Optical Symmetry Score

Audit aligned image brightness asymmetry about declared horizontal/vertical mirror axes, normalized to total flux; unlike paired physical outline error, illumination/registration remain confounders and no automatic alignment.

Description

Optical image symmetry depends on corresponding brightness under mirror reflection.

Optical image symmetry depends on corresponding brightness under mirror reflection. Normalizing pairwise differences by total brightness separates relative asymmetry from exposure scale.^[1]

When to use Optical Symmetry Score

Use this tool to audit aligned image brightness asymmetry about declared horizontal/vertical mirror axes, normalized to total flux; unlike paired physical outline error, illumination/registration remain confounders and no automatic alignment.

Prepare the gemstone measurements, spectra or comparison data and any supplied calibration parameters. Check units, reference conditions and record alignment.

How to use Optical Symmetry Score and understand its results

Prepare the gemstone measurements, spectra or comparison data and any supplied calibration parameters. Check units, reference conditions and record alignment.
Enter alignedOpticalBrightnessMatrix using the field table and calculation rules, then run the tool.
Read normalizedLeftRightOpticalAsymmetry, normalizedTopBottomOpticalAsymmetry. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
alignedOpticalBrightnessMatrix	Aligned optical brightness matrix	list of list of number	Required

Supply a nonempty rectangular matrix of nonnegative already aligned brightness with positive total. Compare each pixel with its left-right and top-bottom mirror and return the two normalized asymmetries.

asymmetry=Σ|pixel−mirrored pixel|/(2 × total brightness)

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
normalizedLeftRightOpticalAsymmetry	Normalized left right optical asymmetry	number
normalizedTopBottomOpticalAsymmetry	Normalized top bottom optical asymmetry	number

json

{
  "input": {
    "alignedOpticalBrightnessMatrix": [
      [
        1,
        2
      ],
      [
        1,
        3
      ]
    ]
  },
  "output": {
    "normalizedLeftRightOpticalAsymmetry": 0.42857142857142855,
    "normalizedTopBottomOpticalAsymmetry": 0.14285714285714285
  }
}

Limitations and assumptions

Illumination and registration can confound the result. Physical outline symmetry and laboratory grading are not determined.

Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Matrices are limited to 128 rows and 128 entries per row; other numeric lists are limited to 100,000 entries. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Outline Deviation Symmetry Check: Audit corresponding measured outline points about caller already-aligned mirror axis, preserving pair deviations; no automatic alignment, mineral shape ideal or inferred optical symmetry. For a complementary task, use Hearts and Arrows Precision Check: Audit caller aligned eight-arrow angular/radial measurements against declared pattern precision; no automated hearts detection, branded cut certification or correction for lighting/registration.

References

Optical Symmetry Score — tool.io

Similar or alternative tools

Outline Deviation Symmetry Check
Audit corresponding measured outline points about caller already-aligned mirror axis, preserving pair deviations; no automatic alignment, mineral shape ideal or inferred optical symmetry.
Hearts and Arrows Precision Check
Audit caller aligned eight-arrow angular/radial measurements against declared pattern precision; no automated hearts detection, branded cut certification or correction for lighting/registration.