Affine Spatial Normalization

Apply a supplied nonsingular voxel-to-world image affine including translations; voxel indexing and world-axis convention must match the image header, and registration is not fitted.

Description

A voxel-to-world affine maps image-grid coordinates to physical coordinates through scaling, rotation, shear and translation.

A voxel-to-world affine maps image-grid coordinates to physical coordinates through scaling, rotation, shear and translation. A homogeneous coordinate carries translation in the same matrix operation.

The tool returns worldCoordinatesMm (world coordinates mm). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.

When to use Affine Spatial Normalization

Use Affine Spatial Normalization when you already have voxelCoordinates, voxelToWorldAffine and want worldCoordinatesMm. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.

How to use Affine Spatial Normalization and understand its results

Enter voxelCoordinates, voxelToWorldAffine using the field table below. Match the units, ordering and data boundaries described in the calculation.
Run the tool after checking the stated bounds and matching paired observations or categories. A malformed request gives a tool error rather than a usable measurement.
Read worldCoordinatesMm. Use the calculation and interpretation below to distinguish amounts, ratios, signs and decision flags where applicable.
Review the supplied parameters and assumptions before using the result in a report or comparing it with another observation.

Input field	Meaning	Value type and bounds	Requirement
voxelCoordinates	Voxel coordinates	list of list of number	Required
voxelToWorldAffine	Voxel to world affine	list of list of number	Required

Require a nonsingular 4×4 affine with final row [0,0,0,1] and nonempty three-component coordinates. Return coordinates in mm without adding a half-voxel offset.

world = first three rows of affine × [voxelX,voxelY,voxelZ,1]

The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.

json

{
  "input": {
    "voxelCoordinates": [
      [
        0,
        0,
        0
      ],
      [
        1,
        2,
        3
      ]
    ],
    "voxelToWorldAffine": [
      [
        2,
        0,
        0,
        10
      ],
      [
        0,
        3,
        0,
        20
      ],
      [
        0,
        0,
        4,
        30
      ],
      [
        0,
        0,
        0,
        1
      ]
    ]
  },
  "output": {
    "worldCoordinatesMm": [
      [
        10,
        20,
        30
      ],
      [
        12,
        26,
        42
      ]
    ]
  }
}

Limitations and assumptions

Coordinate origin and axis conventions come from the supplied matrix. No image file, header or registration is read.

Numerical inputs must be finite. The tool checks its declared input shape and calculation constraints; those checks do not verify the quality, calibration or representativeness of the supplied observations.

Alternative or Complementary methods

Midline Shift: Measure signed landmark distances from the explicit reference plane n·x=offset; this does not identify anatomical landmarks or severity. Slice Gap: Audit adjacent slice edge gaps and overlaps along a common slice-normal axis; centers and physical slice thicknesses share millimetre units.

Methodological background: NIfTI coordinates and affine transformations.^[1]

References

NIfTI coordinates and affine transformations — Robert W. Cox; National Institute of Mental Health

Similar or alternative tools

Midline Shift
Measure signed landmark distances from the explicit reference plane n·x=offset; this does not identify anatomical landmarks or severity.
Slice Gap
Audit adjacent slice edge gaps and overlaps along a common slice-normal axis; centers and physical slice thicknesses share millimetre units.