, 117, 118, 119, 122, 122, 120, 120, 119, 116, 115, 
            117, 116, 112, 111, 111, 115, 117, 117, 116, 110, 112, 119, 124, 
            118, 115, 113, 108, 109, 110, 113, 110, 112, 118, 120, 119, 126, 
            133, 131, 129, 137, 157, 118, 114, 114, 117, 117, 115, 110, 
            130}, {130, 113, 115, 112, 76, 6, 59, 103, 103, 102, 104, 106, 
            110, 107, 108, 115, 115, 117, 119, 113, 110, 116, 113, 110, 110, 
            110, 109, 112, 111, 114, 117, 115, 117, 117, 118, 114, 113, 114, 
            115, 119, 119, 119, 121, 122, 119, 120, 122, 124, 124, 128, 131, 
            133, 130, 129, 141, 154, 85, 108, 116, 115, 114, 115, 115, 
            128}, {129, 114, 116, 112, 61, 30, 85, 102, 99, 104, 110, 107, 
            109, 108, 112, 113, 113, 114, 114, 109, 109, 111, 107, 108, 113, 
            113, 108, 106, 111, 116, 112, 112, 119, 117, 116, 116, 117, 112, 
            114, 115, 115, 118, 123, 124, 121, 125, 127, 127, 127, 130, 133, 
            130, 130, 131, 135, 154, 131, 111, 114, 115, 115, 115, 113, 
            130}, {132, 111, 116, 113, 52, 47, 101, 99, 102, 106, 107, 108, 
            108, 110, 113, 112, 112, 113, 112, 112, 112, 110, 107, 109, 110, 
            108, 112, 114, 110, 111, 116, 114, 112, 116, 116, 112, 114, 115, 
            111, 113, 113, 115, 119, 117, 123, 122, 126, 128, 129, 130, 130, 
            130, 130, 130, 131, 149, 160, 117, 114, 115, 115, 115, 112, 
            131}, {131, 112, 116, 112, 61, 20, 80, 103, 106, 106, 105, 110, 
            111, 109, 114, 114, 114, 113, 115, 115, 112, 111, 114, 110, 112, 
            111, 111, 111, 114, 115, 113, 117, 118, 112, 115, 114, 111, 113, 
            114, 114, 113, 113, 115, 117, 120, 123, 125, 125, 126, 129, 130, 
            130, 129, 133, 132, 148, 157, 117, 114, 115, 115, 115, 113, 
            130}, {129, 111, 117, 108, 50, 41, 105, 105, 103, 105, 105, 107, 
            108, 110, 112, 111, 112, 112, 113, 114, 112, 112, 115, 112, 112, 
            114, 114, 112, 115, 118, 114, 113, 113, 116, 113, 115, 113, 116, 
            119, 116, 118, 116, 116, 120, 123, 124, 124, 126, 129, 128, 127, 
            127, 129, 132, 131, 148, 157, 117, 114, 116, 115, 115, 113, 
            130}, {131, 112, 115, 109, 54, 71, 122, 105, 102, 104, 109, 110, 
            110, 112, 111, 113, 112, 112, 114, 114, 112, 114, 115, 115, 112, 
            112, 114, 115, 116, 116, 116, 118, 117, 116, 117, 119, 116, 117, 
            114, 117, 120, 122, 120, 123, 125, 124, 121, 126, 126, 124, 125, 
            127, 132, 130, 128, 150, 157, 118, 114, 115, 115, 115, 113, 
            131}, {130, 115, 115, 115, 79, 42, 94, 104, 103, 104, 107, 110, 
            109, 110, 109, 112, 110, 110, 114, 113, 112, 115, 113, 114, 116, 
            118, 120, 119, 118, 119, 119, 117, 117, 119, 117, 117, 117, 116, 
            122, 119, 119, 121, 124, 125, 121, 121, 125, 127, 125, 125, 126, 
            128, 128, 128, 132, 150, 156, 115, 114, 115, 115, 116, 113, 
            130}, {130, 113, 115, 113, 88, 32, 81, 108, 106, 103, 108, 110, 
            110, 114, 110, 112, 111, 111, 113, 111, 111, 115, 114, 117, 115, 
            115, 117, 121, 121, 119, 118, 115, 117, 116, 119, 116, 118, 120, 
            120, 119, 120, 122, 125, 124, 124, 125, 128, 126, 126, 125, 128, 
            128, 128, 134, 131, 148, 172, 119, 114, 115, 115, 114, 113, 
            129}, {130, 112, 115, 114, 87, 49, 87, 110, 104, 101, 108, 108, 
            108, 112, 108, 110, 109, 112, 114, 114, 113, 115, 116, 117, 118, 
            118, 120, 122, 121, 121, 122, 120, 120, 121, 121, 121, 123, 125, 
            123, 125, 125, 128, 125, 121, 125, 123, 123, 124, 126, 126, 125, 
            134, 135, 133, 133, 154, 166, 120, 114, 115, 115, 114, 113, 
            130}, {130, 112, 115, 115, 94, 53, 100, 107, 104, 106, 108, 110, 
