Our world heavily relies on images and digitization, so we are accustomed to thinking in terms of pixels and the dimensions X and Y when looking at images. But when we think of a third dimension (Z, or depth) then pixels become voxels. You can imagine a voxel to be a 3D pixel, which is a cube rather than a square.

But even though we think of pixels mostly as a square, the reality is that pixels and voxels do not necessarily have the same X, Y, and Z dimensions. Therefore, instead of a square or cube, you need to think about rectangles and cuboid.

So why does this matter in image analysis?

Think about Lego, the pieces can be longer than wide – which represents our depth and width of voxels, i.e. they are longer than wide.

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If you were to process these images (for example with a filter), you then need to take into account that the sides of the voxel can have different sizes.

Understanding these diverse voxel sizes is pivotal, especially in biomedical imaging. For example, in classical medical imaging, such as MRI or CT, voxels are typically cubes, whereas in biomedical imaging (e.g. confocal microscopy), voxels are cuboid.  

For accurate volume quantifications and filter applications, it's essential to consider the dimensions and shape of the voxels in your image.

Why have Voxel Sides a Different Length?

Some key reasons for the differing lengths of voxel sides are the diffraction limit and optical aberrations (there are others, but these are the two main ones).

The diffraction limit is a fundamental constraint in optical microscopy that prevents the resolution of features smaller than half the wavelength of light used. This limit impacts the X, Y, and Z dimensions differently. Due to diffraction, the axial (Z) resolution is typically lower than the lateral (X and Y) resolution, leading to elongated voxel shapes.

On the other hand, optical aberrations, such as spherical aberration or astigmatism, can distort the point spread function (PSF) of a microscope. These distortions contribute to non-uniform voxel dimensions, particularly affecting the Z dimension

Conclusion

In summary, understanding voxel properties is critical when working with 3D data. So, whether you're quantifying volumes or applying filters, remember to think about voxels as 3D objects.

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