Reading Relative Standard Error

Note: Migration Warning: The relative standard error cannot be computed for XMP generated prior to 2019 R1 version. The precision map is computed instead.

For more information on the Precision Map, see Reading Precision.

Relative Standard Error Value

The relative standard error value acts as a convergence indicator. It expresses the standard error of a pixel relative to an average.

When a pixel did not integrate enough rays or when the rays that hit the pixel have varying flux values, the standard error value is high.

A high error value indicates that the pixel has not converged correctly and lacks definition.

The more rays or passes, the lower the statistical noise.

Standard Error Formula

Important: The standard error is the average standard deviation and corresponds to the Standard Deviation calculated in the Measure tool. Do not confuse the Standard Deviation calculated in the Measure tool and the standard deviation used to calculate the standard error.

The standard error formula is

  • σ: standard deviation from the mean of the rays' energy

  • N: number of rays (integrated or emitted)

    For direct simulation, N is the total number of emitted rays.

    For inverse simulation, N is the number of rays integrated in the pixel.

Relative Standard Error Formula

The relative standard error formula is the following:

  • σ: standard deviation from the mean of the rays' energy
  • μ: average of the rays' energy

  • N: number of rays (integrated or emitted)

    For direct simulation, N is the total number of emitted rays.

    For inverse simulation, N is the number of rays integrated in the pixel.

Warning:
  • When no rays are integrated on a pixel (black pixel), the error is null. The relative standard error value is 0%.
  • The higher the standard error, the lower the image quality.
  • In inverse simulation using deterministic or photon map algorithms, relative standard error does not have any meaning.

Relative Standard Error Map

To display the relative standard error map, from Virtual Photometric Lab, click Tools, Precision map...

The relative standard error map allows you to evaluate how well pixels have converged.

This map is useful tool when using the Monte Carlo algorithm.

Indeed, as the rays are drawn randomly in the scene, the results might present noise or uneven convergence. The standard error map allows you to quickly evaluate the pixels needs and see if an adjustment of the ray number launched during simulation needs to be made or not.

Warning: The relative standard error map is only valid for:
  • an original map without filtering,
  • a map with all the sources set at 100%.