var_thresholdvar_thresholdvar_thresholdVarThresholdVarThreshold (Operator)

Name

var_thresholdvar_thresholdvar_thresholdVarThresholdVarThreshold — Threshold an image by local mean and standard deviation analysis.

Signature

Description

The operator var_thresholdvar_thresholdvar_thresholdVarThresholdVarThreshold selects from the input image ImageImageImageImageimage those regions RegionRegionRegionRegionregion in which the pixels fulfill a threshold condition. The threshold is calculated from the mean gray value and the standard deviation in a local window of size MaskWidthMaskWidthMaskWidthMaskWidthmaskWidth x MaskHeightMaskHeightMaskHeightMaskHeightmaskHeight around each pixel (x,y). If MaskWidthMaskWidthMaskWidthMaskWidthmaskWidth or MaskHeightMaskHeightMaskHeightMaskHeightmaskHeight is even, the next larger odd value is used. The mask window should be greater than the image features to be segmented and it should comprise at least three pixels.

Let g(x,y) be the gray value at position (x,y) in the input image ImageImageImageImageimage and m(x,y) and d(x,y) the corresponding mean and standard deviation of the gray values in the window around that pixel and

  v(x,y) = max( StdDevScaleStdDevScaleStdDevScaleStdDevScalestdDevScale * d(x,y),AbsThresholdAbsThresholdAbsThresholdAbsThresholdabsThreshold)
  for StdDevScaleStdDevScaleStdDevScaleStdDevScalestdDevScale >= 0

or

  v(x,y) = min( StdDevScaleStdDevScaleStdDevScaleStdDevScalestdDevScale * d(x,y),AbsThresholdAbsThresholdAbsThresholdAbsThresholdabsThreshold)
  for $StdDevScaleStdDevScaleStdDevScaleStdDevScalestdDevScale < 0$.

The standard deviation is used as a measure of noise in the image and scaled by StdDevScaleStdDevScaleStdDevScaleStdDevScalestdDevScale to reflect the desired sensitivity. The threshold condition is determined by the parameter LightDarkLightDarkLightDarkLightDarklightDark:

LightDarkLightDarkLightDarkLightDarklightDark = 'light'"light""light""light""light":

  g(x,y) >= m(x,y) + v(x,y).

LightDarkLightDarkLightDarkLightDarklightDark = 'dark'"dark""dark""dark""dark":

  g(x,y) <= m(x,y) - v(x,y).

LightDarkLightDarkLightDarkLightDarklightDark = 'equal'"equal""equal""equal""equal":

  m(x,y) - v(x,y) <= g(x,y)
      <= m(x,y) + v(x,y).

LightDarkLightDarkLightDarkLightDarklightDark = 'not_equal'"not_equal""not_equal""not_equal""not_equal":

  m(x,y) - v(x,y) > g(x,y)   or   g(x,y) < m(x,y) + v(x,y).

All pixels fulfilling the above condition are aggregated into the resulting region RegionRegionRegionRegionregion.

For the parameter StdDevScaleStdDevScaleStdDevScaleStdDevScalestdDevScale values between -1.0 and 1.0 are sensible choices, with 0.2 as a suggested value. If the parameter is too high or too low, an empty or full region may be returned. The parameter AbsThresholdAbsThresholdAbsThresholdAbsThresholdabsThreshold places an additional threshold on StdDevScaleStdDevScaleStdDevScaleStdDevScalestdDevScale*dev(x,y). If StdDevScaleStdDevScaleStdDevScaleStdDevScalestdDevScale*dev(x,y) is below AbsThresholdAbsThresholdAbsThresholdAbsThresholdabsThreshold for positive values of StdDevScaleStdDevScaleStdDevScaleStdDevScalestdDevScale or above for negative values StdDevScaleStdDevScaleStdDevScaleStdDevScalestdDevScale, AbsThresholdAbsThresholdAbsThresholdAbsThresholdabsThreshold is taken instead.

Parallelization

• Multithreading type: reentrant (runs in parallel with non-exclusive operators).
• Multithreading scope: global (may be called from any thread).
• Automatically parallelized on tuple level.
• Automatically parallelized on domain level.

Parameters

Complexity

Let A be the area of the input region, then the runtime is O(A).

Result

var_thresholdvar_thresholdvar_thresholdVarThresholdVarThreshold returns 2 (H_MSG_TRUE) if all parameters are correct. The behavior with respect to the input images and output regions can be determined by setting the values of the flags 'no_object_result', 'empty_region_result', and 'store_empty_region' with set_system. If necessary, an exception is raised.

Alternatives

dyn_thresholddyn_thresholddyn_thresholdDynThresholdDynThreshold, thresholdthresholdthresholdThresholdThreshold

References

W.Niblack, ”An Introduction to Digital Image Processing”, Page 115-116, Englewood Cliffs, N.J., Prentice Hall, 1986

Module

Foundation