Plot3D and NMinimize do not work correctly?

Question

See my code:

ref = Rasterize[Graphics3D[Sphere[]], ImageResolution -> 16, 
Background -> LightYellow]
Model[{x_, y_}] := 
Rasterize[Graphics3D[Sphere[], ViewPoint -> {x, y, 1}], 
ImageResolution -> 16, Background -> LightYellow]
CostFunction[{x_, y_}] := 
Total[Flatten[ImageData[ImageSubtract[ref, Model[{x, y}]]]]]
 Plot3D[CostFunction[{x, y}], {x, -1, 3}, {y, -1, 3}].// My problem is here?????

But When I use

list = ParallelTable[{x, y, CostFunction[{x, y}]}, {x, -10, 
10}, {y, -10, 10}];
list = ParallelTable[{x, y, CostFunction[{x, y}]}, {x, -10, 
10}, {y, -10, 10}];

I get the function graphics! What is the problem?

In the other hand:

I want to minimize the cost function using NMinimize[]

NMinimize[CostFunction[{x, y}], {x, y}]
{22083.2,{x->0,y->0}}

But When I calculate

CostFunction[{0,0}] 

I obtain 8758.65? What is the issue please?

Answer 1

The problem is the you CostFunction which is extremely slow because in each call it has to render a graphics, rasterize it and compute the difference of the two images. You can see that Plot3D basically works by restricting the number of points if computes. With 10 plot points, which results in 10x10 values to compute, the graphic needs about 20 seconds here

Plot3D[CostFunction[{x, y}], {x, -1, 3}, {y, -1, 3}, 
 MaxRecursion -> 0, PlotPoints -> 10]

In default mode, Plot3D will divide each interval further if the surface is *too rough**. I have suppressed that by setting MaxRecursion to 0.

Update

About your second question. I cannot reproduce your behavior, because when I compute on my machine

NMinimize[CostFunction[{x, y}], {x, y}]

I obtain

{6493.44, {x -> 0.500146, y -> -0.500021}}

When I calculate CostFunction[{.5, -.5}] then I get the same value.