Plotting values above a threshold in ListPlot3D

Question

I'm able to plot a 3D plot of a grayscale image using ListPlot3D, where it plots a 3D surface of the image pixel intensity. But I would like not to plot the pixel value below a certain value. In the specific case I'm working on, I want to remove all the pixels with value zero but still plot the pixels that are above zero at there original position. Does anyone knows of how to do this?

Answer 1

threshold = 0;
f[x_, y_] := Clip[Sin[1/5 x y], {0, 1}]
t = Table[f[x, y], {x, -2 Pi, 2 Pi, .1}, {y, -2 Pi, 2 Pi, .1}];
GraphicsRow@{it = Image@t, ListPlot3D[ImageData@it, PlotRange -> {threshold + 10^-10, 1}, 
                           ClippingStyle -> None, MeshFunctions -> {#3 &}, Mesh -> 5, 
                           ColorFunction -> "SunsetColors"]}