            109, 109, 112, 111, 110, 113, 113, 114, 113, 114, 118, 117, 121, 
            119, 119, 119, 118, 118, 119, 117, 116, 121, 121, 121, 121, 126, 
            124, 125, 125, 123, 122, 121, 123, 122, 122, 122, 126, 127, 127, 
            131, 133, 136, 136, 154, 134, 114, 116, 114, 115, 115, 114, 
            129}, {130, 114, 115, 114, 113, 76, 104, 109, 99, 102, 110, 107, 
            107, 111, 110, 109, 112, 112, 111, 111, 113, 115, 118, 116, 121, 
            120, 120, 120, 118, 117, 118, 118, 117, 119, 120, 122, 120, 122, 
            121, 124, 126, 123, 122, 123, 124, 124, 125, 126, 126, 126, 128, 
            131, 138, 135, 136, 175, 126, 115, 114, 115, 115, 115, 113, 
            130}, {131, 113, 115, 115, 119, 91, 82, 121, 99, 105, 109, 107, 
            110, 112, 110, 111, 110, 112, 114, 112, 113, 116, 118, 116, 119, 
            120, 121, 119, 117, 118, 120, 119, 117, 119, 118, 120, 121, 118, 
            121, 121, 121, 121, 121, 122, 124, 123, 123, 127, 126, 128, 131, 
            135, 139, 137, 151, 161, 117, 115, 114, 115, 115, 115, 113, 
            129}, {129, 113, 115, 115, 117, 108, 76, 108, 103, 101, 105, 113, 
            105, 113, 110, 111, 112, 114, 115, 114, 115, 116, 116, 118, 118, 
            117, 115, 117, 119, 119, 118, 119, 118, 117, 115, 117, 119, 120, 
            123, 120, 119, 119, 122, 122, 122, 123, 124, 126, 131, 130, 133, 
            139, 143, 134, 159, 133, 115, 115, 115, 115, 115, 115, 113, 
            130}, {130, 112, 114, 115, 115, 116, 86, 104, 101, 104, 108, 101, 
            109, 108, 115, 113, 114, 114, 114, 115, 114, 114, 114, 117, 117, 
            116, 117, 117, 116, 116, 117, 117, 117, 119, 117, 117, 119, 120, 
            121, 120, 121, 121, 123, 122, 121, 122, 125, 127, 129, 131, 137, 
            143, 137, 146, 169, 128, 113, 115, 115, 115, 115, 115, 113, 
            131}, {130, 113, 115, 114, 114, 120, 92, 82, 107, 98, 102, 105, 
            113, 107, 111, 116, 113, 113, 113, 116, 114, 114, 114, 113, 115, 
            116, 118, 118, 114, 114, 116, 115, 115, 120, 120, 118, 121, 118, 
            118, 120, 121, 122, 122, 120, 121, 123, 124, 126, 131, 132, 136, 
            140, 141, 164, 157, 115, 114, 115, 115, 115, 115, 115, 113, 
            130}, {130, 111, 115, 114, 113, 115, 107, 76, 116, 109, 105, 109, 
            109, 111, 108, 113, 113, 114, 114, 115, 115, 115, 116, 115, 117, 
            116, 114, 115, 118, 118, 117, 118, 120, 117, 118, 116, 120, 119, 
            120, 119, 120, 122, 121, 120, 123, 126, 126, 128, 132, 137, 141, 
            146, 159, 200, 135, 117, 115, 115, 115, 115, 115, 115, 113, 
            130}, {131, 114, 115, 114, 116, 115, 120, 85, 89, 112, 105, 108, 
            110, 111, 113, 112, 113, 115, 116, 116, 116, 115, 117, 115, 117, 
            117, 114, 115, 119, 119, 117, 119, 121, 116, 120, 117, 119, 119, 
            120, 120, 122, 121, 121, 124, 126, 128, 129, 132, 135, 141, 146, 
            143, 199, 179, 118, 114, 115, 115, 115, 115, 115, 115, 113, 
            130}, {125, 111, 111, 111, 111, 112, 113, 108, 65, 103, 111, 104, 
            106, 113, 111, 109, 110, 111, 112, 111, 110, 112, 112, 112, 111, 
            112, 114, 114, 113, 112, 112, 113, 114, 111, 113, 115, 116, 115, 
            116, 115, 117, 116, 117, 122, 124, 125, 128, 131, 134, 135, 146, 
            179, 199, 121, 113, 112, 112, 112, 112, 112, 112, 112, 110, 
            126}, {141, 125, 127, 128, 128, 128, 128, 131, 107, 89, 130, 125, 
            130, 136, 133, 133, 134, 136, 136, 134, 135, 136, 128, 130, 128, 
            128, 131, 132, 129, 127, 129, 130, 129, 129, 128, 132, 130, 131, 
            137, 141, 142, 143, 144, 146, 145, 148, 151, 153, 153, 156, 178, 
            211, 161, 130, 127, 126, 128, 128, 128, 128, 128, 128, 125, 
            141}};

