How to Create a Population Average

December 6, 2018

What is a Population Average?

A population average merges together several individual specimens to form a consensus of the group being studied. A population average is useful for computing and understanding what “normal” means for a specific group. For example, what is the normal 3D shape of crania, mandible, condyle, femoral head, tibial plateau, etc. Understanding “normal” can, possibly more importantly, allow you to analyze the “abnormal” since the normal baseline can be used for comparison to reveal abnormalities.

Within the normal population, you can determine the normal variation from the population average. Knowing this normal variation is useful when comparing an unknown specimen to the normal baseline enabling you to classify or diagnose a disease --- in that if your specimen is outside the ranges of normal variation, then you can confidently determine abnormality.

Two types of population averages are described here and can be performed within Stratovan Checkpoint:

  1. The first type of population average is landmark based where you place anatomic landmark points onto specimen and perform a population average of just the landmark points. In this case, the output is a set of landmark points that represent the population average.
  2. The second method for population average uses landmark points to guide a volumetric nonlinear deformation to merge full volumetric CT (MRI, CBCT, etc.) scans into the volumetric population average. The output of this process is a new volumetric CT (MRI, CBCT, etc.) scan that is a blended average of the population.


Steps to Create a Population Average

The following steps can be performed in our Stratovan Checkpoint software. Checkpoint allows you to load a wide variety of data such as CT, micro CT, CBCT, MRI, and surface scans. Once loaded, you have access to traditional 3D visualization tools and can place 3D landmarks both on surfaces and on internal structures on the anatomic region of interest.

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Create your Landmark Template

Load a specimen that is representative of your population and place a set of 3D landmark points that cover the surface variation you are interested in studying. There must be a one-to-one mapping for each landmark point across all your specimen for this to work. Use the standard landmark placement tools that support placing single points, curves, patches, and opposing joint surface patches to your anatomic region of interest. This can be any number of landmark points, planes, angles, etc.

From the Template tab, Checkpoint allows you to create a landmark template (a collection of landmark points, positions, and names) which maintains the proper sequence of landmark points, names, and relation to one another when applying to many more specimens. You will need to designate at least four points as anchor points which you will need to manually specify on each new specimen to which you want to apply the landmark template. These anchor points should cover the widest extents of your anatomic region in all three directions.

The Checkpoint landmark template can then be applied to new specimen to reduce the amount of time spent placing a complex set of 3D landmark points.


Apply Landmark Template to Each Specimen

Load each new specimen and place your initial anchor points onto your new specimen. From the Template tab, apply your landmark template using the tools in the Template Wizard section. Choose the Anchor Points option and click Start. This helps you designate your anchor points in relation to the template and ultimately allows you to apply the remaining points to your specimen.

Click through automatically added landmark points and make final adjustments to ensure that the landmark points are placed precisely.


To Create a Volumetric Population Average

Once you have placed your landmark template on your population of volumetric scans (CT, MRI, CBCT, etc.), click on the Population Average button from Checkpoint’s Warping tab.

Use the “+” button to add your list of specimens within your population to be averaged. This allows you to point at each .ckpt file so that Checkpoint can load, potentially hundreds, of specimen in sequence to create averages of massive populations that consist of large CT scan data, for example.

Once you’ve specified your list of specimens, choose a folder for output and the type of averaging to perform. There are two types of averages that Checkpoint can prepare for you:

  1. Conventional average. This performs a rigid alignment of the 3D landmark points and then applies a traditional average of the points to form the resulting average.
  2. Procrustes average: this method uses Generalize Procrustes Analysis (GPA) to remove scale variation while maintaining shape variation. A good way to think of this is to consider the following example; if you were comparing the shape variation between a mouse and an elephant, you know that the scale is substantially different between them, so perhaps you want to ignore the scale differences and focus on just the shape variation among the two. As such Generalized Procrustes Analysis method removes scale and focuses just on pure shape variation.

Checkpoint’s options for volumetric population average are as follows:

  • Only the Population Average (default): This combines all specimen into a conventional average as most people would expect. If you are not sure which option to choose, use this one. The output is a single volumetric scan that represents the population average.
  • Only the Procrustes* Average of the Population: This performs Generalized Procrustes Analysis to remove scale variation. The output is a single volumetric scan that represents the Procrustes (with scale variation removed) population average.
  • Only the Specimen Warps to the Population Average: This method generates the average volume, warps the specimens to the average, and exports only the warped specimen.
  • Only the Specimen Warps to the Procrustes* Average: This method generates the average volume, warps the specimens to the Procrustes average (with scale variation removed), and exports only the warped specimen.
  • The Population Average and the Specimen Warps: Same as corresponding option above, but also outputs the average.
  • The Procrustes* Average of the Population and the Specimen Warps: Same as corresponding option above, but also outputs the Procrustes (with scale variation removed) average.

Click the Start Warp button and wait while Checkpoint merges your specimen together. You may want to test this on two or three specimens first prior to running a large batch to make sure your landmark points have been specified properly on each specimen.

You can then load the output volumetric scans and work with them as if they were a real CT (MRI, CBCT, etc.) scan.


To Create a Landmark-based Population Average

For landmark-based population averages, you need to add each specimen to a population database from within Checkpoint’s Shape Analysis tab.

If this is your first specimen, create a new population by clicking the “+” in the upper-left corner near the Population list.

To add your specimen, click the “+” in the lower-left corner at the bottom of the specimen list.

Once all of your specimen have been added to the population, choose the Analysis method, such as “Average” or “Generalized Procrustes Analysis” and click Analyze. The Generalized Procrustes Analysis method can be used to remove shape variation as described above in the volumetric average section.

Once analysis is completed (should only take a second), you can review the results in the 3D window. Various options for selection and rendering are available via the user interface. You can export the results using the Export button.

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For more information on the how population averages are computed, visit the Population Average Methodolgy post.

David F. Wiley, PhD

President & CTO

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