Filtering empty points

The source object dimensions are 512x121x60.
It is a vtkStructuredPoints object.
The interesting data are inside a black block which is made of zero values.
Only the back face of the block is visible.
Here are screenshots of the original block (front and back) and the same block after having been freed by a vtkThreshold.
Displaying the original block is fast : it takes a few seconds. Using the Threashold needs about 90 seconds on my (slow) computer.





I tried to change black points opacity to zero in the lookup table but it does not work. It takes about 20 seconds to see the result.


Here is a Python example of what I am doing. You can get the source here. 
from vtk import *

def main():
    math = vtkMath()

    # 20x10x10 points
    nx = 20
    ny = 10
    nz = 10

    # create the cloud of 20x10x10 points
    scalars = vtkUnsignedCharArray()
    for z in range(0, nz):
        for y in range(0, ny):
            for x in range(0, nx):
                if x < 5:
                    scalars.InsertNextTuple1( 0 )
                else:
                    scalars.InsertNextTuple1( math.Random( 0, 255 ) + 1 )

    cloud = vtkStructuredPoints()
    cloud.SetDimensions( nx, ny, nz )
    cloud.SetOrigin( 0, 0, 0 )
    cloud.SetSpacing( 1, 1, 1 )
    cloud.GetPointData().SetScalars( scalars )

    # create mapper + change black points opacity
    mapper = vtkDataSetMapper()
    mapper.SetInput( cloud )
    mapper.SetScalarRange( cloud.GetScalarRange() )
    mapper.SetColorModeToMapScalars()
    lut = mapper.GetLookupTable()
    lut.Build()
    lut.SetTableValue( 0, 0, 0, 0, 0 )

    # render it
    actor = vtkActor()
    actor.SetMapper( mapper )

    ren = vtkRenderer()
    ren.AddActor( actor )
    ren.SetBackground( 1, 1, 1 )

    renWin = vtkRenderWindow()
    renWin.AddRenderer( ren )
    iren = vtkRenderWindowInteractor()
    iren.SetRenderWindow( renWin )

    renWin.SetSize( 500, 500 )
    renWin.Render()
    iren.Start()

if __name__ == '__main__':
    main()

Output without modifying the lut : I want to filter red values

without modifying the lut

Output after modifying the opacity of red points to 0

After modifying the lut