Spatial calibration
Prerequisites
Before starting this lesson, you should be familiar with:
Learning Objectives
After completing this lesson, learners should be able to:
Understand that a pixel index is related to a physical coordinate.
Understand that a spatial calibration allows for physical size measurements.
Motivation
We would like to relate the image dimensions to a physical size. The relation between pixels and physical size is referred to as spatial calibration. Image calibration is dictated by acquisition and detection parameters of a microscope, such as magnification, camera detector size, sampling, etc, and is usually stored within the so-called image metadata. Before performing quantitative measurements, e.g. volume, area, …, you should make sure that the spatial calibration has been set appropriately.
Concept map
Figure
Activities
Inspect spatial calibration metadata and add a scale bar
- Open an image and inspect the spatial calibration metadata
- Add a scale bar to the image
Image data
Show activity for:
ImageJ GUI
- Open one of the above images using
Plugins › Bio-Formats › Bio-Formats Importer
[X] Display OME-XML metadata
- Find the pixel calibration in the metadata text
- Also inspect the pixel size in
Image > Properties
- Check that those information are consistent
- Add a scale bar to the image using
Analyze › Tools › Scale Bar...
- Explore the various options for where and how to place the scale bar
- Export the image using
Plugins › BioVoxxel Figure Tools › Export SVG
(requires BioVoxxel update site)
- SVG preserves the rendering of the scale bar at different zoom levels.
- Open the raw data image again using
File > Open...
instead of Bio-Formats
- Are you getting the same pixel calibration?
ImageJ Macro
Explore the spatial calibration of a 3D image
- Open an image and find the spatial calibration metadata
- Understand that this is important for both rendering and measurements
- Measure Euclidian calibrated distances in the image
- Example image: xyz_8bit__mitotic_plate_calibrated.tif
Show activity for:
ImageJ GUI
- Open image: xyz_8bit__mitotic_plate_calibrated.tif
- Check the pixel sizes (calibration) of this image
- Where to see the calibration?
- Next to the pixel indices in the ImageJ menu bar
- Properties of the image [Image > Properties] or [Shift-Ctrl-P]
- How to check whether the calibration makes sense?
- Explore the typical size of objects in 3D.
- Orthogonal view [Image > Stacks > Orthogonal Views] or [Ctrl-Shift-H]
- An example of a wrong calibration: xyz_8bit__mitotic_plate_badZcalibrated.tif
- Appreciate that image calibration might be necessary, e.g.
- 2D distance measurement between two pixels
- One can use the Line tool
- 3D distance measurement between two voxels
- One cannot use the Line tool but needs to measure manually:
sqrt( (x0-x1)^2 + (y0-y1)^2 + (z0-z1)^2 )
- Note: It is critical to use the calibrated voxel positions and not the voxel indices in above formula!
- Appreciate that image calibration can be confusing, e.g.
- It is not consistently used in image filter parameter specification
skimage napari
Modify spatial calibration
- Open xy_8bit__nucleus_calibrated.tif and note down the pixel width and pixel height.
- Open xyz_8bit__nucleus.tif and add the spatial calibration in x & y of the previous image; add a voxel-depth of 0.52 um.
- Measure the length of the longest axis of the nucleus.
Show activity for:
ImageJ GUI
- [File > Open ] the image and then [Image > Properties …] or [Ctrl-Shift-P]. Pixel-height = pixel-width = 0.13 um.
- Open the 3D image and change the properties from the [Image > Properties …] gui and the unit.
- Maximal extension is ~ 19.2 um. Move to the middle of the nucleus (~ z-slice 3) and draw a line using the line-tool.
skimage napari
Assessment
Answer these questions
- Given a 2D image with
pixel height
=pixel width
=dxy
=0.13 micrometer
, what distance do the pixels at the (x,y) indices (10,10) and (9,21) have in micrometer units? - Given a 3D image with
dx
=dy
=0.13 micrometer
anddz
=1 micrometer
, what is the calibrated (micrometer units) distance of two pixels at the indices(10,10,0)
and(9,21,3)
? - What is the calibrated (micrometer units) area covered by 10 pixels, given a spatial calibration of
dx
=dy
=0.13 micrometer
? - What is the calibrated (micrometer units) volume covered by 10 voxels, given a spatial calibration of
dx
=dy
=0.13 micrometer
anddz
=1 micrometer
?
Solution
sqrt( (x0*dxy-x1*dxy)^2 + (y0*dxy-y1*dxy)^2 )
=sqrt( (x0-x1)^2 + (y0-y1)^2 ) * dxy
=sqrt( (10-9)^2 + (10-21)^2 ) * 0.13
=11.04536 * 0.13 micrometer = 1.435897 micrometer
. The fact that one can separate out the isotropic calibrationdxy
in the formula allows one to perform measurements in pixel units and convert the results to calibrated units later, by means of multiplication withdxy
.sqrt( (x0*dx-x1*dx)^2 + (y0*dy-y1*dy)^2 + (z0*dz-z1*dz)^2 )
=sqrt( (10*0.13-9*0.13)^2 + (10*0.13-21*0.13)^2 + (0*1.0-3*1.0)^2 ) micrometer
=3.325928 micrometer
. Unfortunately, in an anisotropic 3D image one cannot separate out a calibration factor from the formula, making life more difficult.10 * 0.13 micrometer * 0.13 micrometer
=10 * 0.0169 micrometer square
=0.169 micrometer square
10 * 0.13 micrometer * 0.13 micrometer * 1.0 micrometer
=10 * 0.0169 micrometer cube
=0.169 micrometer cube
. This shows that measuring volumes in 3D can be done first in voxel units, as the calibration factor can easily taken into account later (in contrast to the distance measurements). Thus, somewhat surprisingly, is in practice easier to measure volumes than distances in 3D.
Explanations
Isotropy
One speaks of isotropic sampling if the pixels have the same extent in all dimensions (2D or 3D).
While microscopy images typically are isotropic in 2D they are typically anisotropic in 3D with coarser sampling in the z-direction.
It is very convenient for image analysis if pixels are isotropic, thus one sometimes resamples the image during image analysis such that they become isotropic.
Follow-up material
Recommended follow-up modules:
Learn more: