Advanced Measurements

The Advanced Measurements interface allows you to define measurement functions for your analysis results. Several functions and operators are provided for use in Advanced Measurement expressions; for example, the built-in Summary function computes a given summary statistic for a given measurement and displays the result in the Summary tab of the Spreadsheet.

Interface

To open the Advanced Measurements interface, first open the Spreadsheet tab of the Contents Panel, and then click on the Measurement Tool icon (see right) to open the Image Measurements window. Click on the Advanced tab to view the Advanced Measurements interface (see below).

Advanced Measurement Tool

In the default mode, the complexity of advanced measurements is hidden and presented are some of the most common cases. Presented are simple options to help guide in the process of creating more complex measurements.

Section for creating and editing Advanced Measurements

The top section of the Advanced Measurements interface includes textboxes and dropdowns for creating/editing measurements; the available options and fields are described in the following table:

Name	Description
Name	Allows you to edit the name of the measurement
Type	The category of advanced measurement to create
Object Set	Allows selection of which objects to measure and which object set they will appear in under the spreadsheet tool

Options

After setting up the advanced measurement, different options may be displayed depending on which ‘Type’ of advanced measurement was selected. The Types of advanced measurements are as follows:

Advanced Measurement Type	Description	Inputs
Summary	Summarizes a measurement by a given statistical function. Objects summarized are defined by the selected ‘Object Set’ defined above. Any object that belongs to that Object Set which has the defined measurement will be included during the measurement processing. The summary per time frame or whole image is determined by the measurement being summarized. If the measurement changes over time the summary will be per time frame (eg: Velocity: per time frame/multiple values, Track Length: spans time frames/one value.)	Summarization type (eg: Total, Mean, etc.) The measurement to summarize Note the measurement must be selected in the ‘General’ tab to be available to select here.
Count	Retrieves the number of objects in a chosen ‘Object Set or Group’.	Object Group to retrieve the number of objects Note this can be an Object Set, Classification Group, Subset or any other group defined objects Optional flag to count per time frame or all time frames combined
Colocalization	Allows access to the varying different types of colocalization functions available in Aivia.	Colocalization Type Pearson’s Correlation Coefficient Manders' Overlap Manders' Coefficient Intersection Analysis Setting Intersection Full Object Comparison Object Set First Channel Second Channel Object Analysis Setting Per Object Whole Image
Vesicle Count	Retrieves the number of objects from a Vesicle set which is a child of the defined ‘Object Set’ above. This function acts uniquely in that it references the index of the child meaning it can be migrated to different object sets. This is analogous to ‘Count’ in which the Object Set selected is static regardless of ‘Parent’. Note this function only works will ‘Cell’ type object sets.	Object Set to retrieve the number of vesicles from Note the select-able sets here will change depending on the ‘Object Set’ input that is selected above the options area.
Custom	This type denotes that the advanced measurement does not fall into the above default ‘Types’ and to modify/edit/create using this option the user must click the ‘Advanced Mode’ and type in an expression.	N/A

On this page:

Measurement Tool icon

Using Advanced Measurements

To add an Advanced Measurement, first navigate to the Image Measurements window by going to the Spreadsheet in the Contents Panel and then clicking on the Measurement Tool icon. Open the Advanced tab of the window, and type the name of the measurement into the designated box. Then, select the object set that the Advanced Measurement will belong to from the Set menu, and type the expression for the Advanced Measurement in the Expression box. More information on how to include existing measurements as well as which operators and functions are available for use can be found in the following sections as well as the Advanced Measurement Functions page. Once the expression is complete and valid, click on Confirm to add the measurement to the table of Advanced Measurements. Click Finish to initiate measurement calculation and to exit the Image Measurements window.

To edit an Advanced Measurement, select the measurement from the dropdown; this populates the top section of the interface . Edit the information for the measurement, and then click Confirm to update the Advanced Measurement. Custom expression advanced measurements require switching to the Advanced Mode.

Custom Measurement Definitions

Custom advanced measurements allow the user to input expressions which combine different measurements, functions and arithmetic to produce a result greater than the individual components. Note that when measuring the advanced measurement, unless a function is used to reference measurements from another object set, only measures and/or uses measurements from the object set the measurement is defined on. eg: if “Cells” object set is selected, only measurements from “Cells” and the members of that object set will be measured.

