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
graph TD
Im("Image") -->|has many| P("Pixel/Voxel")
Im --> |has| C("Calibration")
P -->|has| Va("Value")
P -->|has| I("Indices")
P --> |has| RWC("Real world coordinate")
C --> RWC
I --> RWC
Figure
Spatial calibration and size measurements
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.
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
#######################################################
## To follow along you need to complete the tool
## installation activity for skimage napari.
#######################################################
# Import python packages.
fromnapari.viewerimportViewerfromload_from_urlimportload_from_url# Read image with AICSImage.
image=load_from_url("https://github.com/NEUBIAS/training-resources/raw/master/image_data/xyz_8bit__mitotic_plate_calibrated.tif")# Display information about dimensions.
print(image.dims)# Display physical pixel size read from the metadata.
print(image.physical_pixel_sizes)# Create a new napari_viewer
napari_viewer=Viewer()# Add image with scaling to the viewer.
napari_viewer.add_image(image.data,scale=image.physical_pixel_sizes)# Napari GUI: Change order of visible axes.
# Napari GUI: Explor 3D visualization.
# Note: As of now napari lacks funcitonality to easily measure distances between points in an open image.
# Currently, no orthogonal view plugin exists for napari.
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
#######################################################
## To follow along you need to complete the tool
## installation activity for skimage napari.
#######################################################
# Import python packages.
fromnapari.viewerimportViewerfromload_from_urlimportload_from_url# Read image with AICSImage.
image=load_from_url("https://github.com/NEUBIAS/training-resources/raw/master/image_data/xyz_8bit__mitotic_plate_calibrated.tif")# Display information about dimensions.
print(image.dims)# Display physical pixel size read from the metadata.
print(image.physical_pixel_sizes)# Create a new napari_viewer
napari_viewer=Viewer()# Add image with scaling to the viewer.
napari_viewer.add_image(image.data,scale=image.physical_pixel_sizes)# Napari GUI: Change order of visible axes.
# Napari GUI: Explor 3D visualization.
# Note: As of now napari lacks funcitonality to easily measure distances between points in an open image.
# Currently, no orthogonal view plugin exists for napari.
Open xyz_8bit__nucleus.tif and add the spatial calibration.
The pixel width and pixel height is the same as previous image. Voxel-depth is 0.52 um.
What is the length of the longest axis of the nucleus?
Solution
[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.
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 and dz = 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 and dz = 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 calibration dxy in the formula allows one to perform measurements in pixel units and convert the results to calibrated units later, by means of multiplication with dxy.
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 * 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.