interillumface[t_] := t*leftillumface + (1-t)*rightillumface;

Table[ListDensityPlot[interillumface[t],Mesh->False,PlotRange->{0,255}],{t,0,1,.25}];

QUESTIONS

You will be graded on the following

1. Evaluate each step in this notebook. Then answer the following:

2. Suppose an experimentalist tells you that his human subjects could recognize an object equally well from all views (i.e. from any point on the 3D viewing sphere), even though they had initially been trained on only two views. As a modeler, would you be inclined to favor a scene-based or image-based theory? Why?

3. Suppose an experimentalist tells you that after training on two different illuminations, her human observers can handle images of "in-between" illuminations equally well, but not others? Would this support the 2D image-based model of illumination change described above or not? Why?

4. There are two major theoretical/computational problems with the image-based model for dealing with view-point change in non-wire objects: a) self-occlusion; b) identifying geometrical feature points. Write a paragraph explaining why these are minor problems for the wire-objects above, but are major problems for a typical "everyday" object.

References

Belhumeur, P., & Kriegman, D. (1996). What is the set of images of an object under all possible lighting conditions? Paper presented at the IEEE Conf. on Computer Vision and Pattern Recognition, San Francisco, CA.
Braje, W. L., Kersten, D., Tarr, M. J., & Troje, N. F. (1998). Illumination effects in face recognition. Psychobiology, 26(4), 371-380.
Fiser, J., & Biederman, I. (2001). Invariance of long-term visual priming to scale, reflection, translation, and hemisphere. Vision Res, 41(2), 221-234.
Grill-Spector, K., Kushnir, T., Edelman, S., Avidan, G., Itzchak, Y., & Malach, R. (1999). Differential processing of objects under various viewing conditions in the human lateral occipital complex. Neuron, 24(1), 187-203.
Liu, Z., Knill, D. C., & Kersten, D. (1995). Object Classification for Human and Ideal Observers. Vision Research, 35(4), 549-568.
Liu, Z., & Kersten, D. (1998). 2D observers for human 3D object recognition? Vision Res, 38(15-16), 2507-2519.
Poggio, T., & Edelman, S. (1990). A network that learns to recognize three-dimensional objects. Nature, 343, 263-266.
Rock, I., & Di Vita, J. (1987). A case of viewer-centered object perception. Cognitive Psychology, 19, 280-293.
Tarr, M. J., Kersten, D., & Bulthoff, H. H. (1998). Why the visual recognition system might encode the effects of illumination. Vision Res, 38(15-16), 2259-2275.
Tarr, M. J., & Bülthoff, H. H. (1995). Is human object recognition better described by  geon-structural-descriptions or by multiple-views? Journal of Experimental Psychology: Human Perception and Performance, 21(6), 1494-1505.
Ullman, S., & Basri, R. (1991). Recognition by linear combinations of models. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(10), 992-1006.
Ullman, S. (1996). High-level Vision: Object Recognition and Visual Cognition. Cambridge, Massachusetts: MIT Press.
Vogels, R., & Biederman, I. (2002). Effects of illumination intensity and direction on object coding in macaque inferior temporal cortex. Cereb Cortex, 12(7), 756-766.