Functions

Functions are always denoted in the same format “‘NAME’('Parameter', ‘Parameter’, …)”. A function will always have a name followed by ‘(' and 0 to many number of parameters, separated by commas and followed by a ‘)’. Each function will have it’s own definition and specific expected parameters as input.

Refer to Advanced Measurement Functions for all available advanced measurement functions.

Measurements

Measurements which have been turned on in the ‘General’ tab of the measurement tool are available to use for parameters of functions, components of arithmetic, or simply by themselves. Measurements are always denoted in the following format [Measurement Name (Channel Name)]. Also, if a measurement’s channel is not relevant than any channel name can be used but a channel name is required regardless.

Object Sets

Some functions allow input of object sets. Object Sets or Groups are formatted as “[Objects:'NAME']”. This differentiates them from measurements by adding the ‘Objects:’ prefix before the listed name of the object set or group.

Relation Rules

Some functions allow input of relation rules. Relation rules are formatted as “[RelationRule:'NAME']”. This differentiates them from measurements by adding the ‘RelationRule:’ prefix before the listed name of the rule itself.

Expression Examples

Description	Expression	Output
Volume over surface area	[Volume (Red)] / [Surface Area (Red)]	Per object, the objects Volume divided by the surface area
Inverse outline area	1 / [Outline Area (Red)]	Per object, the inverse of the Outline Area
Square Root of Velocity	Sqrt([Velocity (Green)])	Per object, the square root of the Velocity per time frame
Total of the Mean Intensity of the ‘Red’ channel	Summary(Total, [Mean Intensity (Red)])	Per time frame, the additive sum of the Mean Intensity of the red channel of all objects of the defined object set
Nearest Object’s distance from a given relation rule	NearestObjectDistance([RelationRule:ClosestObject]) (Note: this requires the relation rule to be defined to be measured, the rule name here is ‘ClosestObject’)	Per object, the nearest distance found in the defined ‘ClosestObject’ relation rule (defined in the Object Relation Tool)
% of image covered by objects (3D and 2D)	ImageVolume() / Summary(Total, [Volume (Red)]) ImageArea() / Summary(Total, [Outline Area (Red)])	Per time frame, (x * x calibration) * (y * y calibration) * (z * z calibration) divided by the additive sum of the ‘size’ of the objects
Count of objects from a different Object Set	Count([Objects:Tracks]) (Note: in this case the ‘different’ object set is named ‘Tracks’)	Returns the number of objects that exist in the ‘Tracks’ object set
Pearson's Correlation Coefficient (Intersection, Per Object)	PearsonsPerObjectIntersection([Channel:Red], [Channel:Green], [Objects:Tracks]) (Note: in this case the object set is named ‘Tracks’)	Pearson’s Correlation Coefficient with ‘Intersection’, ‘Tracks’ as the input comparison object set, Red as the first channel, Green as the second channel and ‘Per Object’
Objects on the left side of the image	[Center of Mass X (Unnamed)] < (ImageWidth() / 2)	Per object, outputs a 1 if the object's center of mass is less than half of the images width, 0 if greater than or equal.

Many other expression can be made combining all of the features provided by this system. Currently the user interface itself does not provide any real time feedback, to validate the expression, click the “Confirm” button towards the bottom of the tool.

Use arithmetic operations

The following arithmetic operators may be used in expressions for Advanced Measurements:

Symbol	Operation
+	Addition
-	Subtraction
*	Multiplication
/	Division
%	Modulo
^	Exponentiation

Use logical operations

The following logical operators may be used (with expressions/values on both sides of the operator) in expressions for Advanced Measurements:

Symbol	Name
=	Equal
!	Not equal
>	Greater than
<	Less than

Use built-in functions

See the Advanced Measurement Functions page for a list of the available functions and their input types and descriptions.

View Advanced Measurements in the Spreadsheet

Advanced Measurements appear alongside other measurements in the Spreadsheet and generally follow the same rules of organization; however, summary measurements are found in their own Summary tab. Please see the Spreadsheet and How to add measurements to analysis results pages for more information about how the Spreadsheet is laid out.

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