how to generate such an image in Mathematica
I am thinking of process an image to generate 
in Mathematica given its powerful image processing capabilities. Could anyone give some idea as to how to do this?
Thanks a lot.
Here's one version, using a textures. It of course doesn't act as a real lens, just repeats portions of the image in an overlapping fashion.
t = CurrentImage[];
(* square off the image to avoid distortion *)
t = ImageCrop[t, {240,240}];
n = 20;
Graphics[{Texture[t],
Table[
Polygon[
Table[h*{Sqrt[3]/2, 0} + (g - h)*{Sqrt[3]/4, 3/4} + {Sin[t], Cos[t]},
{t, 0., 2*Pi - Pi/3, Pi/3}
],
VertexTextureCoordinates -> Transpose[{
Rescale[
(1/4)*Sqrt[3]*(g - h) + (Sqrt[3]*h)/2.,
{-n/2, n/2},
{0, 1}
] + {0, Sqrt[3]/2, Sqrt[3]/2, 0, -(Sqrt[3]/2), -(Sqrt[3]/2)}/(n/2),
Rescale[
(3.*(g - h))/4,
{-n/2, n/2},
{0, 1}
] + {1, 1/2, -(1/2), -1, -(1/2), 1/2}/(n/2)
}]
],
{h, -n, n, 2},
{g, -n, n, 2}
]
},
PlotRange -> n/2 - 1
]
Here's the above code applied to the standard image test (Lena)
"I think this could be well approximated with a calculated offset for the image in each cell" - Mr.Wizard
Exactly! As you can see from reconstructed image there is no lens effect and tiles are just displacements.
What you need is a Hexagonal_tessellation and a simple algorithm to calculate displacement for each hexagon from some chosen central point (weight/2, height/2).
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